Answer:
Step-by-step explanation:
(100xInterest)(RatexTime)
hope this helps
Step-by-step explanation:
The formula for calculating Principal amount would be P = 100I / (RT) where Interest is Interest Amount, R is Rate of Interest and T is Time Period.
The coordinates of 3 of the vertices of a parallelogram are (-3, 4), (-2, 1), and (2, 6). What is the equation for the
line containing the side opposite the side containing the first two vertices? (Remember, opposite sides of a
parallelogram are parallel.)
The equation for the side of the line that contains the first two vertices' opposite side is 3x+y=12
Given that,
Three of a parallelogram's vertices have the coordinates (-3, 4), (-2, 1), and (2, 6).
We have to find what is the equation for the side of the line that contains the first two vertices' opposite side.
We know that,
The equation of the line is
y=mx+b
Here, we find m and d
Take the points (-3,4) (-2,1)
m = y₂-y₁ / x₂-x₁
m = 1 - 4 / -2-(-3)
m = -3 / 1
m = -3
Now take point (2,6)
6 = -3(2) + b
6 = -6 + b
6 + 6 = b
12 = b
We get m =-3 and b=12
The equation will be y=-3x+12
3x+y=12
Therefore, the equation for the side of the line that contains the first two vertices' opposite side is 3x+y=12
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Naomi'sbillforlunchatarestaurantwas$46.Sheleftan18%tip.Whatwastheamountofthetip?
Answer:
$8.28
Step-by-step explanation:
0.18*46=8.28
What is the rule for an acute triangle?
Answer:
it must be less than 90 degrees
Jason and Marie both travel 300 miles. Jason drove at an average speed of 10 miles per hour faster than Marie and made the trip in one hour less time. Find the average speeds of both cars.
Answer:
jason: 60mph
marie: 50mph
Step-by-step explanation:
let jason drive at x miles per hour
let marie drive at x-10 miles per hour
let jason drive for y hours
let marie drive for y+1 hours
distance = speed * time
for jason:
300 = x * y
for marie:
300 = (x-10) * (y+1) = x*y + x - 10y -10
300 = x*y
divide both sides by x to solve for y
300/x = y
plug this into the second equation
300 = (x-10) * (300/x+1) = 300 -3000/x +x -10
300 = 300 -3000/x +x -10
subtract 300 from both sides
0 = -3000/x + x - 10
multiply both sides by x to get rid of the denominator
0 = x^2 -10x -3000
factor
0 = x^2 - 60x +50x -3000
0 = x(x-60) + 50(x-60) = (x+50)(x-60)
x = 60 or -50
x cannot be negative so x = 60mph
marie = 60-10 = 50mph
The length of a rectangle is 3cm longer than its width.
If the perimeter of the rectangle is 58 cm, find its length and width.
The length and width of the rectangle will be 16 centimeters and 13 centimeters, respectively.
What is the perimeter of the rectangle?Let W be the rectangle's width and L its length.
The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be
Perimeter of the rectangle = 2(L + W) units
The length of a rectangle is 3cm longer than its width. If the perimeter of the rectangle is 58 cm. Then the equations are given below.
L = 3 + W ...1
2(L + W) = 58
L + W = 29 ...2
From equations 1 and 2, then we have
3 + W + W = 29
2W = 26
W = 13 cm
Then the length of the rectangle will be given as,
L = 3 + 13
L = 16 cm
The length and width of the rectangle will be 16 centimeters and 13 centimeters, respectively.
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HELP ASAP PLEASE!! The table shows the numbers of cars manufactured in thousands by a company for selected years. Use a calculator to write a quartic model for the number of cars manufactured in a given year since 2000. Then use the model to estimate the number of cars manufactured in 2007
In algebra, a symbol is used to denote an unknown numerical value in an equation or algebraic expression.
What is meant by variables?A variable in mathematics is a letter that is substituted for an unknown integer in equations, expressions, and formulas.
An unknown numerical value in an equation or algebraic expression is represented by a symbol (often a letter) in algebra. A variable is, to put it simply, a quantity that may be altered and is not fixed.
The two primary categories of variables are categorical and numeric. Then, for categorical and numerical variables, respectively, nominal or ordinal and discrete or continuous subcategories are created for each category. This section provides a quick overview of these types.
A.) (x) ≈ 0.572[tex]$$x^4[/tex] − 15.63x³ + 146.273x² − 523.325x + 687.334
Approximately 203 automobiles were produced in 2007, according to estimates.
B.) f(x) ≈ 0.423x³ − 12.463x2 + 123.485x − 223.309
Approximately 178 automobiles were produced in 2007, according to estimates.
C.) f(x) ≈ 0.572[tex]$$x^4[/tex] + 15.63x³ − 146.273x² − 523.325x + 687.334
Approximately 203 automobiles were produced in 2007, according to estimates.
D.) f(x) ≈ 0.423x³ + 12.463x² − 123.485x + 223.309
Approximately 178 automobiles were produced in 2007, according to estimates.
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Number of cars manufactured in 2007 will be equal to 178 or 203 based on quartic model.
What is meant by variables?A variable in mathematics is a letter that is substituted for an unknown integer in equations, expressions, and formulas.
An unknown numerical value in an equation or algebraic expression is represented by a symbol (often a letter) in algebra. A variable is, to put it simply, a quantity that may be altered and is not fixed.
The two primary categories of variables are categorical and numeric. Then, for categorical and numerical variables, respectively, nominal or ordinal and discrete or continuous subcategories are created for each category. This section provides a quick overview of these types.
A.) (x) ≈ 0.572 − 15.63x³ + 146.273x² − 523.325x + 687.334
Approximately 203 automobiles were produced in 2007, according to estimates.
B.) f(x) ≈ 0.423x³ − 12.463x2 + 123.485x − 223.309
Approximately 178 automobiles were produced in 2007, according to estimates.
C.) f(x) ≈ 0.572 + 15.63x³ − 146.273x² − 523.325x + 687.334
Approximately 203 automobiles were produced in 2007, according to estimates.
D.) f(x) ≈ 0.423x³ + 12.463x² − 123.485x + 223.309
Approximately 178 automobiles were produced in 2007, according to estimates.
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Solve the following system of equations algebraically:
y = x² - 15x + 60
y=x-3
Since the square root of a negative number does not exist in the real numbers, there are no real solutions for x. Therefore, the system of equations has no solutions.
Define Algebric expression.An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.
What is variables and constants ?A constant has a fixed value and does not vary over time. For instance, the size of a shoe, a piece of clothing, or any other article of clothing will never alter. x+y = 8 is an algebraic equation, and 8 is a constant that cannot be altered. Variables are concepts that change or fluctuate throughout time.
To solve this system of equations algebraically, we can substitute y = x-3 into the first equation
y = x² - 15x + 60
x-3 = x² - 15x + 60
x² - 16x + 63 = 0
We know that this quadratic equation has no real solutions because its discriminant (b^2 - 4ac) is negative, so the system of equations has no real solutions.
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PLEASE HELP PICTURE ATTACHED
Given the diagram below, which statement is true?
A. /1 and /2 are vertical angles and supplementary.
B. /2 and /3 are complementary angles and congruent.
C. /1 and /3 are vertical angles and congruent.
D. /2 and /4 are supplementary angles and congruent.
Therefore , the solution of the given question of triangle comes out to be the only true option is A.
Triangle definitionAny three points in a plane can be connected to create triangles, which have three sides and three angles. They were one of the very first geometric shapes to be studied. They are particularly important because any polygon, whether it has four, five, six, or n sides, may be split into a triangle.
Here,
Because angles 1 and 2 are close to one another, they are neighboring angles.
A They share a side and are near to each other, making them neighboring angles.
B. The angles are complimentary (add to 90 degrees) False—Angle 2 has a 90 degree angle.
C. They are additional angles. (add to 180) They do not create a straight line, which is untrue.
D. Vertical angles describe them. (Contrary angles) False, they are not created through the intersection of lines.
Therefore , the solution of the given question of triangle comes out to be the only true option is A.
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Is an isosceles triangle always 60 degrees?
No, an isosceles triangle is not always 60 degrees. The angles of an isosceles triangle must be equal, but the overall measure of the angles can be any value greater than 0 degrees.
A triangle having two equal sides and two equal angles is known as an isosceles triangle.. The equal sides create two equal angles that are opposite each other. The two equal angles are the only two angles that define an isosceles triangle. There is no specific measure for the angles of an isosceles triangle, so the angles do not necessarily have to be 60 degrees and The angles can be any value greater than 0 degrees. The two equal angles, however, must be equal in measure to make the triangle an isosceles triangle. Therefore, an isosceles triangle is not always 60 degrees.
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Use the number line to find the difference of 4 1/2-8
Using the number line, the difference between 4 1/2 and 8 will come to -31/2.
What is a number line?A number line is a depiction of a graded straight line that serves as a visual representation of real numbers in primary mathematics. Every point on a number line is presumed to be a real number, and every real number is assumed to be a point.
Subtraction on a number line makes it much easier to subtract smaller values. When subtracting numbers from a number line, we must leap (move) to the left side of the number line.
Thus, moving to the left, 8 times from 4.5 will help us arrive at -3.5. See attached Number line.
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Q 9-1 Pythagorean Theorem and Trig
A girl is 20 ft. east of her school and her bike is 21 ft. south of the school. How far is she from her bike? Round to the nearest hundredth.
Answer: 29 ft
Step-by-step explanation:
Based on the description we are given. we know that we can form a right triangle, where 20 and 21 are the legs. The length from the girl to the bike would be the hypotenuse. To do this, we need to use the Pythagorean Theorem, which is [tex]a^2+b^2=c^2[/tex], where a and b are legs, and c is hypotenuse. We can go ahead and plug them in.
[tex]20^2+21^2=c^2[/tex] [exponent]
[tex]400+441=c^2[/tex] [add]
[tex]841=c^2[/tex] [square root both sides]
[tex]c=29[/tex]
Therefore, the distance from the girl to the bike is 29 ft.
What are the 5 operations of functions?
The 5 operations of functions are
1. Input
2. Processing
3. Output
4. Storage
5. Maintenance
Input: When a function is used, it takes in an input value. This input value is used to compute the output. For example, if a function is used to calculate the area of a circle, the input would be the radius of the circle.
Processing: Once the input value is taken, the function will use the input to perform some type of operation on it. For example, if the function is used to calculate the area of a circle, the operation would be to multiply the input by itself and then multiply it by the constant pi.
Output: The output of a function is based on the input. For example, if the function is used to calculate the area of a circle, the output would be the area of the circle.
Storage: Once the output of a function is computed, it can be stored for later use. This allows the same output to be used multiple times without having to recalculate the output.
Maintenance: Functions need to be maintained and updated over time. This can include updating the input, operation, and output, as well as any additional changes that might be needed. This ensures the function is up-to-date and still provides accurate results.
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Help please,I’ll give 20points (if I can)
On solving the provided question, we can say that - here in the given equation we got x- 1 = 0; x = 1, y = 2
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
y = 2x +1
y = 3x - 1
x- 1 = 0
x = 1, y = 2
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How do you find area?
Answer:
You do length time width
A balloon ascending at a rate of 12 ft/s is at a height of 80 ft above the ground when a package is dropped. How long does it take the package to reach the ground
The time taken by the package to reach the ground will be 5.45 seconds.
What governs motion, according to Newton?The motion of an object is related to the forces acting on it by Newton's laws of motion. According to the first law, unless a force acts on an object, it will not alter its motion. According to the second law, an object's force is determined by multiplying its mass by its acceleration. According to the third law, when two objects interact, they exert equal-sized and opposite-direction forces upon one another.
Solution:-
vo=12m/s
h=80m=yo
Then,
[tex]y-yo= vot-1/2gt^2[/tex]
⇒[tex]0-80m=(12m/s)t - 1/2(9.8m/s^2)t^2[/tex]
⇒[tex](4.9m/s^2)t^2-(12m/s)t-80m=0[/tex]
⇒[tex](4.9m/s^2)t^2-(12m/s)t-80m=0[/tex]
⇒[tex]t=5.45s, t=-3.00s[/tex]
∴[tex]t=5.45s[/tex]
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PLEASE HELP f(x)=x^2-12x+35 g(x)=x−5, find(f⋅g)(x)
Step-by-step explanation:
this is a multiplication dot, right ?
so,
(f.g)(x)
or
(f×g)(x)
any arithmetic operation (like +, -, ×, ÷) between 2 functions is done by applying that operation to the functional expressions.
(f×g)(x) = (x² - 12x + 35)(x - 5) =
= x³ - 5x² - 12x² + 60x + 35x -175 =
= x³ - 17x² + 95x - 175
Step-by-step explanation:
(f.g)(x) = f(x) . g(x)
= (x² - 12x + 35)(x - 5)
=x(x²-12x+35) - 5(x²-12x+35)
= x³-12x²+35x-5x²+60x-175
(f.g)(x)=x³-17x²+95x-175
A retail store sold a case of candles for $17.85 that had been marked up 110%. What was the original price of the table
The original price of the case of candles before markup was $8.50.
Markup price is the price that comes after setting up additional layer of pricing on the original price of a good. In this case also markup price is there. To find the original price of the case of candles before markup, we can use the following formula:
Original price = Marked up price / (1 + markup percentage)
In this case, the original price would be:
$17.85 / (1 + 110%) = $17.85 / 2.10 = $8.50
So the original price of the case of candles before markup was $8.50.
Thus, Original price is $8.5
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Mrs. Campos is making cupcakes for a bake sale. She uses the equation c = 0. 55x to determine the cost, c, for x cupcakes. Which best represents the constant rate at which cupcakes are sold at the bake sale?
55 cupcakes per dollar
$0. 55 per cupcake
$4 per cupcake
4 cupcakes per dollar
Best represents the constant rate at which cupcakes are sold at the bake sale $0. 55 per cupcake
Mrs. Campos is making cupcakes for a bake sale. She uses the equation c = 0. 55x to determine the cost, c, for x cupcakes. Which best represents the constant rate at which cupcakes are sold at the bake sale?
55 cupcakes per dollar
$0. 55 per cupcake
$4 per cupcake
c = 0. 55x
to determine the cost, c,
for x cupcakes.
CASE 1
55 cupcakes per dollar
therefor x = 55
c = 0. 55x
c = 0. 55 × 55
= 30.25
case2
$0. 55 per cupcake
x = 1
c = 0. 55x
c = 0. 55 × 1
= 0. 55
case 3
$4 per cupcake
x = 1
c = 0. 55x
c = 0. 55 × 1
= 0. 55
therefor conclusion is best represents the constant rate at which cupcakes are sold at the bake sale $0. 55 per cupcake
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Dange measures and finds that she can do a vertical jump that is27.5 % her height f dange can jump 13.2 inches how tall is she
The height of Dange who can jump 27.5% of her height is 10.4 inches.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, Dange measures and finds that she can do a vertical jump that is 27.5 % of her height f and the distance of the jump is 13.2 inches.
Therefore. (100 + 27.5)% = 127.5% of f is 13.2 inches, This can be numerically expressed as,
(127.5/100)×f = 13.2.
1.275f = 13.2.
f = 13.2/1.27.
f = 10.4 feet.
So, The height of Dange is 10.4 inches.
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Jonathan opened an auto repair shop. In the first month, 11 cars were serviced at his shop. After the first month, the total number of cars serviced at Jonathan's shop increased by 9 cars per month.
How many total cars were serviced at Jonathan's shop at the end of the 7th month?
Answer:
65 cars
Step-by-step explanation:
if x is a binomial random variable with n=10 and p=0.8, the mean value of x is _____.
Answer:
8
Step-by-step explanation:
[tex]\bar{x}=np=10(0.8)=8[/tex]
when processing an invoice what account is debited
a. cash
b. accounts payable
c. accounts receivable
d. the answer depends on the transaction
Answer:
D
Step-by-step explanation:
Because the account that gets debited depends on the specific transaction
a stadium is filled to 80% capacity. If 2,560 people are in the stadium, how many people would fill the stadium to its full capacity?
2048 people would fill the stadium to its full capacity
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that a stadium is filled to 80% capacity
There are 2,560 people are in the stadium
We need to find how many people would fill the stadium to its full capacity.
We have to convert 80% to decimal by dividing 2560 with 100
80/100
0.8
Now multiply 0.8 with 2560
0.8×2560
2048
Hence, 2048 people would fill the stadium to its full capacity
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The pairs of polygons below are similar. Give the scale factor of figure A to figure B.
3/5
2/5
25/18
5/2
5/3
18/25
In the given pairs of polygons the scale factor of figure A to figure B is 2:4.
How is scale factor calculated?The scale factor is calculated using the following fundamental formula: Scale factor = Dimension of the new shape Dimension of the old shape. The formula for calculating the scale factor is expressed as Scale factor = Larger figure dimensions Smaller figure dimensions in the event that the original figure is magnified.
The ratio of a smaller figure's side to its corresponding side in the bigger figure is the scale factor between the two figures.
As a result, the smaller figure's side length of 4 units and its side length of 10 units are equivalent.
Therefore:
Scale factor = 4:10
i.e. 2:5
Simplify
Scale of the smaller figure to the larger is equal to 2:4.
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Please help ASAP
Angie is working on solving the exponential equation 23x = 6; however, she is not quite sure where to start. Using complete sentences, describe to Angie how to solve this equation.
Hint: Use the change of base formula: log base b of y equals log y over log b.
Step-by-step explanation:
I'm assuming that its 23 to the power x since you said it is an exponential equation.
as for the hint there is no specific base specified so I'll do the best I can with the answer.
Angie can begin solving by applying log to the base 23 on both sides. when this is done, Angie will be left with:
[tex] log_{23}( {23}^{x} ) = log_{23}(6) [/tex]
and as we know the power rule in logarithms allows us to remove the power within the expression.
hence, we'll get:
[tex]x log_{23}(23) = log_{23}(6) [/tex]
furthermore, if we have the same number and base within a logarithmic expression it will simply become 1 giving us the final answer:
[tex]x = log_{23}(6) [/tex]
if the question that I've answered is different to yours please let me know and I'll make sure to fix it.
hope this helps :)
2x+5=2x+6
equations please help
8th grade math
Answer:
Step-by-step explanation:
What is the inverse of 9 by 7?
-9/7 is the inverse of 9/7.
-9/-7 = 9/7
9/7 + (-9/7) = 0
-9/7 is consequently the additive opposite of -9/-7.
By merely switching the integer's sign, you can add the original number and the additive inverse to produce a result equal to 0. The value that, when added to the original number, results in zero is known as a number's additive inverse. It is what we add to a number to make it equal to zero. Considering that an is the starting number, its additive inverse will be a minus one, or -a, such that;
a+(-a) = a – a = 0
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A plumber charges $80 for a house call and $20 per hour for labor. If the plumber worked from 2:30 pm to 8:00 pm, how much does he earn?
Answer:
The plumber would earn $190 in 5 hrs and 30 mins
Step-by-step explanation:
- We know the plumber worked from 2:30-8:00 which is 5 hrs and 30 min [5.5 hrs]
- We know the plumber charges the client $80 for the call and $20/hr for the work
1. I multiplied $20 x 5.5= $110+80=$190
or you could just do 100 x 5.5 [but it would it work since the plumber is charging per hour]
Have a great day, hope this helped <3
can someone please help ( check link for question )
Hence, The equation of the line is y=5x/3-3
What is the slope-intercept form of a line?The slope-intercept form of a line is represented by y=mx+c where m=slope and c is the y-intercept of the line
Given here: The line 3x+5y=15 , Rearranging in the slope intercept form we get y=-3x/5+3 and thus slope of the line that is perpendicular to this line must be equal to 5/3 and it passes through (3,2) then we get the equation of the line as y=5x/3+c and putting (3,2) in the equation we get the value of c as c=-3
∴ The equation of the line is y=5x/3-3
Hence, The equation of the line is y=5x/3-3
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HEEELLLLP MEEEEE PLEASEEEE
The positive value of the distance between the two objects
is [tex]r = +\sqrt \frac{GM_1M_2}{F_g}[/tex].
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given, The formula to calculate the gravitational force between two objects
is [tex]F_g = \frac{GM_1M_2}{r^2}[/tex] where r is the distance between the objects M is the individual masses and G is the gravitational constant.
Solving for r would result in two values one positive and one negative and distance can not be negative so we want the positive value.
[tex]F_g = \frac{GM_1M_2}{r^2}[/tex].
[tex]r^2 = \frac{GM_1M_2}{F_g}[/tex].
[tex]r = \pm\sqrt \frac{GM_1M_2}{F_g}[/tex].
[tex]r = +\sqrt \frac{GM_1M_2}{F_g}[/tex].
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