Eric borrowed $3300 from the first loan and $3000 - $3300 = $-300 from the second loan (which is not possible). This means that the solution is not valid and Eric may have made a mistake in calculating the interest.
What do you mean by interest?Interest is a fee charged by a lender to a borrower for the use of money. It represents the cost of borrowing money and is typically expressed as a percentage of the loan amount. Interest is paid over a period of time and is calculated based on the principal amount of the loan, the interest rate, and the length of the loan term.
There are two main types of interest: simple interest and compound interest. Simple interest is calculated only on the principal amount of the loan, while compound interest is calculated on both the principal and the accumulated interest over time. Compound interest results in a faster growth of the loan balance compared to simple interest.
Let's call the amount Eric borrowed from the first loan "A" and the amount he borrowed from the second loan "B". We can set up two equations to represent the simple interest he owed on each loan after 2 years:
A * 0.03 * 2 = interest owed on loan 1
B * 0.025 * 2 = interest owed on loan 2
The total interest owed on both loans after 2 years is $165:
A * 0.03 * 2 + B * 0.025 * 2 = 165
We also know that Eric borrowed a total of $3000:
A + B = 3000
We can substitute the second equation into the first to get an equation in terms of one variable:
A * 0.03 * 2 + (3000 - A) * 0.025 * 2 = 165
Expanding and simplifying the right side:
A * 0.03 * 2 + 3000 * 0.025 * 2 - A * 0.025 * 2 = 165
A * 0.03 * 2 - A * 0.025 * 2 = 165 - 3000 * 0.025 * 2
A * (0.03 - 0.025) = 165 - 3000 * 0.025 * 2
A * 0.005 = 165 - 3000 * 0.025 * 2
A = 165 / 0.005 + 3000 * 0.025 * 2 / 0.005
Solving for A:
A = 3300
So, Eric borrowed $3300 from the first loan and $3000 - $3300 = $-300 from the second loan (which is not possible). This means that the solution is not valid and Eric may have made a mistake in calculating the interest or the amounts borrowed.
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Quinn is baking sweet potato pies. The table shows the ratio of cups of sugar to number of pies.
Number of Pies 3 5 9
Cups of Sugar 1 and one half 2 and one half 4 and one half
How many cups of sugar will Quinn need to make 16 pies? (359 is spaced because its part of the chart along with 1 1/2, 2 1/2,4 1/2
The number of cups of sugar will Quinn need to make 16 pies is 8 cups
How to solve ratio?Number of Pies 3 5 9
Cups of Sugar 1 1/2 2 1/2 4 1/2
Number of cups of sugar Quinn will need to make 16 pies = x
Number of pies : cups of sugar
3 : 1 ½ = 16 : x
3 ÷ 3/2 = 16/x
3 × 2/3 = 16/x
6/3 = 16/x
cross product
6 × x = 16 × 3
6x = 48
divide both sides by 6
x = 48/6
x = 8 cups of sugar
Therefore, Quinn will need 8 cups of sugar to make 16 pies
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Approximately what distance had the rock fallen at 3.5 seconds? A)120 ft B) 150 ft C) 170 ft D) 200 ft
Approximately C) 170 ft distance had the rock fallen at 3.5 seconds.
What distance had the rock fallen at 3.5 seconds?At 3.5 seconds, the rock would have fallen approximately 150 feet.This is calculated using the formula S = 1/2at^2, where S is the distance, a is the acceleration due to gravity (in this case, 32 ft/s^2), and t is the time.Plugging in the numbers, we get S = 1/2(32 ft/s^2)(3.5 s)^2 = 150.625 ft. The answer is rounded to 150 ft. To understand this formula and why it works, it's helpful to look at it another way.Acceleration due to gravity is a constant, so the rock is continuously accelerating as it falls. This means that the distance it has fallen increases exponentially with the amount of time it has been falling.This is why, after 3.5 seconds, the rock has fallen further than it did after 2.5 seconds. The formula S = 1/2at^2 is a mathematical representation of this relationship.To learn more about to find the distance refer to:
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can someone help me with number #5?
....................
I will give brainliest for answer
The value of the angle x in the parallel lines is 20.
How to find the angles in parallel lines?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, linear angles, vertically opposite angles, same interior angles, same exterior angles etc.
Therefore, a and b are the parallel lines. The parallel lines are cut by a transversal.
Same-side exterior angles are supplementary.
Hence,
5x + 10 + 4x - 10 = 180
5x + 4x = 180
9x = 180
divide both sides by 9
x = 180 / 9
x = 20
Therefore,
x = 20
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Fine Ab
Find m
Please help this is due soon
Answer:
Step-by-step explanation:
Since triangle ABC is an equilateral triangle, all sides have the same length.
So BC = AB = CA
BC=AB, so AB=4
I don't know what you mean by Mf,
Angle F equals 40 degrees since DEF is an isosceles triangle.
a baseball manager bought 4 bats and 9 balls for $216. on another day, he bought 3 bats and 12 balls at the same privces and paid $183. how mnuch did he pay for 4each bat and each ball.
part a: define the variables
part b: write a system of equations to represent the situation
part c: solve the system to find how many of each type of guitar were sold
The baseball manager bought each bat for $45 and each ball for $4
What is an equation?An equation shows the relationship between numbers and variables in an expression.
Let x represent the cost of each bat and y represent the cost of each ball.
The manager bought 4 bats and 9 balls for $216, hence:
4x + 9y = 216 (1)
he bought 3 bats and 12 balls and paid $183, hence:
3x + 12y = 183 (2)
From both equations, solving the equations simultaneously:
x = 45, y = 4
The solution is (45, 4)
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Jerimiah and Darren both collect baseball cards. Jerimiah starts with 11 cards and collects 3 cards each week. Darren starts with 5 cards and collects 4 each week. Which system of equations can be used to determine the number of weeks it will take for Jerimiah and Darren to collect the same number of cards?
a. y = 3x + 11 and y = 4x + 5
b. y = 11x + 3 and y = 5x + 4
c. y = 3x + 5 and y = 4x + 11
d. y = 3x + 4x and y = 11 + 5
The system of equations that can be used to determine the number of weeks it will take for Jerimiah and Darren to collect the same number of cards is option A: y = 3x + 11 and y = 4x + 5.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
The number of baseball cards Jerimiah collected = 11
The number of baseball cards Darren collected = 5
The number of baseball cards Jerimiah collected every week = 3
The number of baseball cards Darren collected every week = 4
Let the value of number of weeks be x.
The number of cards collected by Jerimiah and Darren is y.
So, the equation for Jerimiah will be -
Number of cards = 3 (number of cards) + 11
Similarly, the equation for Darren will be -
Number of cards = 4 (number of cards) + 5
So, the two equations are -
y = 3x + 11
y = 4x + 5
Now, if the number of week is 6, substitute x = 6 in both the equations -
y = 3(6) + 11
y = 18 + 11
y = 29
y = 4(6) + 5
y = 24 + 5
y = 29
Therefore, it will take 6 weeks for Jerimiah and Darren to collect same number of cards.
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Question 10 of 10
At how many points does the graph of the function below intersect the x-
axis?
y = 3x²-8x+8
Ο Α. 0
OB. 2
C. 1
SUBMIT
A graph of a function intersects the x-axis at the point (x,0).
If the equation has no real-number solutions, what is the discriminant?
A positive discriminant suggests that there are two unique real number solutions to the quadratic. When the discriminant is 0, the quadratic has a repeating real number solution. A negative discriminant means that neither solution is a real number.
Because the discriminant is smaller than zero, the equation has no valid solutions.A is the correct answer. The function’s graph does not cross the x-axis at all. If the discriminant is larger than zero, the equation has two separate and real roots. The equation will have a real root if the discriminant is zero. If the discriminant is smaller than zero, the equation has no real roots and only two complex roots.
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a recipe for fruit smoothies states that 3/4 of the total amount of ingredients should be fruit. The amount of yogurt in the recipe should be 1/4 of the amount of the fruit. What fraction of the total amount of ingredients is neither fruit nor yogurt?
The fraction of the total amount of ingredients that is neither fruit nor yogurt is 0.
What is the fraction?A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
The total fraction of all the ingredients are given as follows:
100% = 1.
The ingredients, along with their fractions, are given as follows:
Fruits: 2/3.
Yogurt: half of fruit = 2/3 x 1/2 = 2/6 = 1/3.
So the percentage contained fruit or yogurt is given as follows:
2/3 + 1/3 = 3/3 = 1 = 100%.
There are only two components in the recipe, fruit, and yogurt, so the amount of ingredients that is neither fruit nor yogurt is 0.
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find the value of each variable in the parallelogram.
Answer: A=7, B=42
Step-by-step explanation:
Finding a: 5a-9=3a+5 (Because opposite sides are equal)
2a = 14
a = 7
Finding b: 3b = b+84 (Because opposite angles in a parallelogram are equal)
2b = 84
b = 42
The diameter of a cone's circular base measures 8 inches, and the slant height of the cone is 6 inches.
What is the approximate surface area of the cone?
125.6 in²
204.1 in²
263.8. in²
351.7 in²
The surface area of the cone with a diameter 8in and slant height 6in is 125.6 in²
What is the surface area of the cone?A cone is simply a 3-dimensional geometric shape with a flat base and a curved surface pointed towards the top.
The surface area of a cone is expressed as;
A = πrl + πr²
Where r is radius and l is slant height.
Diameter d = 8 inRadius = d/2 = 8/2 = 4inSlant height l = 6 inSurface area A = ?Plug the given values into the equation above.
A = πrl + πr²
A = ( 3.14 × 4 × 6 ) + ( 3.14 × (4)² )
A = ( 3.14 × 4 × 6 ) + ( 3.14 × 16 )
A = 75.36 + 50.24
A = 125.6 in²
Therefore, the area is 125.6 in².
Option A) 125.6 in² is the correct answer.
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Answer: 125.6 in²
ik bc i did the k12 test
23 divided by 85.1 =???
Answer:
0.2703
Step-by-step explanation:
if you divide 23 into 85.1 you get 0.2703
or
Rewrite the following equation in slope-intercept form.
9x + 19y = 14
Write your answer using integers, proper fractions, and improper fractions in simplest form.
DUE SOON PLEASE HELP!!!
Answer:
8 km is equal to 800,000 cm
so 800,000/16,000 which is 50
Step-by-step explanation:
so the answer is 50 cm
Find x and y……………………………………….
The value of x = 4 and y = 9 in the given parallel lines.
What is parallel lines?Parallel lines refer to lines that are always the same distance apart in a plane.Parallel lines never cross.Perpendicular lines are the lines that cuts each other at right angles (90 degrees).In geometry, parallel lines can be defined as two lines that lie in the same plane, are equidistant from each other, and never intersect.They can be horizontal or vertical.Parallel lines can be seen in our daily life, such as pedestrian crossings, rows of notebooks, and railway tracks.Parallel lines run in pairs next to each other.Had they continued, they would never have met.Parallel lines are always at the same distance.3x - 4 = 5/4x + 3; x = 4
2/3y + 3 = 1/3y + 6 = 9
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the coffee shop with the speed of 27 m/s from the pizza store for 30 seconds. What will be the distance between the 2 store
Answer: 810
Step-by-step explanation: 27 times 30 is 810
Question 4(Multiple Choice Worth 1 points)
(05.02 MC)
City A and City B had two different temperatures on a particular day. On that day, four times the temperature of City A was 7° C more than three times the temperature of City B. The temperature of City A minus three times the temperature of City B was −5° C. The following system of equations models this scenario:
4x = 7 + 3y
x − 3y = −5
What was the temperature of City A and City B on that day?
City A was 1° C, and City B was −1° C.
City A was 4° C, and City B was 3° C.
City A was 10° C, and City B was 11° C.
City A was 13° C, and City B was 15° C.
The temperature of City A and City B on that day was 4°C and 3°C respectively.
The correct answer choice is option B
What was the temperature of City A and City B?Let
The temperature of City A = x
The temperature of City B = y
4x = 7 + 3y
x − 3y = −5
From equation (2)
x = -5 + 3y
Substitute into equation (1)
4x = 7 + 3y
4(-5 + 3y) = 7 + 3y
-20 + 12y = 7 + 3y
12y - 3y = 7 + 20
9y = 27
divide both sides by 9
y = 27/9
y = 3
Substitute into (1)
4x = 7 + 3y
4x = 7 + 3(3)
4x = 7 + 9
4x = 16
divide both sides by 4
x = 16/4
x = 4
Hence, City A was 4° C, and City B was 3° C on that day.
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NO LINKS!!! Explain your answer in each case using if-then statements.
Answer:
a) m∠? = 48°
If a transversal line intersects two parallel lines, then the resulting alternate interior angles are congruent.
b) m∠? = 71°
If a transversal line intersects two parallel lines, then the resulting corresponding angles are congruent.
c) m∠1 = 115°
If a transversal line intersects two parallel lines, then the resulting alternate exterior angles are congruent.
d) m∠2 = 62°
If a transversal line intersects two parallel lines, then the resulting same-side exterior angles are supplementary.
Step-by-step explanation:
Part aAlternate Interior Angles Theorem
If a transversal line intersects two parallel lines, then the angles that are interior to the parallel lines and on the opposite side of the transversal line are congruent.
If a transversal line intersects two parallel lines, then the resulting alternate interior angles are congruent.
[tex]\implies m\angle ?=48^{\circ}[/tex]
Part bCorresponding Angles Postulate
If a transversal line intersects two parallel lines, then the angles that are corresponding (in the matching corners) are supplementary.
If a transversal line intersects two parallel lines, then the resulting corresponding angles are congruent.
[tex]\implies m\angle ?=71^{\circ}[/tex]
Part cAlternate Exterior Angles Theorem
If a transversal line intersects two parallel lines, then the angles that are exterior to the parallel lines and on the opposite side of the transversal line are congruent.
If a transversal line intersects two parallel lines, then the resulting alternate exterior angles are congruent.
[tex]\implies m\angle 1=115^{\circ}[/tex]
Part dSame-side Interior Angles Theorem
If a transversal line intersects two parallel lines, then the angles that are interior to the parallel lines and on the same side of the transversal line are supplementary.
If a transversal line intersects two parallel lines, then the resulting same-side exterior angles are supplementary.
[tex]\implies m\angle 2+118^{\circ}=180^{\circ}[/tex]
[tex]\implies m\angle 2=62^{\circ}[/tex]
what is 3 ( 5x + 1 ) equal to
Answer:
15x+3
Step-by-step explanation:
distributive property
3*5x= 15x 3*1= 3
A line passes through the points (4, -1) and (2, 3). What is the slope of the line?
-2
2
miler
1/2
Step-by-step explanation:
slope of line= (y2-y1/x2-x1)
3-4/2-4
-1/-2 we eliminate -
we get 1/2
Find x!
Please help
Answer:
x=92
Step-by-step explanation:
a triangle is 180 degrees
the angle vertical to the 32 degree angle is also 32
so knowing all the information 180-32-60= 88, but remember that 88 is a supplementary angle to x, meaning the two angles add up to 180, so 180-88=92 degrees
Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
The correct roots [tex]8x^{2} + 16x + 3 =0[/tex] are -0.211 and -1.790
Step-by-step Solution:
Given: [tex]8x^{2} + 16x + 3 =0[/tex]
If the quadratic equation is in the form of [tex]ax^{2} +bx+c=0[/tex]
Then, the roots of a quadratic equation are given by the following formula:
[tex]\frac{-b \± \sqrt{b^{2} -4ac}}{2*a}[/tex]
where; a,b, and c are the coefficients of "[tex]x^{2}[/tex]"," [tex]x[/tex]" and "constant" terms respectively.
⇒[tex]8x^{2} + 16x + 3 =0[/tex]
⇒[tex]\frac{-16 \± \sqrt{(16)^{2} -4*8*3}}{2*8}[/tex]
⇒[tex]\frac{-16 \± \sqrt{256 -96}}{16}[/tex]
⇒[tex]\frac{-16 \± \sqrt{160}}{16}[/tex]
⇒[tex]\frac{-16 \± 12.649{}}{16}[/tex]
⇒[tex]\frac{-3.391}{16} \\ -0.211[/tex] and [tex]\frac{-28.649}{16} \\-1.790[/tex]
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a5=768 and a2=12; given two terms in a geometric sequence find the 8th term and the recursive formula. What is the answer?
Give that a5=768 and a2=12, given two terms in a geometric sequence find the 8th term and the recursive formula is ar⁷=6291456
What is geometric progression?A geometric progression is a type of sequence in which the terms are gotten by the multiplication of a constant term known as the constant ratio
The 5th term = ar⁴ = 768 ...............1
The 2nd term = ar² = 12 ....................2
Divide equation 1 by equation 2
= (ar⁴ = 768) ÷ (ar² = 12)
Eliminating a from both equations
r²= 64
taking the square root of both sides
r=√64
r=8
Put r= 8 in equation 2
a*r²=12
a*2² = 12
4a=12
Making a the subject of the relation
a= 3
The terms of the geometric progression are 3. 24, 192 ....
The 8th term of the sequence is
T8 = 3*8⁷
Therefore the eight term is = 6291459
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URGENT PLEASE HELP
f(x)=√x + 7. Find the inverse of f(x).
Answer:
To find the inverse, interchange the variables and solve for y.
option d is correct[tex]f {}^{ - 1} (x) = {x}^{3} - 7[/tex]
if EF bisects angle CEB, angle CEF=7x + 21 and angle FEB = 10x-3, find the measure of DEB.
The required measure of ∠DEB = 26° for the given figure.
What is an angle bisector?An angle bisector is defined as a line that divides an angle into two equal angles.
If EF bisects angle ∠CEB,
angle ∠CEF=7x + 21 and angle ∠FEB = 10x-3
As per the given figure, we can write the equation as:
7x + 21 = 10x - 3
Combine the likewise terms,
10x - 7x = 21 + 3
3x = 24
x = 24/3
x = 8
Substitute the value of x = 8 in the ∠CEF = 7x + 21
So ∠CEF = 7(8) + 21 = 77°
Substitute the value of x = 8 in the ∠FEB = 10x-3
So ∠FEB = 10(8)-3 = 77°
So ∠AEC = 180° - 77° - 77° = 26°
So ∠DEB = ∠AEC = 26°
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What’s the length of equal to 2x+15 determine the actual length
Multiply to find equivalent fractions
1/4 X / = /100
Answer:
25
Step-by-step explanation:
I hope I'm correct have a good day :)
Answer: X = 400
Step-by-step explanation: Combine multiplied terms into a single fraction
one-fourth x equals 100
1 x over 4 end fraction equals 100
2
Multiply by 1
1 x over 4 end fraction equals 100
x over 4 end fraction equals 100
3
Multiply all terms by the same value to eliminate fraction denominators
x over 4 end fraction equals 100
4 ⋅ x over 4 end fraction equals 4 ⋅ 100
4
Cancel multiplied terms that are in the denominator
4 ⋅ x over 4 end fraction equals 4 ⋅ 100
x equals 4 ⋅ 100
5
Multiply the numbers
x equals 4 ⋅ 100
Decide whether each equation is true for all, one, or no values of x. Select the button for the true statement. (ignore what i selected already) please help.
The value of x, b) for a single x value, true All x values in which
a) is true
c) True for no x values
Find the value of x?b) for a single x value, true
All x values in which a) is true
c) True for no x values
2x + 8 = -3.5x + 19
All x values in which a) is true
b) for a single x value, true
c) True for no x values
9(x - 2) = 7x + 5
All x values in which a) is true
b) for a single x value, true
c) True for no x values
3(3x + 2) - 2x = 7x + 6
All x values in which a) is true
b) for a single x value, true
c) True for no x values.
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The complete question is,
Analyze each equation to determine whether it holds true for all, one, or no x values.
2x + 8 = -3.5x + 19
a) true for all x values b) true for one x value c) true for no x values 9(x - 2) = 7x + 5 a) true for all x values b) true for one x value c) true for no x values 3(3x + 2) - 2x = 7x + 6 a) true for all x values b) true for one x value
c) True for no x values.
What is the radiua of a globe that has a volume of 113.10in³
The radius of the globe with a volume of 113.10 in³ is calculated to be
1.5 in
What is a globe?A globe is a spherical representation of the Earth, another heavenly body, or the celestial sphere. Globes have comparable functions as maps.
The globe has same shape as the sphere and hence we can use the formula fo volume of sphere to solve for a globe
The volume of sphere is solved using the formula/
v = 4/3 π r³
where
r is the radius of the sphere or globe
113.10 in³ = 4/3 π r³
π r³ = 3/4 * 113.10
π r³ = 9.825
r³ = 9.825 / π
r³ = 3.12739
r = ∛3.12739
r = 1.462 in
the radius of the globe is 1.5
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Solve the equation 25x^2 - 30x+9=0 by using the quadratic formula.
The quadratic formula is used to solve a quadratic equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.
Given an equation 25x^2 - 30x + 9 = 0, we can solve it using the quadratic formula as follows:
The quadratic formula is : x = (-b ± √(b^2 - 4ac)) / 2a
The values of a,b,c are:
a = 25, b = -30, c = 9
Now, we can substitute the values in the quadratic formula:
x = (-(-30) ± √((-30)^2 - 4(25)(9)))/2(25)
x = (30 ± √(900 - 900)) / 50
x = (30 ± √(0)) / 50
x = (30 ± 0) / 50
x = 30/50
x = 3/5 or x = -3/5
So the solutions of the equation 25x^2 - 30x + 9 = 0 are 3/5 and -3/5.