The inequality when apples cost $3 and oranges cost $2 and Aleris can spend no more than $24 on the gift is 3a + 2o ≤ 24.
How to illustrate the inequality?Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.
In this case, Aleris is sending a fancy organic fruit basket to her grandma for her birthday. apples cost $3 and oranges cost $2 and Aleris can spend no more than $24 on the gift.
Let apple = a
Let orange = o
Therefore, the inequality will be:
3a + 2o ≤ 24.
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find the probability that a point chose a t random on the part of the number line shown will lie between points B and C. (anwser should be in a fraction or decimal)
The probability of point being in between B and C is 0.167
A probability definition is what?Probability is a statistic used to indicate the likelihood or potential that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to express probabilities.
What are examples and probability?The likelihood is based on the range of potential outcomes. the total number of possible outcomes. As an illustration, since there is only one way to get a head and a total of two possible results, the likelihood of flipping a coin and getting heads is one in two. a tail or a head.
Distance between B and C= 4 units
Total distance=24
Probability that point lie between B and C = 4/24 =1/6
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find the missing angle
Answer:
Step-by-step explanation:
180-120=60
60+50=110
180-110=70
the missing angle is 70 degrees
Which of the following statements are true? (select more than one answer)
Answer:
➜ ∠4 = ∠2
➜ ∠2 + ∠3 = 180°
➜ ∠1 = ∠3
Step-by-step explanation:
We can use vertical angles to prove the first statement true, ∠4 = ∠2.
Next, ∠2 and ∠3 are supplementary angles, so if you add them together you will get 180 degrees. This statement is also true.
Then, ∠1 and ∠2 are not complimentary angles. This statement is false.
Lastly, we can use the same reasoning of the first one to prove this statement true as well. They are vertical angles, ∠1 = ∠3.
What does an inverse function look like?
Inverse functions are indicated by the symbol [tex]f^{-1}[/tex] and are functions whose inverse is the function itself (x).
A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function. The inverse function, which also returns the beginning value, returns the result of a function.
The relationship that results from swapping out an independent variable for a variable that depends on a given equation, and which may or may not be a function. Consider the inverse relationship between the functions f and g: f(g(x)) = g(f(x)) = x.
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Points p and q are negative integers plotted on a number line. If |p| > |q|, which statement is true?
A. Point p is closer to 0 than point q, and to the right of point q.
B. Point p is closer to 0 than point q, and to the left of point q.
C. Point p is further from 0 than point q, and to the right of point q.
D. Point p is further from 0 than point q, and to the left of point q.
Point p is further from 0 than point q, and to the left of point q.
The correct option is D.
What is an absolute value?The absolute value of a number is the distance value from zero without considering the sign of a number. It is also represented as |x|, where x is any number.
Given:
Points p and q are negative integers plotted on a number line.
And |p| > |q|.
That means,
The absolute value of p is greater than the absolute value of q.
|p| and |q| are the positive integers.
So, p < q.
So, the q is closer to zero.
And p is left to point q.
Therefore, the q is closer to zero and p is left to point q.
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pleasee helpp !! <33
What is the circumference of a circle with sector area 9π and arc measure 90 degrees?
By using the area of circle formula, the solution of the given problem of circle comes out to be 6 + π cm
Describe the circle.Every location in the plane of a circle is equally separated from the center and is a closed, as double object. Each line tracing the circle contributes to the formation of a line of reflection symmetry. Additionally, each angle has axis of symmetry around the center.
Here,
A 9 Pi square centimeter circle's sector has a 60 degree center angle. The sector's exterior border is
Circle area is equal to. πR² = 9π
Circumference =2πR
=> 2π*3 = 6π cm
Arc length equals (60/360)*6 to cm
Arc's perimeter is calculated as follows: Radius + Length of Arc + Radius = π +3 + 3 = 6 + π cm
Therefore , the solution of the given problem of circle comes out to be
6 + π cm.
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By using the area of circle formula and circumference of a circle formula, the solution of the given problem of circle comes out to be 12π cm
Describe the circle.Every location in the plane of a circle is equally separated from the center and is a closed, as double object. Each line tracing the circle contributes to the formation of a line of reflection symmetry. Additionally, each angle has axis of symmetry around the center.
Here,
sector area of circle = 9π
arc measure = 90°
Area of sector = (arc/360°)*πr²
⇒ 9π = (90°/360°)πr²
⇒ 9π = (1/4)πr²
⇒ 4*9π = πr²
⇒ 36 = r²
⇒ 6² = r²
r = 6
and Circumference of circle = 2πr
=> 2π*6 = 12π cm
Therefore , the solution of the given problem of circle comes out to be
12π cm.
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For what value of a the system of linear equations Ax 3y a 3?
The system of linear equations has no solution for any value of a.
The equations Ax + 3y = a and 3x + 3y = a can be written in matrix form as
[A 3] [x] [a]
[3 3] * [y] = [a]
By using the Gaussian elimination method, the reduced form of the matrix is
[A 3] [x] [a]
[0 0] * [y] = [0]
This implies that the system has no solution for any value of a.
The system of linear equation
Ax + 3y = a and 3x + 3y = a can be written in matrix form as
[A 3] [x] [a]
[3 3] * [y] = [a]
We can use the gaussian method to solve this system. First, we subtract 3 times the first equation from the second equation to get
[A 3] [x] [a]
[0 0] * [y] = [0]
This implies that the system has no solution for any value of a.
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What are 3 examples of perfect squares?
Three examples of perfect squares is 1) 9, as it is equal to 3 x 3.2) 16, as it is equal to 4 x 4.3) 25, as it is equal to 5 x 5.
What is perfect squares?Perfect squares are numbers that can be expressed as the product of two equal integers, such as 4, 9, and 16. These numbers can be written as the square of a single number, such as 2² = 4, 3² = 9, and 4² = 16. Perfect squares are also known as whole squares, and they provide an easy way to find the square root of a number.
Perfect squares are numbers that are the result of multiplying a number by itself. For instance, 4 is a perfect square because it is equal to 2 x 2.
Similarly, 9 is a perfect square because it is equal to 3 x 3. Perfect squares can be easily identified by their square root, which is the number that can be multiplied by itself to produce the perfect square.
For example, the square root of 16 is 4, since 4 x 4 = 16.
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What is the pattern?
For how many integer values of $n$ between 1 and 349 inclusive does the decimal representation of $\frac{n}{350}$ terminate
The decimal form of n/350 terminates after 49 integer values of n between 1 and 349 inclusive.
What is prime factorization?The technique of expressing all numbers as a product of primes is known as prime factorization. As an example, suppose we have the number 20. We may divide this into two categories. "Well, that's 4 times 5," we may remark. Also, 5 is a prime number. The number four is not a prime number. All numbers are made up of prime numbers. "Factors" are numbers that are multiplied to generate another number. As an example. "Prime factorization" is the process of determining which prime numbers multiply to produce the original number.
Here,
first, find the prime factorization of 350. (2*5^2*7)
then we need to find all multiples of 7 that are between 1 and 350.
the first multiple of 7/350.
The first multiple of 7 between 1 and 350 is 7.
so 7/350=0.02.
Then, drop the two zeros and find out what is 100% (1 whole, ignoring the percent) /2.
Then, we get 49.
49 integer values of n between 1 and 349 inclusive does the decimal representation of n/350 terminate.
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How do you factor with 4 parts?
When a polynomial has four or more terms, the easiest way to factor it is to use grouping.
Grouping can be understand more better with an example:
for eg: factor x^3 + x^2 – x – 1 by using grouping. Just follow these steps:
Break up the polynomial into sets of two. You can go with (x^3 + x^2) + (–x – 1). Put the plus sign between the sets, just like when you factor trinomials. The square x2 is the GCF of the first set, and –1 is the GCF of the second set. Factoring out both of them, you get x^2(x + 1) – 1(x + 1).one can Factor again as many times as you can. The two terms you’ve created have a GCF of (x + 1). When factored out, you get (x + 1)(x^2 – 1).However, x^2 – 1 is a difference of squares and factors again as (x+1)(x-1). This gives you a final factorization of: (x + 1)(x + 1)(x – 1), or (x + 1)2(x – 1).
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What linear equation means?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.
When a linear equation is graphed, it always produces a straight line since each term in the equation has an exponent of 1 or 0. A linear equation is an algebraic equation. If an equation has the formula y=mx+b, with m representing the slope and b the y-intercept, it is said to be linear.
The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
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Equivalent expression
The ladder touches the building at 4.53 meters right angle triangle vertical distance from the ground.
What is right-angled triangle?The triangle that has one 90 degrees angle is called right-angled triangle. The Pythagorean theorem is applicable for right-angled triangle.
What is the height of the point where the ladder touches the building A ladder leans up against a building at an angle of 65 degrees with the ground. the length of ladder = 5 meters
we understand that the ladder, building and ground together formed a right-angled triangle. The right angle is in between the building and ground. The length of ladder acts as a hypotenuse of this triangle. If we consider the angle 65 degrees,
then sin 65° = opposite side length / hypotenuse here, opposite side length = the required length we need to determine sin 65° × hypotenuse = opposite side opposite side = 0.9063 × 5 =4.53 meters
the ladder touches the build at 4.53 meters vertical distance from the ground.
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what are the domain and range of the function f(x)=2^x+1
Answer: The domain is all values of x that make the expression defined. The range is the set of all valid y values
Step-by-step explanation:
Therefore , the solution of the given problem of function comes out to be Domain: (-∞, ∞) and Range: (0,∞).
What is function?Any input will only result in one or zero outcomes for the function. The expression does not define the function if there are several outputs for a given input. Each value of x must have only one output value of y variable in order for anything to be a function.
Here,
Given : f(x)=[tex]2^{x}[/tex]+1
If a value has not been added, an exponential function's curve normally approaches a horizontal asymptote at y=0 or the x-axis. The curve changes if it has.
The asymptote is unaffected by this function's addition on the exponent because it does not apply to the entire function.
The values of its y-axis remain between 0 and. This is the set of y values, or the range.
However, depending on the leading coefficient, the range of exponentials can vary. If the value is negative, the graph turns inside-out and the range reaches -. It's also lacking in this.
The exponent's addition to 1 moves the function to the left without changing the range.
The x values in exponential functions are often unaffected and all are taken into account in the function. The domain stays the same even while it changes. Its range is (0,∞)
Range: (0,∞)
Therefore , the solution of the given problem of function comes out to be
Domain: (-∞, ∞) and Range: (0,∞).
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Determine whether the lines tangent to the curve at the x-intercepts of the curve are parallel. Show the analysis that leads to your conclusion.
For the curve [tex]x^{2} +xy+y^{2} = 27[/tex] , the line tangents to the curve at the x intercepts of the curve are parallel .
The Slope of tangent line to a function at any point is denoted by [tex]\frac{dy}{dx}[/tex] .
The Curve is given as ⇒[tex]x^{2} +xy+y^{2} = 27[/tex] ;
On differentiating both sides of the curve with respect to "x" ,
we get ;
the slope of the line as ⇒ [tex]Slope = \frac{dy}{dx} = -\frac{2x+y}{x+2y}[/tex] ;
Now for the x- intercepts , the value [tex]y = 0 ,[/tex]
On substituting [tex]y=0[/tex] in the curve [tex]x^{2} +xy+y^{2} = 27[/tex] ,
we get ;
[tex]x^{2} +x(0)+0^{2} =27[/tex]
On simplifying further ,
we get ;
[tex]x=\pm 3\sqrt{3}[/tex] ;
So , the two x intercepts of the curve are [tex](3\sqrt{3},0)[/tex] and [tex](-3\sqrt{3},0)[/tex] ;
to find the slopes , we substitute the values in the slope equation .
On substituting the values in the slope equation ,
we get ;
[tex]Slope_{(3\sqrt{3} ,0)} = -\frac{2(3\sqrt{3}) +9}{3\sqrt{3} +2(0)}[/tex] = [tex]-2[/tex] and
[tex]Slope_{(-3\sqrt{3} ,0)} = -\frac{2(-3\sqrt{3}) +9}{-3\sqrt{3} +2(0)}[/tex] = [tex]-2[/tex].
we see that the slope at both the intercepts is same ,
Therefore , the lines tangents of the curve at the x intercepts are parallel .
The given question is incomplete , the complete question is
Consider the curve defined by [tex]x^{2} +xy+y^{2} = 27[/tex] . Determine whether the lines tangent to the curve at the x - intercept of the curve are parallel .
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Which statement about the order of operations is TRUE?
Complete all subtraction operations before addition.
Simplify operations within the innermost grouping symbols first.
Complete all division operations before multiplication.
Simplify exponents before operations in grouping symbols.
If f(x) =x - 5 and g(x) = 2x + 3, find values for each of the following.
a. f(g(1)) =
b. g(f (2)) =
c. g(g(0)) =
d. (f 0 9) (-2) =
e. (g o f) (3) =
f. (f o f) (-1) =
When f(x) = x - 5 and g(x) = 2x + 3, the value of f(g(1)) is 0 and the value of g(f (2)) is -2.
what is function ?Mathematics encompasses the study of numbers, formulas and related structures, shapes and the spaces in which they exist, quantities and their variations, and spaces in which they exist. A function is an association between a set of inputs, each of which has an output. Simply described, a function is a relationship between inputs and outputs, where each input results in a single, distinct output. Each function has a domain and a codomain, often known as a scope. Typically, the letter f is used to denote functions (x). is the input. There are four different categories of functions. one-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions
given
a) f(g(1)
g(1) = 5 and f(g(1)) = 0
b) g(f (2))
f(2) = -3
g(f (2)) = -2
so When f(x) = x - 5 and g(x) = 2x + 3, the value of f(g(1)) is 0 and the value of g(f (2)) is -2.
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Maria had lunch at a restaurant. If the bill was $12.25 and Maria wants to leave a 20% tip, what is a reasonable estimate for the amount she should leave for tip?
Please explain how you got the answer
Answer: $2.45
Step-by-step explanation:
An easy way to find the correct tip is to learn what 20% of 12.25 is
Let's convert the percentage to a decimal by moving the decimal point two spaces to the left. Now we have .2
.2 X 12.25 = 2.45
2.45 is 20% of 12.25
What is the simplified form of StartRoot 144 x Superscript 36 Baseline EndRoot?
The simplified form of expression is, 12x⁶.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ √144 x³⁶
Now, By the property of square root;
⇒ √ ab = √a × √b
We get;
⇒ √144 x³⁶ = √144 × √x³⁶
And, By using the exponent property, we get;
⇒ xᵃᵇ = xᵃ × xᵇ
So, We get;
⇒ √144 x³⁶ = √144 × √x³⁶
= √144 × √x⁶ × √x⁶
= √12×12 × √x⁶ × √x⁶
= 12 × x⁶
= 12x⁶
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Abraham ran 3.18 miles on Monday. On Tuesday, he ran 1.6 times further than he did on Monday. How many more miles did he run on Tuesday than on Monday?
1.908 miles Abraham run on Tuesday than on Monday.
How miles more miles he run on Tuesday than on Monday?Step 1
Monday he run 3.18 miles
Tuesday he run 1.6 times than Monday
how many more miles miles he run?
Step 2
3.18*(1.6-1)
1.6-1 is 1.6 times further than he did on Monday
Step3
3.18*(1.6-1)
=3.18*0.6
=1.908
he run on Tuesday than on Monday is 1.908
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Abraham ran 1.908 more miles on Tuesday than it was on Monday, based on the information provided.
Why is math referred to as arithmetic?The fundamental ideas in number theory, measurement, and computation are frequently referred to as "arithmetic" (which is derived from the Greek word "arithmos," "number") (that is, the processes of addition, subtraction, multiplication, division, raising to powers, and extraction of roots).
First, he ran 3.18 miles on Monday.
He ran 1.6 times more on Tuesday than on Monday.
how many kilometers did he run in total?
Step 2\s3.18*(1.6-1) (1.6-1)
One and a half times closer than he was on Monday at 1.6-1
Step3\s3.18*(1.6-1)\s=3.18*0.6\s=1.908
He ran 2.908 more on Tuesday than it does on Monday.
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When Bruce got his first job, he put $6,225 of his earnings into an investment account to save for retirement. The value of the account is predicted to double each decade.
Write an exponential equation in the form y=a(b)x that can model the predicted value of Bruce's investment account, y, x decades after starting the account.
Use whole numbers, decimals, or simplified fractions for the values of a and b
The exponential function to model the predicted value of Bruce's investment account is
y = 6225 * 2^x.
What is an exponential function?The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
here, we have,
we know that,
An exponential function is written in the form - y=a*(b)^x
Here, y is the function, a is the base value b is the rate and x is time period.
now, we have,
from the given information, we get,
This equation uses the initial value of the account (6225)
and the base of the exponent (2) representing the account will double in value every decade.
if, we have,
the predicted value of Bruce's investment account is y.
time period is, x decades after starting the account.
So, the exponential equation will be -
y = 6225 * 2^x.
Therefore, the exponential equation is .
y = 6225 * 2^x.
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How is rotation and dilation similar?
Rotation is the process of turning a figure a specific amount around a point. When we dilate a figure, we increase or decrease its size.
The circular movement of an item about a primary axis is referred to as rotation or spin. A revolving object in two dimensions only has one conceivable central axis and can revolve either clockwise or counterclockwise. There are many conceivable central axes and rotating orientations for a three-dimensional object.
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.
On a coordinate plane, forms can be rotated and dilated in addition to translated and reflected. When a shape is rotated, the new shape is consistent with the old. When you dilate a shape, the resulting shape is similar to the original.
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What is a 3 degree equation called?
A three-degree equation is referred to as a cubic equation. The polynomials are referred to as cubic polynomials if they have a degree of three.
what is cubic equation ?A three-degree equation is referred to as a cubic equation. All cubic equations have roots that are either three real roots or one real root and two imaginary roots. The polynomials are referred to as cubic polynomials if they have a degree of three. The opposite of cubing an integer is finding the cube root of that number. It can be determined by first determining how the given integer can be divided into prime factors, and then by using the cube root formula.
given
A three-degree equation is referred to as a cubic equation.
All cubic equations have roots that are either three real roots or one real root and two imaginary roots.
The polynomials are referred to as cubic polynomials if they have a degree of three.
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help help help help help help
The equation point slope is y - y1 = m(x - x1)
we got y - (-16)=3(x-7)
what is meant by point of slope?Point-slope is the general form y-y₁=m(x-x₁) for linear equations. It emphasizes the slope of the line and a point on the line (that is not the y-interceptThe slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept pointA simple definition of point-slope form is an equation of a line written using one point on the line and the slope of the line. The point form is written as (x,y) and the slope is the rise over run, or the ratio of the change in the y values over the change in the x valuesThe slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).To learn more about point of slope refers to:
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SA triangle has side lengths of 11, 60, and 61. When using the converse of the Pythagorean theorem to determine if this is a right triangle, what is the value of c in the formula a² +b²=c²?
61
11
11²
60
Value of c is determined 61 unit.
What is right-angled triangle?
Triangle that has one angle 90 degree is called right-angled. In case of a right triangle the square of the largest side length is equal of the sum of the square of the other two side length.
what is the value of c in the above formula?
SA triangle has three side length 11-unit, 60 unit and 61 unit respectively.
The triangle is verified as a right-angled triangle by Pythagorean theorem.
And as the properties of a Pythagorean theorem the sum of the square of two side length is equal to the square of the largest side length.
if we say, one side length, a = 11 unit
second side length, b = 60 unit
the largest side length, c
now we will check,
√(11²+60²) = c² =√3721 = 61
the value of c = 61 unit.
hence, the SA is right-angled triangle.
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The figure below to the left is a graph of f(x), and below to the right is g(x).
The figure below to the left is a graph of f(x), a
(a) What is the average value of f(x) on 0≤x≤2? avg value = __________
(b) What is the average value of g(x) on 0≤x≤2? avg value = __________
(c) What is the average value of f(x)?g(x) on 0≤x≤2? avg value = _________
(d) Is the following statement true?
Average(f)?Average(g)=Average(f?g)
A. Yes
B. No
The average value of both f(x) and g(x) on 0≤x≤2 is 1/4. The average value of (f.g) on 0≤x≤2 is 0 and the statement avg(f) . avg(g) = avg(f . g) is false.
avg value of a function = 1/(b - a) ∫f(x) with limts a and b. Here a and b are the constraints under which the average has to be calculated.
a)
Hence average value of f(x) on 0≤x≤2
= 1/2 ∫f(x) with 0 and 2 as intervals
Since integration is basically the area under the curve we get
avg of f(x) = 1/2[area under curve from 0 to 1 + Area under the curve from 1 to 2]
Since from 0 to 1, the figure is a triangle and beyond that a straight line we get
1/2[1/2 X 1 X 1 + 0]
= 1/4 sq units
b)
Similarly, the average value of g(x) on 0 ≤ x ≤ 2
1/2[area from 0 to 1 + area from 1 to 2]
= 1/2[0 + 1/2]
= 1/4 sq units
c) here we need to find the average of f(x) . g(x)
Here we see that f(x) is 0 from x = 1 to x = 1 while g(x) id 0 from x = 0 from x = 1
Hence we see that on multiplying the functions, the resultant has to be a 0 function.
Hence its average value will be 0.
d)
Average(f) . Average(g) = 1/4 X 1/4
= 1/16
Average of (f.g) = 0
Hence the statement is false
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Complete Question
The figure attached to the left is a graph of f(x), and below to the right is g(x).
The figure below to the left is a graph of f(x), a
(a) What is the average value of f(x) on 0≤x≤2? avg value = __________
(b) What is the average value of g(x) on 0≤x≤2? avg value = __________
(c) What is the average value of f(x) . g(x) on 0≤x≤2? avg value = _________
(d) Is the following statement true?
Average(f) . Average(g)=Average(f.g)
A. Yes
B. No
help me, please. I can't figure out if this is zero or infinite??
Answer:
it doesn't have any solutions bc the lines are parallel and don't share any points in common. hope this helps!
A laboratory uses liquid nitrogen tanks of two different sizes. The combined volume of 3 large tanks and 2 small tanks is 24 liters. The combined volume of 2 large tanks and 3 small tanks is 21 liters. What is the volume of each size of tank? JUSTIFY YOUR ANSWER.
The size of the large tank is 6 liters and the size of the small tank is 3 liters.
What is the size of each type of tank?The first step is to form a system of equations using the information provided in the question:
3l + 2s = 24 equation 1
2l + 3s = 21 equation 2
Where:
l = volume of the large tank s = volume of the small tankThe elimination method would be used to solve the equations:
Multiply equation 1 by 2 and equation 2 by 3:
6l + 4s = 48 equation 3
6l + 9s = 63 equation 4
Subtract equation 3 from equation 4:
5s = 15
Divide both sides of the equation by 5
s = 15 / 5
s = 3 liters
Substitute for s in equation 1 :
3l + 2(3) = 24
3l + 6 = 24
3l = 24 - 6
3l = 18
l = 18 / 3
l = 6
To learn more about system of equations, please check: https://brainly.com/question/12129107
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How many 1/3 ounce cups can be taken
Answer:
90
Step-by-step explanation:
If we know that for every cup, we can take 3 of 1/3-ounce cups, we can use an equation that looks like this:
number of cups × 3 = total 1/3-ounce cups
If there are 30 cups, then we can simply insert 30 into the equation.
30 × 3 = 90
Therefore, you can make 90 1/3-ounce cups from the cereal box.