The interest earned by Peter after 42 months is $1,335.60 and the total amount in his account is $9,125.60.
How to determine the accrued ( A ) and interest ( I ) amount in a compound interest?The formula for compound interest is expressed as;
A = P(1 + r/n)^nt
Where A is accrued amount, P is principal, r is interest rate, n is compound, and t is time period.
Given the data in the question;
Principal P = $7,790Annual interest r = 4 5/8%Compounded annually n = 1Time t = 42 monthsAccrued amount A = ?Interest I = ?First, convert the interest rate to decimal.
Rate r = 4 5/8% = (4×8 + 5 )/8%
Rate r = 37/8%
Rate r = 4.625%
Rate r = 4.625/100 = 0.04625 per pear
Next, convert time from months to years
Time t = 42 month = ( 42/12 )years
Time t = 3.5 years
To determine the accrued amount, plug the given values into the compound interest formula and solve for A.
A = P(1 + r/n)^nt
A = $7,790(1 + 0.04625/1)^( 1 × 3.5 )
A = $7,790(1 + 0.04625 )^( 3.5 )
A = $7,790(1.04625 )^( 3.5 )
Accrued amount A = $9,125.60
Note that; Accrued amount A = Principal P + Interest I
Hence;
Interest I = A - P
Interest = $9,125.60 - $7,790
Interest = $1,335.60
Amount in the account after 42 months is the same as the accrued amount A, this is $9,125.60.
Therefore, the interest earned is $1,335.60 and the accrued amount is $9,125.60.
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a rectangle is x units long and y units wide what is it area what its perimeter
HELP PLS Determine which integers in the set S: {−2, −3, −4, −5} will make the inequality 3p − 10 ≥ 7p + 6 true.
Answer:
{-4; -5}
Step-by-step explanation:
just put any integer from set S in place of p and you will know. the inequality is false with -2 and -3, but with other two numbers is true
Multiply 3.7x and 6x.
09.7x
09.7x²
O 22.2x
22.2x²
HELP ASAP
The product of 3.7x x 6x = (3.7 x 6) x (x x x) = 22.2x².
In mathematics, a product is the outcome of multiplication or an expression that specifies the factors to be multiplied.The outcome of multiplying two or more numbers is known as the product of those numbers, and the numbers that are multiplied are referred to as the factors.What is Multiplication?For whole numbers, multiplication can be used as counting objects arranged in a rectangle or as calculating the area of a rectangle whose sides have a certain length. Because of the commutative principle, a rectangle's area is independent of which side is measured first.A new kind of measurement is the sum of two measures. For instance, the area of a rectangle can be calculated by multiplying the lengths of its two sides. An analysis of this product's dimensions is performed.One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication.Multiply in mathematics refers to the continual addition of sets of identical sizes.To learn more about Multiplication, refer to:
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If p (x) is a polynomial of degree 3 with p(0) = p(1) = p(-1) = 0 and p(2) = 6, then
a show that p(-x) = -p (x).
b find the interval in which p(x) is less than zero.
Answer:
p(x) is a function, and a polynomial of degree 3, then
By remainder theorem and factor theorem,
p(0) = p(1) = p (-1) = 0 if and only if
x = 0, 1, -1 are zeroes if and only if
p(x) = k(x - 0)(x - 1)(x + 1) = k(x)(x^2 - 1) = k(x^3 - x) = kx^3 - kx
p(2) = k(2)^3 - k(2) = 6
8k - 2k = 6
6k = 6
k = 1
Thus p(x) = x(x - 1)(x + 1) = x(x^2 - 1) = x^3 - x
p(-x) = (-x)^3 - (-x) = x^3 + x
-p(x) = -(x^3 - x) = -x^3 + x
As you can see, p(x) does not equal to -p(x), unless x = 0, 1, -1,
because p(0) = -p(0) = 0, p(-1) = - p(1) = 0, p(1) = -p(-1) = 0
p(x) = x(x - 1)(x + 1)
If x < -1, then x < 0, x - 1 < 0, x + 1 < 0
That means p(x) < 0
If -1 < x < 0, then x < 0, -2 < x - 1 < -1 < 0, 0 < x + 1 < 1
That means p(x) > 0
If 0 < x < 1, then x > 0, -1 < x - 1 < 0, 0 < 1 < x + 1 < 2
That means p(x) < 0
If x > 1, then x > 0, x - 1 > 0, x + 1 > 2 > 0
That means p(x) > 0
Thus p(x) < 0 if x < -1 or 0 < x < 1
NEED HELP ASAP - 100 Points (Algebra 2 - Complex Numbers)
Every complex number has the form a+bi with a and b as real numbers. Is it possible to create a complex number in which b=0? If so, create two examples to show your hypothesis is true. If not, explain why it is not possible.
Your response must be at least 50 words.
It is not possible to create a complex number in which b = 0, as it would be equivalent to a real number.
Complex numbersThe general format of a complex number is given as follows:
z = a + bi.
The meaning of the parameters a and b are given as follows:
a is the real component of the number.b is the imaginary component of the number.If the coefficient b has a value of zero, then the complex number is written as follows:
z = a + 0i.
z = a.
Which is equivalent to a real number, that is, the number would have only a real component, hence it is not possible to find an imaginary number with b = 0.
Basically, any real number can be represented as a complex number with imaginary part 0, but then the number would not be complex.
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10 Please help I’ll give brainly
Answer:
11) 7d + 28 and 7(d+4)
12) y^2 + 3y and y(y+3)
Step-by-step explanation:
A number, m, rounded to 1 d.p. is 48.2 Another number, n, rounded to 1 d.p. is 6.7 What are the lower and upper bounds of m - n?
The corresponding values of the lower and upper bounds of m - n are 41.41 and 41.59.
What are the values of the lower and upper bounds of m - n?
Upper and lower bounds are the possible maximum and minimum values of a number before it was rounded.
The upper and lower bounds can be expressed using the error interval
The lowest value of m is 48.15
The highest value of m is 48.24
The lowest value of n is 6.65
The highest value of n is 6.74
Therefore, lower bound of m - n = 48.15 - 6.74 = 41.41
Also, the upper bound of m - n = 48.24 - 6.65 = 41.59
So values of the lower and upper bounds of m - n are 41.41 and 41.59 respectively.
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what value of makes the equation true 7+3(x - 1)=5x+-2(x+1)
An equation is a collection of variables and constants with the value of x which will make the equation 7+3(x - 1)=5x+-2(x+1) to be true is 1/2.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
As per the given equation,
7+3(x - 1)=5x+-2(x+1)
7 + 3x - 3 = 5x + 2x + 2
3x + 4 = 7x + 2
7x + 2 = 3x + 4
7x - 3x = 4 - 2
4x = 2
x = 1/2
Hence "The value of x which will make the equation 7+3(x - 1)=5x+-2(x+1) to be true is 1/2".
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Pls help if able to send a picture of answer and work
Joan walked 20 brown dogs.
As per the question, the 40% of total number of dogs are brown. So, finding 40% of the number 50 will give us the number of brown dogs.
Number of brown dogs = 50×40%
Converting Percentage to fraction
Number of brown dogs = 50×40/100
Cancelling zero as it is common
Number of brown dogs = 5×4
Performing multiplication to find the number of brown dogs
Number of brown dogs = 20
Thus, out of 50 dogs, Joan walked 20 brown dogs.
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the domain of f(x) = -3x is (0, 1, 2). State the range of f (x) using set notation
The range of the function f (x) = -3x are (0, -3, 6).
What is Domain?
The set of all inputs of the function is called Domain of set.
Given that;
The domain of f(x) = -3x is (0, 1, 2).
Now, Domain of the function are the values of x.
So, We find the Range of the function as;
Substitute all the values of domain (x) in the given function as;
The function is;
f (x) = -3x
For x = 0
Range = f (x) = - 3 × 0 = 0
For x = 1;
Range = f (x) = - 3 × 1 = -3
For x = 2
Range = f (x) = 3 × 2 = 6
Thus, Range of the function are (0, -3, 6)
Therefore, The range of the function f (x) = -3x are (0, -3, 6).
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what is 3/4+65/8-23+78+92-6+g
Answer:
g + 1199 / 8
Step-by-step explanation:
3/4+65/8-23+78+92-6+g
1199/8+g
What is 2/5 divided by 1/10?
Answer:
4
Step-by-step explanation:
2/5 divided by 1/10
Division of fractions
Use copy dot flip
2/5 * 10/1
20/5
4
Round to the nearest thousandth 88.6217
Answer:
88.6000 = 88.622
12. Find m<1 and m<2 for a//t
0
please help
Answer:
Angle 1 & 2 are both 100 degrees
Step-by-step explanation:
In the picture,
angles on the same side of the line must add up to 180degrees.
Angles directly opposite of each other(same vertices) must be equal.
with parallel lines, angles that are made by the same intersecting line are also equal.
image really helps :( sry its hard to explain in words
Can someone help me answer the top one?
When the spacecraft launched, it was 254 miles away from the Earth and its distance away from the Earth is increasing at a rate of 270 miles per hour.
How do we interpret the linear equation?The equation that represents the distance of the space craft is known as a linear equation. A linear equation is an equation that has only one variable that is raised to the power of one.
A linear equation increases or decreases at a constant rate. When drawn on a graph, a linear equation is a straight curve that slopes either upward or downward.
A linear equation usually has this form y = mx + b
Where:
m = slope b = interceptD = 254 + 270t
Where:
254 = intercept = initial distance from the Earth270 = slope = change in the speed of the spacecraft per hourTo learn more about linear functions, please check: https://brainly.com/question/26434260
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Evaluate 5(x - 1) - 2 when x = 3.
OA. 8
OB. 0
O C. 12
OD. -4
The value of f(3) for the given expression is 8.
What is evaluation of an expression?
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Finding the value of an algebraic expression when a specified integer is used to replace a variable is known as evaluating the expression. We use the given number to replace the expression's variable before applying the order of operations to simplify the expression. The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.
Given, the expression is 5(x - 1) - 2
Let y = f(x) = 5(x - 1) - 2 = 5x - 5 - 2 = 5x - 7
Therefore, f(3) using the equation above is: f(3) = 5(3) - 7 = 8
Thus, the value of f(3) or y at x = 3 for the given expression is 8.
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A square and a rectangle have equal perimeters. The length of a side of the square is 2x+1. The length of the rectangle is x+2 and the width is x. Write and solve an equation to find x
When a square and a rectangle have the same perimeters. If the length of a side of the square is 4x-1 and the length of the rectangle is 2x+1 and the width is x+2. then the value of x=1
The perimeter of the square is equal to the perimeter of the rectangle.
The length of a side of the square=4x-1
The perimeter of the square=4a
Where a is the side of the square
Substitute the values in the equation
The perimeter of the square=4(4x-1)=16x-4
The length of the rectangle=2x+1
The width of the rectangle=x+2
The perimeter of the rectangle=2(l+w)
where l is the length and w is the width
The perimeter of the rectangle =2(2x+1+x+2)
=2(3x+3)
= 6x+6
A square and a rectangle have equal perimeters
16x-4=6x+6
16x-6x=6+4
10x=10
x=1
Hence, when a square and a rectangle have the same perimeters. If the length of a side of the square is 4x-1 and the length of the rectangle is 2x+1 and the width is x+2. then the value of x=1
The complete question is
A square and a rectangle have the same perimeters. The length of a side of the square is 4x-1. The length of the rectangle is 2x+1 and the width is x+2, Write and solve an equation to find x
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ABCD is a rectangle that represents a park. The lines show all the paths in the park. The circular path is in the centre of the rectangle and has a diameter of 10 m. Calculate the shortest distance from A to C across the park, using only the lines shown. B 40 m A 70 m C D
Does anyone know the answers to this problem?
The cups of sugar needed is 2.5 cups.
The cups of flour needed is 3.75 cups
The cups of butter needed is 1.25 cups.
How much sugar, flour and butter is needed?Given the information in the question, the ratio of sugar to flour to butter is 1 : 1.5 : 0.5
Cups of sugar needed = (ratio representing sugar / sum of ratios) x total number of cups
Sum of ratios = 1 + 1.5 + 0.5 = 3
Cups of sugar needed = (1 / 3) x 7.5 = 2.5 cups
Cups of flour needed = (ratio representing flour / sum of ratios) x total number of cups
Cups of flour needed = (1.5 / 3) x 7.5 = 3.75 cups
Cups of butter needed = (ratio representing butter / sum of ratios) x total number of cups
Cups of butter needed = (0.5 / 3) x 7.5 = 1.25 cups
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When simplified, i⁹⁹ is equivalent to
Complex number :
[tex]i^{99}[/tex]= - i.
Why is it called a complex number?A complex number is one that has the notation a + b I a + bi a+bi, where a and b are real numbers and I is the imaginary unit denoted by the expressions I 2 = 1 I 2 = -1 I 2 = 1. Real numbers (R) and pure imaginary numbers (I) are both included in the set of complex numbers, represented by the letter C.In the 19th century, the phrase "complex numbers"—which denotes that they have both real and imaginary components—became widely used. Occasionally, the term "imaginary number" is used to describe a complicated number that is not real or, more commonly, a number whose real portion is zero (a.k.a "pure imaginary").here,
i = [tex]\sqrt{-1}[/tex]
If the power is
even then the value could be -1 or 1odd then the value could be -i or i99 is odd so now is
-i if (99+1)/2 is even or is
i is (99+1)/2 is odd
Now check (99+1)/2= 100/2= 50,
50 is even so
i^99 = -i
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What are the y-intercept and the horizontal asymptote of g(x) = 7x + 2?
(0, 3) ; y = 2
(0, 4) ; y = 7
(0, 7) ; y = 2
(0, 9) ; y = 7
The y-intercept and the horizontal asymptote of g(x) = 7ˣ + 2 is (a) (0, 3) ; y = 2
How to determine the y-intercept?The equation of the function is given as
g(x) = 7ˣ + 2
To calculate the y-intercept, we set x = 0
So, we have
g(0) = 7⁰ + 2
Evaluate the exponent
g(0) = 1 + 2
Evaluate the sum
g(0) = 3
So, we have
(x, y) = (0, 3)
How to determine the horizontal asymptote?The equation of the function is given as
g(x) = 7ˣ + 2
To calculate the horizontal asymptote, we set 7ˣ
So, we have
y = 0 + 2
Evaluate the sum
y = 2
Hence, the solution is (a) (0, 3) ; y = 2
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The required y-intercept of the given function is (0,3) and the horizontal asymptote is y = 2.
What is an asymptote?Asymptote is the line on the curve that does not intersect the curve but passes as near to the maximum and minimum of the graph.
Here,
The y-intercept of the given function is evaluated as put the x coordinate to zero,
So,
g(0) = 1 + 2
g(0) = 3
Now, the horizontal asymptote is a line that passes near to the line but does not intersect with the curve,
So,
Terminating the x compositon of the function 7ˣ = 0 the rest will be the horizontal asymptote,
y = 7ˣ + 2
y = 0 + 2
y = 2
Thus, the required y-intercept of the given function is (0,3) and the horizontal asymptote is y = 2.
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a red light flashes every 17 seconds
a green light flashes every 15 seconds
they both flash at the same time
after how many seconds will they both flash at the same time?
please help
Answer:
Both the lights will flash 1440 times a day. Proof: Red light flashes after every 30 seconds and green light flashes after every 20 seconds.
Step-by-step explanation:
Shureka Washburn has scores of 69, 74, 79, and 62 on her algebra tests. a. Use an inequality to find the scores she must make on the final exam to pass the course with an average of 71 or higher, given that the final exam counts as two tests. b. Explain the meaning of the answer to part (a).
If Shureka Washburn has scores of 69, 74, 79, and 62 on her algebra tests, then by using the inequality, the score she must make on the final exam to pass the course with an average of 71 or higher is 71
The scores she scored on test = 69, 74, 79, 62
Consider the final score she must make on the final exam as x
Sum of the scores = 69+74+79+62+2x
= 284+2x
Consider the average of score = Sum of scores / Number of subjects
= (284+2x)/6
She need average of 71 or higher
Then the inequality equation will be
(284+2x)/6 ≥ 71
284+2x ≥ 426
2x ≥ 426-284
2x ≥ 142
x ≥ 71
Hence, if Shureka Washburn has scores of 69, 74, 79, and 62 on her algebra tests, then by using the inequality, the score she must make on the final exam to pass the course with an average of 71 or higher is 71
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How many terms are in this expression?
9c + a
Answer:
2
9c and a
Step-by-step explanation:
Answer:
2, (a and c)
Step-by-step explanation:
write and simplify a division expression to find the number of cups of flour max needs to use if he has just 1 egg
The division expression to find the number of cups of flour Max needs to use if he has only 1 egg is M ÷ N cups of flour.
1 egg = M/N cups of flour.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Let M cups of flour be needed for N eggs.
This can be written as:
N eggs = M cups of flour
Divide both sides by N.
1 egg = M/N cups of flour
Thus,
The division expression to find the number of cups of flour Max needs to use if he has only 1 egg is M ÷ N cups of flour.
1 egg = M/N cups of flour.
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Subject: Trigonometry, Evaluation of Functions
Hi, I only need help matching the graphs to the questions :) Brainly only allows me to attach 5/10 of the graphs, if the ones i've attached aren't the answer i posted a similar question before this one with the rest of the graph choices. Sorry!!
1. Find <0 if cos0 = 4/7 and sin0 is negative.
2. Find <0 if sec0 = -13/5 and tan0 is negative.
3. Find <0 is sin0 = 7/10 and cot0 is positive.
4. Find <0 if tan0 = 3/4 and sin0 is negative.
(i) cosФ = 4/7 and sinФ is negative → It lies in the 4th quadrant 304.8° and the suitable graph is not provided here.
(ii) secФ = -13/5 and tanФ is negative → It lies in the IInd quadrant 112.6° and the suitable graph is J.
(iii) sinФ = 7/10 and cotФ is positive → It lies in Ist quadrant =44.4° and the suitable graph is I.
(iv) tan0 = 3/4 and sin0 is negative → It lies in the IIIrd quadrant 216.9° and the suitable graph is not provided here.
What is quadrant?
The point is in the first quadrant if both x and y were positive. If both x and y are negative, the point will reside in the second quadrant. In the third quadrant, if either x and y are negatives, the point is located. The point is situated in the fourth quadrant if both x and y are positive.(i) cosФ = 4/7 and sinФ is negative
Ф=cos^(-1)(4/7)= 55.2°
It lies in 4th quadrant (360-55.2)°=304.8°
A suitable graph is not provided here.
(ii) secФ = -13/5 and tanФ is negative.
Ф=sec^(-1)(-13/5)=67.4°
It lies in IInd quadrant (180-67.4°)=112.6°
A suitable graph is J.
(iii) sinФ = 7/10 and cotФ is positive.
Ф=sin^(-1)(7/10)=44.4°
It lies in Ist quadrant =44.4°
A suitable graph is I.
(iv) tan0 = 3/4 and sin0 is negative.
Ф=tan^(-1)(3/4)=36.9°
It lies in IIIrd quadrant (180+36.9)=216.9°
A suitable graph is not provided here.
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Complete the empty table from the provided information.
Transform the graph of f(x) by dilating it by a factor of -2 and then shift it up 3.
Write the equation of the resulting line in slope intercept form.
The empty table should be completed with the coordinates of the transformed graph after a dilation with a scale factor of 3 as follows;
x m(x)
4 -2
2 -1
0 0
-2 1
-4 2
The equation of the resulting line in slope-intercept form is y = -0.5x + 3.
How to transform the graph of f(x) through dilation?Based on the given coordinates of the graph of function f(x), the dilation with a scale factor of 3 from the origin (0, 0) or center of dilation would be calculated as follows:
Point 1 (-2) → Point 1' (-2 × -2) = Point 1' (4).
Point 2 (-1) → Point 2' (-1 × -2) = Point 2' (2).
Point 3 (0) → Point 3' (0 × -2) = Point 3' (0).
Point 4 (1) → Point 4' (1 × -2) = Point 4' (-2).
Point 5 (2) → Point 5' (2 × -2) = Point 5' (-4).
Next, we would translate the graph of function f(x) 3 units up as follows:
Point 1 (-2) → Point 1' (-2 + 3) = Point 1' (1).
Point 2 (-1) → Point 2' (-1 + 3) = Point 2' (2).
Point 3 (0) → Point 3' (0 + 3) = Point 3' (3).
Point 4 (1) → Point 4' (1 + 3) = Point 4' (4).
Point 5 (2) → Point 5' (2 + 3) = Point 5' (5).
Now, we can determine the slope of the transformed graph:
Slope, m = Δy/Δx
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (2 - 1)/(2 - 4)
Slope, m = -1/2 or -0.5
Mathematically, the slope-intercept form of a straight line is given by;
y = mx + c
Where:
x and y are the points.m represents the slope.c represents the y-intercept.At point (2, 2) and y-intercept c = 3, we have:
y = mx + c
y = -0.5x + 3
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The time required to load a truck is exponentially distributed with a mean of 15 minutes. What is the probability that a truck will be loaded in 20 minutes or more? enter your answer as a decimal not as a percent and round your answer to 3 decimal places.
Using the exponential distribution, there is a 0.263 probability that a truck will be loaded in 20 minutes or more.
Exponential distributionThe exponential probability distribution, with mean m, is described by the following probability mass function:
[tex]f(x) = \mu e^{-\mu x}[/tex]
[tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
The integral has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
Hence the probability of finding a value higher than x is given by:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
In the context of this problem, the mean and the decay parameter are given, respectively, by:
[tex]m = 15, \mu = \frac{1}{15} = 0.0667[/tex]
Hence the probability that a truck will be loaded in 20 minutes or more is:
[tex]P(X > 20) = e^{-0.0667 \times 20} = 0.263[/tex]
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Part III: Verify that
f(g(x)) = F(x)
f(g(x)) = √3x - 4
(2 points)
they seem to be right :p
Step-by-step explanation:
when a cold drink is taken from a refrigerator, its temperature is 5°c. after 25 minutes in a 20°c room its temperature has increased to 10°c. (round your answers to two decimal places.) (a) what is the temperature of the drink after 55 minutes? °c (b) when will its temperature be 13°c? min
use the cross multiplication method :)