5. If x= 3 solves the system shown below, what must be the value of a?(1) -4(3) 3y = 5x - 8(2) -1(4) 7y = ax +19
Answers
Given data:
The given value is x=3.
Subtitute 3 for x in the expression y = 5x - 8.
\(\begin{gathered} y=5(3)-8 \\ =7 \end{gathered}\)Substitute 7 for y, and 3 for x in the expression y=ax+19.
\(\begin{gathered} 7=3a+19 \\ 3a=-12 \\ a=-4 \end{gathered}\)Thus, the value of a is - 4, so option (i) is correct.
Related Questions
Find the area of the regular pentagon with apothem 3.5 and side. Not drawn to scale.
100 POINTS
SHOW WORK PLEASE
Answers
Answer:
52.5 inch square
Step-by-step explanation:
Area of pentagon: A = 1/2 × p × a;
where 'p' is the perimeter of the pentagon and 'a' is the apothem of the pentagon.
A = 1/2 x (6 x 5) x 3.5 = 1/2 x 30 x 3.5 = 15 x 3.5 = 52.5
The area of the regular pentagon with apothem 3.5 and side 6 is 52.5
What is the area of the regular pentagon?In Mathematics, a pentagon is a polygon with 5 sides. A pentagon can be classified as a regular pentagon and irregular pentagon. When all the sides and the angles of a pentagon are of equal measure, then it is called a regular pentagon.
How to find the area of the regular pentagonGiven the question, we need to find the area of the regular pentagon with apothem 3.5 and side 6.
In order to find the area, the formula to calculate the area of the regular pentagon is given by:
\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times s \times a\)
Where “s” is the side length. And “a” is the apothem length.Now,
\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times s \times a\)
\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times 6 \times 3.5\)
\(\text{Area of pentagon} =52.5\)
Therefore, the area of the regular pentagon with apothem 3.5 and side 6 is 52.5
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PLEASE HELP
solve: |3x| = 9
Answers
Answer:
Step-by-step explanation:
X=3 or x=-3
Answer:
3x=93x/3=9/3x=3 and x=-3Please mark my answer as a brainliest.❤❤❤❤❤with expression 1. the options are, 2 factors, 3 factors, 2 terms, 3 terms.
with expression 2. the options are, 2 factors, 3 factors, 2 terms, 3 terms.
its a multiple choice question ;-;
Answers
Consider the expression 4(8x + 5)
Complete 2 descriptions of the parts of the expression.
1. The entire expression is the product of 2 factors.
1 factor is 42 factor is (8x + 5)2. On its own, (8x + 5) is a sum with 2 terms.
1 term is 8x2 term is 5A student is making a trail mix. Create a graph to
Determine if the quantities of nuts and fruit
are proportional for each serving Size listed in
the table. If the quantities are proportional for each serving size listed in the table. If the quantities are proportional,
what is the constant of proportionality or unit
rate that defines the relationship? Explain how
you determined the constant of proportionality
and how it relates to both the table and graph.
Answers
Answer:
if the relationship between two quantities is a proportional relationship, this relationship can be represented by the graph of a straight line through the origin with a slope equal to the unit rate. For each point (x, y) on the graph, ž is equal to k, where k is the unit rate. The point (1, k) is a point on the graph.
Step-by-step explanation:
Hi, can you help me answer this question please, thank you!
Answers
Given:
\(\begin{gathered} HypothesisMean,H_0\colon\mu=23.915 \\ Sample\text{ mean, }\bar{\text{x}}=25.8 \\ \text{Standard deviation, }\sigma=4.57 \\ Sample\text{ size, n=43} \end{gathered}\)To find the test statistics, t:
The formula for the test statistics is,
\(t=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt[]{n}}}\)On substitution we get,
\(\begin{gathered} t=\frac{25.8-23.915}{\frac{4.57}{\sqrt[]{43}}} \\ =\frac{1.885}{0.69692} \\ =2.70476 \\ \approx2.705 \end{gathered}\)Hence, the answer is, t = 2.705 (rounded to 3 decimal places).
In the summer the median number of minutes late was 12.7 minutes.
The range of the number of minutes late was 11 minutes.
The results below show the number of minutes late in the winter.
8, 32, 44,
5, 17, 67, 9,
14, 10, 26
Calvin thinks that in the winter
the median number of minutes late increases
the train service is less consistent.
.
Is Calvin correct?
Show why you think these giving reasons with your answers.
Answers
what is the slope and y-intercept of line that passes through (1,5) and (4,10)
Answers
Answer:
5/3 (I think)
Step-by-step explanation:
What is the volume of the prism?
Answers
Answer:
Step-by-step explanation:
When a patient is given a vitamin B-12 treatment to promote red blood cell formation, the dose D, in
micrograms, is a function of the patient's weight, in pounds. Let D = f(w) define the dosage. Interpret
the meaning of each statement.
A. f(155) = 425
B. f'(155) = 20
C. Estimate the dosage for a person weighing 175 pounds.
Answers
B. f'(155) = 20 means that the rate of change of the dosage with respect to weight at a weight of 155 pounds is 20 micrograms per pound. In other words, for every one-pound increase in weight at 155 pounds, the dosage is expected to increase by 20 micrograms.
C. To estimate the dosage for a person weighing 175 pounds, we need to know the specific function or equation that defines the relationship between dosage and weight. Without this information, we cannot estimate the dosage accurately.
An equilateral triangle has an
area of 97.5 square meters. If the
height of the triangle is 13 meters,
find the perimeter of the triangle.
Answers
The perimeter of the equilateral triangle is 45 meters.
What is the perimeter?An equilateral triangle is a polygon that has three sides that are of equal length. The sum of angles in an equilateral triangle is 180 degrees. The perimeter of an equilateral triangle is the distance round the triangle. It can be determined by adding the length of the three sides of the triangle together.
The first step is to determine the side length of the triangle. The base can be determined from the area.
Area of a triangle = 1/2 x base x height
97.5 = 1/2 x 13 x b
b = (97.5 x 2) / 13
b = 15 meters
Perimeter = 15 x 3 = 45 meters
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NO LINKS!! URGENT HELP PLEASE!!
1. Find the area of a regular octagon. Each side is 12 m.
2. The perimeter of a regular polygon is 72 feet. An exterior angle of the polygon measures 40°. Find the length of each side.
3. If the perimeter of a regular pentagon is 50 in. Find the area. Show a drawing and work please.
Answers
Answer:
1) 695.3 m²
2) 8 ft
3) 172.0 in²
Step-by-step explanation:
Question 1To find the area of a regular polygon, we can use the following formula:
\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)
Given the polygon is an octagon, n = 8.
Given each side measures 12 m, s = 12.
Substitute the values of n and s into the formula for area and solve for A:
\(\implies A=\dfrac{(12)^2 \cdot 8}{4 \tan\left(\dfrac{180^{\circ}}{8}\right)}\)
\(\implies A=\dfrac{144 \cdot 8}{4 \tan\left(22.5^{\circ}\right)}\)
\(\implies A=\dfrac{1152}{4 \tan\left(22.5^{\circ}\right)}\)
\(\implies A=\dfrac{288}{\tan\left(22.5^{\circ}\right)}\)
\(\implies A=695.29350...\)
Therefore, the area of a regular octagon with side length 12 m is 695.3 m² rounded to the nearest tenth.
\(\hrulefill\)
Question 2The sum of an interior angle of a regular polygon and its corresponding exterior angle is always 180°.
If the exterior angle of a polygon measures 40°, then its interior angle measures 140°.
To determine the number of sides of the regular polygon given its interior angle, we can use this formula, where n is the number of sides:
\(\boxed{\textsf{Interior angle of a regular polygon} = \dfrac{180^{\circ}(n-2)}{n}}\)
Therefore:
\(\implies 140^{\circ}=\dfrac{180^{\circ}(n-2)}{n}\)
\(\implies 140^{\circ}n=180^{\circ}n - 360^{\circ}\)
\(\implies 40^{\circ}n=360^{\circ}\)
\(\implies n=\dfrac{360^{\circ}}{40^{\circ}}\)
\(\implies n=9\)
Therefore, the regular polygon has 9 sides.
To determine the length of each side, divide the given perimeter by the number of sides:
\(\implies \sf Side\;length=\dfrac{Perimeter}{\textsf{$n$}}\)
\(\implies \sf Side \;length=\dfrac{72}{9}\)
\(\implies \sf Side \;length=8\;ft\)
Therefore, the length of each side of the regular polygon is 8 ft.
\(\hrulefill\)
Question 3The area of a regular polygon can be calculated using the following formula:
\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)
A regular pentagon has 5 sides, so n = 5.
If its perimeter is 50 inches, then the length of one side is 10 inches, so s = 10.
Substitute the values of s and n into the formula and solve for A:
\(\implies A=\dfrac{(10)^2 \cdot 5}{4 \tan\left(\dfrac{180^{\circ}}{5}\right)}\)
\(\implies A=\dfrac{100 \cdot 5}{4 \tan\left(36^{\circ}\right)}\)
\(\implies A=\dfrac{500}{4 \tan\left(36^{\circ}\right)}\)
\(\implies A=\dfrac{125}{\tan\left(36^{\circ}\right)}\)
\(\implies A=172.047740...\)
Therefore, the area of a regular pentagon with perimeter 50 inches is 172.0 in² rounded to the nearest tenth.
Answer:
1.695.29 m^2
2.8 feet
3. 172.0477 in^2
Step-by-step explanation:
1. The area of a regular octagon can be found using the formula:
\(\boxed{\bold{Area = 2a^2(1 + \sqrt{2})}}\)
where a is the length of one side of the octagon.
In this case, a = 12 m, so the area is:
\(\bold{Area = 2(12 m)^2(1 + \sqrt{2}) = 288m^2(1 + \sqrt2)=695.29 m^2}\)
Therefore, the Area of a regular octagon is 695.29 m^2
2.
The formula for the exterior angle of a regular polygon is:
\(\boxed{\bold{Exterior \:angle = \frac{360^o}{n}}}\)
where n is the number of sides in the polygon.
In this case, the exterior angle is 40°, so we can set up the following equation:
\(\bold{40^o=\frac{ 360^0 }{n}}\)
\(n=\frac{360}{40}=9\)
Therefore, the polygon has n=9 sides.
Perimeter=72ft.
We have
\(\boxed{\bold{Perimeter = n*s}}\)
where n is the number of sides in the polygon and s is the length of one side.
Substituting Value.
72 feet = 9*s
\(\bold{s =\frac{ 72 \:feet }{ 9}}\)
s = 8 feet
Therefore, the length of each side of the polygon is 8 feet.
3.
Solution:
A regular pentagon has five sides of equal length. If the perimeter of the pentagon is 50 in, then each side has a length = \(\bold{\frac{perimeter}{n}=\frac{50}{5 }= 10 in.}\)
The area of a regular pentagon can be found using the following formula:
\(\boxed{\bold{Area = \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *s^2}}\)
where s is the length of one side of the Pentagon.
In this case, s = 10 in, so the area is:
\(\bold{Area= \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *10^2=172.0477 in^2}\)
Drawing: Attachment
Please Give Me The Answer
Answers
The area covered by the signal is 181.37 m²
What is the area covered by the signal?Here we can see that the area covered by the signal is the fourth of a circle of radius R = 15.2m
The area of a circle of radius R is given by:
A = 3.14*R²
Then the area of a fourth of a circle is:
A = (3.14/4)*R²
Replacing the value of the radius in the formula we will get:
A = (3.14/4)*(15.2m)² = 181.37 m²
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You decide to reduce the amount you spend eating out by $150 a month and invest the total saved at
the end of each year in your retirement account. How much will the account be worth at 5% in 15
years? (Use Table 13.1.) (Do not round intermediate calculations. Round your answer to the
nearest cent.)
Answers
The type of savings is the saving of uniform amount with interest applied to the sum of the amount in the account.
The amount the account is worth after 15 years is approximately $38,841.1Reasons:
The amount saved per month = $150
Amount saved per year, A = 12 × $150 = $1,800
The interest rate on the account, i = 5%
The amount, F, in the account after 15 years is given as follows;
The uniform series compound amount factor formula is presented as follows;
\(\displaystyle F = \mathbf{\frac{A \cdot \left[ \left(1 + i \right)^n - 1 \right]}{i}}\)
Therefore;
\(\displaystyle F = \frac{1,800 \times \left[ \left(1 + 0.05 \right)^{15} - 1 \right]}{0.05} \approx \mathbf{38,841.4}\)
The amount the account is worth after 15 years to the nearest cent is approximately $38,841.4.
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(GIVING AWAY BRAINLIEST AND EXTRA POINTS TO WHO EVER HELPS ME :> BTW THE SUBJECT MATH IS INNCORECT BUT I CHOSE IT BC THEY DIDNT HAVE SCIENCE AS AN OPTION LOL)
Veronica observes how the force of friction causes an object to slow down. She writes the following observation: When an object moves across a smooth surface, there is less friction created than when an object moves across a rough surface. When the object stops moving, friction is created. Which statement corrects the error(s) in Veronica's observations?
A) It is not smooth or rough surfaces that affects friction. It is the size of the push.
B) When an object moves across a rough surface, there is no friction.
C) When an object moves across a smooth surface, the friction increases.
D) When an object stops moving, there is no friction.
(Here is an image if needed) :
Answers
Answer:
C
Step-by-step explanation:
Answer:
A
number is correct answer
Simplify the expression:
10v – 6v + 7 – 4v
Answers
Answer:
7
Step-by-step explanation:
collect like terms
o+7
when adding or subtracting 0, the quantity does not change
7
so 7 is your solution
How many square feet of outdoor carpet will
we need for this hole?
?
ft?
3 ft
I ft
2 ft
4 ft
2 ft
12 ft
Answers
Answer:46
Step-by-step explanation:
The amount of outdoor carpet needed is 40 ft².
What is the Area of a Rectangle?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area.
Area of a rectangle = length × width.
The amount of square feet of outdoor carpet needed
= area of the largest rectangle in the image - (area of medium rectangle + area of the smallest rectangle)
The amount of square feet of outdoor carpet needed
= 12 × 4 - (3 × 2 + 2 × 1)
= 48 - (6 + 2)
= 40 ft²
Thus, 40 ft² outdoor carpet needed.
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A cake recipe calls for the following dry ingredients: 3 ½ cups of flour, 2 ⅔ cups of sugar, and 1 ¾ cups of cocoa. To the nearest cup, how much dry ingredients will be used?
HELO
Answers
The amount of dry ingredients used in the cake recipe is approximately 7 cups.
We have,
3 ½ cups of flour, 2 ⅔ cups of sugar, and 1 ¾ cups of cocoa.
Now, first convert all quantity in same unit.
3 ½ cups of flour
= 3 cups + 0.5 cups
= 3 cups and 8 ounces.
and, 2 ⅔ cups of sugar
= 2 cups + 0.67 cups,
= 2 cups and 10.72 ounces.
and, 1 ¾ cups of cocoa
=1 cup + 0.75 cups
= 1 cup and 12 ounces.
So, the total amount
= 3 cups and 8 ounces + 2 cups and 10.72 ounces + 1 cup and 12 ounces = 6 cups and 14.72 ounces
= 7 cups
Therefore, the amount of dry ingredients used in the cake recipe is approximately 7 cups.
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Simplify the following expression by combining like terms. Select the most simplified expression:
Answers
Option (A) is the correct option and on simplifying the expression by combining like terms we get,
24 - 3p.
Given, the expression 6(4 - 2p) + 9p
On simplifying, we get
24 - 12p + 9p
24 - 3p
So, on simplifying the given expression, we get
24 - 3p
Hence, Option (A) is the correct option and on simplifying the expression by combining like terms we get,
24 - 3p
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Dog food comes in two different sized bags. The 4 lb bag sells for $19.49 while the 30 lb bag sells for $73.99. Which is cheaper per pound and by how much?
Answers
Answer:
30 lb bag is cheaper by about $2.40
Step-by-step explanation:
to find per pound we divide
19.49/4= 4.8725
$4.87per pound
$73.99/30=2.46633
$2.47 per pound
30 lb bag is cheaper per pound
4.87-2.47=2.40
hopes this helps please mark brainliest
17p5
Exponent:
Variable:
tify the term, coefficient, and the variable.
Term:
Coefficient:
Answers
For the given expression, the variable is p, coefficient is 17 and the exponent is 5.
Expression:
Expression refer the algebraic expression that consists of variables, numbers and math operators.
Given,
Here we have the expression 17p⁵
Now, we have to find the exponent, coefficient and variable.
As per the definition of exponent, the term exponent refers the power value of the expression.
So, the exponent is 5.
And the definition of coefficient is an integer that is written along with a variable or it is multiplied by the variable.
So, the coefficient is 17.
And the variable of this expression is p.
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What incremental manufacturing cost will Martinez incur if it increases production from 10,000 to 10,001 units?
Answers
Answer:
Incremental cost is the total cost incurred due to an additional unit of product being produced. Incremental cost is calculated by analyzing the additional expenses involved in the production process, such as raw materials, for one additional unit of production.
Step-by-step explanation:
The incremental manufacturing cost Martinez incurs, if it increases production from 10,000 to 10,001 units, is $21.5.
We have,
Average cost = Sum of cost of all the units / Number of units
From the table given,
The average cost per unit when it produces 10,000 units.
= 6 + 3.5 + 1.5 + 4 + 3 + 2 + 1 + 0.5
= 21.5
Now,
Substituting the values here,
Average cost = Sum of cost of all the units / Number of units
21.5 = Sum of the cost of 10,000 units / 10,000
The sum of the cost of 10,000 units
= 21.5 x 10,000
= 215000
Now,
The incremental cost is the cost of one unit.
= 21.5
Thus,
The incremental manufacturing cost Martinez incurs, if it increases production from 10,000 to 10,001 units, is $21.5.
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Yesterday, vests sold for $42.
Today, vests are on sale for 25% off.
1. Estimate the sale price of a vest.
Round $42 to a convenient value, such as $40. Determine the amount of the discount.
Awnser the following:
1) 25% of $40 = ___ x ___
= __
Subtract the discount from the rounded price. $40 - $10 = $30 Vests are on sale for about $30.
Round $42 to $40.
Determine the percent that is left after the discount.
2) What is the discount percent?
=
Percent left = 100% - 25%
= 75%
Answers
1. The estimated price of vest is $30.
The amount of discount is $10.
1) 25% of $40 is $10.
2) The discount percent is 25%.
What is discount?
A discount is a reduction in the regular selling price of a good or service, either in terms of money or as a percentage.
To estimate the sale price of a vest, we can round the original price of $42 to a convenient value, such as $40.
The amount of the discount can be calculated as 25% of the rounded price -
Discount = 0.25 x $40 = $10
Subtracting the discount from the rounded price gives us the sale price -
Sale price = $40 - $10 = $30
Therefore, the estimated sale price of a vest is $30.
25% of $40 = 0.25 x $40 = $10
Subtracting the discount of $10 from the rounded price of $40 gives us the sale price -
Sale price = $40 - $10 = $30
Therefore, the estimated sale price of a vest is $30.
The discount percent is 25%.
This is the percentage by which the original price is reduced to obtain the sale price.
Since the sale price is 75% of the original price, the discount is 25% of the original price.
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If triangle has a side 16.5 side 29 and side x What is value of x
Answers
The third side of the triangle 12.5
A triangle is a polygon with three edges and three vertices. The important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.
we the measurements of given two sides of the triangle 16.5 and 29
In a triangle, the sum of any two sides should be greater than the third side and the difference between any two sides should be lesser than that of the third side.
The sum of two sides rule
\(x + 16.5 > 29\\ x > 29 - 16.5\\ x > 12.5\\\)
The difference between the two sides rule
\(29 - 16.5 < x \\ 12.5 < x\)
Therefore, the value of x is 12.5
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The six digit number 4abcd6 is the square of an integer where a, b, c, and d each represent a different missing digit. Find the six digit number and its square root.
Answers
A six-digit number is a number whose number of digits is 6
The six-digit number is 401956, and the square root of the six-digit number is 634
How to determine the six-digit numberThe number is given as:
4abcd6
Since the number ends with 6, it means that:
The square root of the number ends with 6 or 4
Also, the square root of the six-digit number is a three-digit number
Using trial by error, the six-digit number is 401956
The square root of 401956 is 634
Hence, the six-digit number is 401956, and its square root is 634
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if the maker of the promissory note fails to pay the note on the due date,the note is said to be
Answers
Answer:
When the maker of a promissory note fails to pay, the note is said to be dishonored.
Step-by-step explanation:
What is the coefficient in the term K ?
Worth 30 points !!!
Answers
Answer:
1
Step-by-step explanation:
There is only one K listed, meaning the coeffiecent would have to be 1.
If it was 30, you would see 30K
if it was zero, it wouldn't be there.
Alice wants to use the stack method to pay down her debts listed in the table below. If she applies an extra $150 a month to her debts, what will be the first debt she targets to pay off and what will be the monthly amount she applies to it?
Debts Interest Rate Minimum Monthly Payment
Debt 1 5.5% $75
Debt 2 2.75% $250
Debt 3 13.25% $150
Alice wants to use the stack method to pay down her debts listed in the table below. If she applies an extra $150 a month to her debts, what will be the first debt she targets to pay off and what will be the monthly amount she applies to it?
Debts Interest Rate Minimum Monthly Payment
Debt 1 5.5% $75
Debt 2 2.75% $250
Debt 3 13.25% $150
Answers
The first debt that Alice would have to pay based on the Stack method would be the third debt. Option C
How to calculate the debt using the stack methodFrom the stack method, the debt that Alice would have to pay off first would be the debt that has the highest interest rate.
The amount of 150 dollars would then be added to the debt that has the second highest rate.
Hence the amount of debt that would be paid off first would be the first debt based on the stack method.
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Write the equation of the line that has slope 3 and passes through the point
(-2,5).
Answers
y=mx +c
where m is the slope, c is a constant, and x and y are variables,
we know the slope is 3 so m=3
rewriting it
y=3x +c
to find c we substitute values x=-2 and y=3 into the equation y=3x +c
so
3= 3(-2) + c
c=9
thus, y=3x+ 9
Explanation:
y = kx+m is the equation of a line. The coefficient of x is the slope i.e 3. So we know that a part of the equation is y = 3x + m.
How to find M?
Well, we already have a point on the equation. Meaning we already have an x and a y. -2 = x and 5 = y.
The equation then becomes 5 = (3 x -2) + m.
Solve for m and the answer will be m = 11.
Now we have both m and K meaning that the whole equation is solved and it’s y = 3x + 11
What is the square root of -1?
-i
i
-1
1
Answers
Answer:
the square root of -1 is i
Step-by-step explanation:
Well, actually, the square root of -1 (or any negative number at that) is not a real number. What I mean by that is that there is no way to square a real number to get a negative number (ie \(2^{2} = 4, -2^{2} =4\), there is no way to square a real number to get -4).
To solve this, mathematicians came up with the "imaginary number" i which, when squared, equals to -1. This allows us to get the square root of negative numbers (\(\sqrt{-4} = 2i\)) or get negative numbers through squaring (\(2i^{2} = -4\)).
The required value of the square root of -1 is i. The correct answer is option B.
As we know that complex number is made up of real and imaginary values. It is represented by the equation z = a + ib, where a, b, and i are real values and i is an imaginary number.
The square root of -1 is denoted as "i" in mathematics, where "i" represents the imaginary unit.
The imaginary unit is defined as the square root of -1. It is important to note that the square root of a negative number is not a real number, but an imaginary number.
⇒ √(-1)
⇒ √(i²)
⇒ i
So, the correct answer is "i."
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The Haddads expected the automatic withdrawal of their gas bill to
be more than last month's bill of $215.85, but did not know by how much. Their
account showed a previous balance of $417.80, $350.00 in deposited checks,
an automatic deposit of $150.00, and $5.25 in interest. If the Haddads' present
balance is $555.82, by how much did this month's gas bill exceed last month's bill?
Answers
The gas bill exceeded $87 from last month to this month.
What is simple interest?We know simple interest (SI) is given by SI = (p×r×t)/100, where
p = principle, r = rate in percentage, and t = time in years.
Given, The Haddad expected the automatic withdrawal of their gas bill to
be more than last month's bill of $215.85 but did not know by how much.
Their account showed a previous balance of $417.80, $350.00 in deposited checks, and an automatic deposit of $150.00.
∴ Their current balance is (417.80 + 250 + 150) = $817.8 and $5.25 in interest which is (105/100)×$817.7 = $858.69.
Haddads' present balance is $555.82,
∴ The gas bill is $(858.69 - 555.82) = $302.87.
So the gas bill s exceeded by $(302.87 - 215.85) = $87.
learn more about simple interests here :
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