Answer:
$31
Step-by-step explanation:
x=cost before tax
$32.55 = x + x * 5% ==> solve for x
$32.55 = x + x * 5/100
$32.55 = x + 5x/100
$32.55 = 100x/100 + 5x/100 ==> make common denominators
$32.55 = (100x+5x)/100
$32.55 = 105x/100 ==> simplify
100 * $32.55 = 100 * 105x/100 ==> multiply by 100 on both sides to remove
fractions
$3255 = 105x
x = $3255/105
x = $31
prove that there are no solutions in integers x and y to the equation 2x2 + 5y2 = 14.
The quadratic equation does not have solutions where both x and y are integers.
How to prove that there are no integer solutions for the equation?Here we have the following quadratic equation:
2x^2 + 5y^2 = 14
We want to check that we can't solve this equation with x and y integers, to see that, we can start by isolating one of the variables:
2x^2 + 5y^2 = 14
5y^2 = 14 - 2x^2
y^2 = (14 - 2x^2)/5
y = ±√((14 - 2x^2)/5)
Now, trivially:
(14 - 2x^2)/5
Is not an integer for any integer value of x, and this happens because 5 is not a factor of 14, thus, for any integer value of x the value of y that we get is non integer, then there aren't two integers that solve the quadratic equation.
Learn more about quadratic equations by reading:
https://brainly.com/question/1214333
#SPJ1
y-b=m(x-a) i being try to do it but i cant
Explanation:
The equation y - b = m(x - a) is a mathematical formula that describes the relationship between the x and y coordinates of a point on a line. The equation is called "point-slope form" because it uses the coordinates of a point on the line (point a) and the slope of the line (m) to describe the line.
The equation has three parts: y, b, and m(x - a).
The y part of the equation represents the y-coordinate of a point on the line. This value can change depending on the x-coordinate of the point.
The b part of the equation is the y-coordinate of a known point on the line. This value is fixed and does not change.
The m(x - a) part of the equation represents the slope of the line and the x-coordinate of the known point on the line. The slope is represented by m, and the x-coordinate of the known point is represented by a.
To use the equation to find the y-coordinate of a point on the line, you first need to know the x-coordinate of the point and the values of b, m, and a. Then, you can substitute these values into the equation and solve for y.
For example, if the x-coordinate of a point on the line is 5, the y-coordinate of a known point on the line is 2, the slope of the line is 3, and the x-coordinate of the known point is 1, then the y-coordinate of the point can be calculated as follows:
y - 2 = 3(x - 1)
y = 3x - 3 + 2
y = 3(5) - 3 + 2
y = 15 - 3 + 2
y = 14
Therefore, the y-coordinate of the point with x-coordinate 5 is 14.
In summary, the equation y - b = m(x - a) is a mathematical formula that describes the relationship between the x and y coordinates of a point on a line. The equation uses the coordinates of a known point on the line and the slope of the line to describe the line, and you can use it to find the y-coordinate of a point on the line if you know the x-coordinate of the point and the values of b, m, and a.
A seed company planted a floral mosaic of a national flag. The perimeter of the flag is 2,200 ft Determine the flag's width and length if the length is 480 ft greater than the width.
The flag's width is ft. Its length is ft.
4
Answer:
the width of the flag is 310 ft and the length is 790 ft.
Step-by-step explanation:
Let "w" be the width of the flag and "l" be the length of the flag. We can set up the following equation to represent the problem:
2w + 2l = 2200
We know that the length of the flag is 480 ft greater than the width, so we can set up the following equation to represent this relationship:
l = w + 480
We can substitute the second equation into the first equation to solve for the width of the flag:
2w + 2(w + 480) = 2200
This simplifies to:
4w + 960 = 2200
Subtracting 960 from both sides gives us:
4w = 1240
Dividing both sides by 4 gives us:
w = 310
So the width of the flag is 310 ft.
We can use this value to find the length of the flag by substituting it into the equation l = w + 480:
l = 310 + 480
This simplifies to:
l = 790
So the length of the flag is 790 ft.
Therefore, the width of the flag is 310 ft and the length is 790 ft.
A quare that ha 21 ha a the perimeter. Find the ide length of the quare and the area of the quare. HELP PLEASE
Answer:
area = 27.5625, side length = 5.25
Step-by-step explanation:
21 is the perimeter of a square (given). We know a square has 4 equal sides, so 4s = p, where s is the side length and p is the perimeter of a square. Thus: 4s = 21 → s = 5.25
We also know that a square has a = s², where s is the side length and a is the area. Thus, a = 5.25² → a = 27.5625
What is the solution of the system of equations? {2x−7y=−154x−14y=30
The system of equations, 2x − 7y = −15 and 4x − 14y = 30, has no solution.
What is the Solution to the System of Equations?To find the solution to the system of equations, we can plot the line of the two equations on a graph, then find the coordinate of the point where both lines of the equations intersect each other.
Alternatively, we can solve simultaneously as shown below:
2x − 7y = −15 --> eqn. 1
4x − 14y = 30 --> eqn. 2
Rewrite eqn. 1:
2x − 7y = −15
-7y = -15 - 2x
y = 15/7 + 2/7*x
Substitute the value of y into eqn. 2:
4x − 14(15/7 + 2/7*x) = 30
4x - 30 - 4x = 30
0 - 30 = 30
0 - 30 + 30 = 30 + 30
0 = 60 [not true]
This means that the system has no solution. If we graph both lines, the two lines of the equations will not intersect each other at any point.
The graph below shows the graph of both lines of the system of equations, meaning that it has no solution.
Learn more about the solution to a system on:
https://brainly.com/question/13729904
#SPJ1
A land developer is splitting up 1.31 hectares of land to form 5 identical properties. What size will each property be?
Answer:
0.262 hectares
Step-by-step explanation:
To find the size of each property, you need to divide the total area of the land by the number of properties. In this case, the total area of the land is 1.31 hectares, and it is being divided into 5 properties, so the size of each property is:
Property size = 1.31 hectares / 5 properties = 0.262 hectares/property
Therefore, each property will be 0.262 hectares in size.
Find the distance between the two points rounding to the nearest tenth (if necessary).
(6,8) and (8,6)
100 points!!!! Please answer ALL 3
Part A
Consider the function f(x) = x3 − 4x2 + 2. Calculate the limit of the difference quotient at x0 = 3 for f(x).
Part B
Find the equation of a line passing through the same point that f(x) passes through at x = 3 with a slope equal to the limit you found in part A.
Part C
Graph the function f(x) and the line you identified in part B. How do the graphs relate to each other? What does the slope of the line represent about the function at the given point?
please answer ALL 3
Part A: Calculation of the limit at x = 3In order to find the limit of the function, we can factorize the numerator by factoring out (x-3). Limit [tex][tex](x 3)\frac{(x^3 - 27)}{ (x-3)} )[/tex]Now, factorize x³ - 27 to get the difference of cubes. The
limit equation becomes, Limit [tex](x 3) \frac{ (x-3)(x² + 3x + 9)]}{(x-3)}[/tex] Now, we can cancel out the term (x-3) from the numerator and denominator to get the limit equation as
Part B: Limit [tex](x 3) (x^2 + 3x + 9)[/tex]The limit of the function at x = 3 is the value of the function as x approaches 3. By plugging in x = 3 in the equation above, we get, Limit ([tex](x 3) (x^2 + 3x + 9) = (3)^2 + 3(3) + 9[/tex] = 27Part B: Equation of line through f(3) with slope = 27
The slope of the line is 27, and it passes through the point (3, f(3)). The equation of the line can be found using the point-slope form. [tex]y - f(3) = 27(x - 3)[/tex]
Part C: Simplifying the equation, we get,[tex]y = 27x - 78[/tex] Part C: Graphical representation of the line and the function
The graph of the function f(x) is a parabola opening upward with a vertex at (3, 0). The slope of the line is positive, which means the line will have a positive y-intercept.
The line will intersect the y-axis at (0, -78).Both the graph of the function and the line pass through the point (3, 0). The line is tangent to the graph of the function at that point.
The slope of the line represents the instantaneous rate of change of the function at the point (3, 0). It is the same as the limit we calculated in Part A.
For such more question on parabola
https://brainly.com/question/29635857
#SPJ8
Enter the letter for the function graphed
below.
3
√x - 3
a) y =
b) y = ³√√x - 3
c)y = 3 = ³√√x
3
d) y = ³√√x +3
e) y = √√x +3
a)
Step-by-step explanation:
we only need to look at the point, where y = 0.
that is clearly at x = 3.
which function gives y = 0 as result, when x = 3 ?
only a)
y =
[tex] \sqrt[3]{3 - 3} [/tex]
the cubic root of 0 is 0.
as 3 is not equal to the cubic root of 3, b), c) and e) are out.
and d) is
[tex]y = \sqrt[3]{3 + 3} [/tex]
the cubic root of 6 is NOT 0.
so, only a) is the only right answer.
if the end behavior is decreasing to the left and increasing to the right, which statement must be true about the function?
The correct statement is end behavior is decreasing to the left and increasing to the right, which statement must be true about the function is The order is odd and the leading coefficient is negative.
As x approaches infinity it is detected by its limit. On the left side, it is given by:
Rim x -> - ∞ f(x)On the right-hand side, it is given byRim x -> ∞ f(x)Since x tends to infinity, this is the limit, so we only consider the highest order term and its predecessors.So the described behavior is i. H. lim→→ = ∞, lim⭑→∞ =1∞ if:The order is odd and the leading coefficient is negative.For more information about borders, visit
https://brainly.com/question/220267
#SPJ4
answer the following questions
and get 20 points
Answer:
3/7 ; -7
Step-by-step explanation:
1)
(7-4)/(10-3)
3/7
2) -7 because is the number that multiplies x
Use m=−8, n=4, p=−12
4 ( 7mp + 3p ) + 4n
Answer: 2560
Step-by-step explanation:
m= -8
n=4
p= -12
4(7mp+3p)+4n= 4((7 x -8 x -12)) +4(4)= 2560
Sam went to TV City to buy
a new TV. When he got
there,
he found that the
manager was offering a 25% discount on every TV in the store. The one Sam
wanted was last year's model sO he got an additional 10% discount on his
purchase. When he got to the cash register, he found
out he would save even
more because
the store offered a 5% discount for paying cash. These
discounts were applied
successively, and he paid $371.93 for the TV. What
was the original price before any discounts were taken?
What was the total percent
discount Sam got?
Answer:
1/ Total percent of discount is 40%
2/ The original price is $520.70
Step-by-step explanation:
1/ We add a 25% discount on every TV store, a 10% discount on purchases, 5% discount for paying cash, so the total is a 40% discount.
2/ Now, let's find the original price
100% - 40% = 60%
We know that the 60% he has to pay is $371.93, so we have to find the 40% discount.
40% = 0.4
Take 371.93 times 0.4 = $148.77
Then we add both numbers together
148.77 + 371.93 = $520.70
Write the following as an algebraic expression. Then simplify.
Five times the sum of some number plus 3 is
equal to 9 times the number minus 9.
Five times the sum of some number plus 3 is equal to 9 times the number minus 9.
5 (x + 3) = 9x - 9
expand left side:
5x + 15 = 9x - 9
subtract 15 from both sides:
5x + 15 - 15 = 9x - 9 - 15
5x = 9x - 24
subtract 9x from both sides:
5x - 9x = 9x - 24 - 9x
-4x = -24
divide both sides by -4:
-4x/(-4) = -24/(-4)
x = 6
Solving a
A garden table and a bench cost $964 combined. The garden table costs $64 more than the bench. What is the cost of the bench?
For the given equation of variable condition, the cost of the bench is $450.
What is the equation of variable?
The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable.
Given, A garden table and a bench cost $964 combined.
i.e. G + B = $964 .............. (i)
and, the garden table costs $64 more than the bench
i.e. G = B + $64 ............. (ii)
From eq (i) and (ii), we get
B + $64 + B = $964
or, 2B = 964 - 64 = 900
or, B = 900/2 = 450
Hence, the cost of the bench is $450.
To learn more about the equation of variable
https://brainly.com/question/13951177
#SPJ1
Which is closest to the volume of the cylinder below?
Answer:
125.5cm³. (your answer is correct)
Step-by-step explanation:
Volume = cross-sectional area×height
= πr²×h
= (3.14)(2²)×10
= 3.14×4×10
= 125.6cm³
Libby receives pay of $734 which she deposits in her cheque account. She then writes out cheques for $558 and $453. If her account Is now $78 overdrawn what was her cheque account balance before she received her pay?
Answer: $355
Step-by-step explanation:
First, find the total of cheques she writes out by taking 558 + 453 = $1011
Then add 78 to it because she is overdrawn by $78 at the end, so we now have $ 1089.
Then we take 1089 - 734 = $355
So, her cheque account balance before she received her pay was $355
Fill in the missing number.
70% of
35
Submit
H
A
what is the answer to 5x-4=y and -2x+2y=8
Answer:
x = 2
y = 6
Step-by-step explanation:
5x-4=y
We add 4 and subtract y from both sides
5x - y = 4
Now we have 2 equation
5x - y = 4
-2x + 2y = 8
Let's find the x first! We time the first equation by 2
10x - 2y = 8
-2x + 2y = 8
Now add both equations
8x = 16
x = 2
Now let find the y by put 2 back in the x
-2(2)+2y=8
-4 + 2y = 8
2y = 12
y = 6
How do I know whether to apply LCM or HCF in real life questions.
Step-by-step explanation:
When you are looking for a no that DIVIDES the no, then you have to find HCF. When you are looking for a no that is DIVISIBLE, then you have to find LCM (mathematical explaination)
HELP PLLZZZZZZZZZZZZZZ
Answer: 2.2 | 4.2 | 4.1
Step-by-step explanation:
Two payment options to rent a car: You can pay $25 a day plus 5¢ a mile (Option A) or pay $15 a day plus 30¢ a mile (Option B). For what amount of daily miles will option B be the cheaper plan?
The table below shows data from a survey about the amount of time students spend doing homework each week. The students were either in college or in high school:
High Low Q1 Q3 IQR Median Mean σ
College 20 6 8 18 10 14 13.3 5.2
High School 20 3 5.5 16 10.5 11 11 5.4
Which of the choices below best describes how to measure the spread of this data? (2 points)
Both spreads are best described with the standard deviation.
Both spreads are best described with the IQR.
The college spread is best described by the standard deviation. The high school spread is best described by the IQR.
The college spread is best described by the IQR. The high school spread is best described by the standard deviation.
Answer:
I dont understand
Step-by-step explanation:
1. Edgar meaure the temperature of a olution at the beginning of an experiment to be. He monitor the temperature of the olution every minute for 10 minute. He record the change in temperature from hi previou reading. Hi data how a decreae of four time, a decreae of three time, no temperature change two time, and an increae of once. (a) Write an expreion to repreent the average change in temperature each minute
The expression to represent the average change in temperature each minute is given as follows:
Mean = (4 x (-4) + 3 x (-3)+2 + 1)/10
How to calculate mean value?Only numerical variables regardless of whether they are discrete or continuous can be used to determine the mean. Simply dividing the total number of values in a data set by the sum of all of the values yields it.
Define mean value.The average of all values is termed as mean value. Add all values given in data and divide with no. of values to get mean.
According to given condition the expression to represent the average change in temperature each minute is represented as:
Mean = (4 x (-4) + 3 x (-3)+2 + 1)/10
To learn more about mean value visit the link:
https://brainly.com/question/14532771
#SPJ4
Which line has a negative slope?
Answer:
Line A
Step-by-step explanation:
Any line facing towards the left side of the coordinate plane will have a negative slope.
Line C is facing towards the right
Line D and B doesn't have a slope
A is the only right answer
zaida took a square piece of paper and folded two of its sides to the diagonal, as shown, to obtain a quadrilateral. what is the size of the largest angle of the quadrilateral?
Answer:
112.5°
Step-by-step explanation:
The corner of the square that remains is a 90° angle.
The opposite corner started as a 90° angle that was folded in half into two 45° angles. Then each 45° angle was folded in half into two 22.5° angles. Then you put two 22.5° angles together to make a 45° angle.
So far we have two opposite angles measuring 90° and 45°.
The quadrilateral is a kite. The other two opposite angles are congruent.
The sum of the measures of the angles of a quadrilateral is 360°.
360° - 90° - 45° = 225°
225°/2 = 112.5°
Samantha visited Forager Family Farm yesterday. She picked a bucket of fresh berries in
the field. She also got 2 pints of pre-picked berries at the farm stand because they were
overripe and perfect for making jam. The farm charges $3 a pint for berries, regardless of
whether they're fresh-picked or pre-picked. Samantha paid $24 in all.
Which equation can you use to find f, the number of pints of fresh berries Samantha
picked?
2(f+ 3) = 24
3f + 2 = 24
Submit
3(f+ 2) = 24
2f + 3 = 24
The solution is Option C.
The number of pints of fresh berries is 6 pints and is calculated by the equation 3 ( f + 2 ) = 24
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of pints of fresh berries be represented as f
Now , the number of pints of berries Samantha got initially = 2 pints
So , the total number of berries Samantha got = f + 2
The cost of 1 pint of berries = $ 3
The total amount Samantha paid for the berries = $ 24
Now , the equation will be
Total amount Samantha paid for the berries = cost of 1 pint of berries x ( total number of berries Samantha got )
Substituting the values in the equation , we get
24 = 3 ( f + 2 ) be equation (1)
On simplifying the equation , we get
Divide by 3 on both sides of the equation , we get
f + 2 = 8
Subtracting 2 on both sides of the equation , we get
f = 6 berries
Hence , the equation is 3 ( f + 2 ) = 24
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ2
Zander has a set of toy pyramids that have a square base and measure of 6 inches tall. The set includes four equal-sized pyramids. What is the combined volume of all four pyramids?
Answer:
72 in^3
Step-by-step explanation:((3*3*6)/3 ) * 4
For this question, use the information given in the situation, as well as your answers to the previous questions.
After looking through different hotel options, Gabriela and Luis decided to estimate a budget of $1,200 for hotel costs. They want to stay 6 nights at a hotel. In addition, they know they should plan to pay $240 in taxes and tips. Let c represent the total cost per night they should plan for the hotel.
1. How do you know that the solution you found in the previous question is correct?
2. What does the solution to the equation mean for the Morales family?
Write 2 or 3 sentences to answer the two questions. Be sure to use clear, correct math language. Number your responses (1 and 2) so that your teacher knows which question you are answering.Your response will be automatically saved. So, once you finish your response, wait a few seconds, and then move on to the next activity.
According to the information given, the equation that represents the situation is 6c - 1200 = 240.
What is a quadratic equation?
Any equation of the form where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
The total costs are:
$240 in taxes and trips.
6 nights at the hotel, each night with a cost of c, hence 6c
Then:
T = 6c + 240
The budget is of $1200, hence, since the total cost is equals to the budget:
T = 1200
6c + 240 = 1200
Rearranging:
6c - 1200 = 240
Hence, according to the information given, the equation that represents the situation is 6c - 1200 = 240.
To learn more about quadratic equations visit,
https://brainly.com/question/1526946
#SPJ1
using a class width of 5, make a frequency distribution table starting with score 26
The frequency distribution table starting with score 26 will be illustrated as:
Class interval Number of data.
26 - 31. 2
32 - 37. 4
38 - 43. 0
44 - 49. 1
How to illustrate the frequency?Based on the information illustrated, let's assume that the numbers that we have include 27, 26, 45, 32, 35, 37, 36.
It should be noted that frequency distribution are portrayed as frequency table me chart. It shows the actual number or observations.
In this case, the class width is 26 - 31, 32 - 37, etc. The frequency distribution is illustrated above.
Learn more about frequency on:
brainly.com/question/2780465
#SPJ1