The original price of the motorcycle is approximately $7,987.
Here, we are given that p represent the motorcycle’s original price.
The sale price of Dealer A will be-
7.5% less that the original price
= 92.5% of p
= 0.925p
Similarly, the sale price of dealer B will be-
$599 less than original price
= (p - 599)
Now, these two prices are equal, so we can equate the two-
0.925p = (p - 599)
0.925p = p - 599
0.925p - p = -599
-0.075p = -599
p = -599/-0.075
p = 599/0.075
p = 599000/75
p = 7,986.67
Thus, the original price of the motorcycle comes out to be approximately $7,987.
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Write an equation for the line parallel to the given line that contains C.
8
C(-1,8); y=8/9x-7
y=
The equation for the line parallel to given line containing C:
y = 8/9x + 64 / 9
What is Parallel line ?
Parallel lines in geometry are coplanar, straight lines that don't cross at any point. In the same three-dimensional space, parallel planes are any planes that never cross. Curves with a predetermined minimum distance between them and no contact or intersection are said to be parallel.
Given that a line's equation is,
y = 8 / 9x - 7
If we contrast this equation with a line's slope-intercept,
this line's slope = 8/9
Since every line parallel to this one will have a same slope,
The parallel line's slope is equal to
The symbol for the line with the slope 'm' and the coordinates (x', y') is
y - y' = m(x - x')
As a result, the equation of the line through (-1, 8) with a slope will be,
y - 8 = 8/9 (x-1)
y =8/9x - 8/9 - 8
y = 8/9x + 64 / 9
Hence, The equation for the line parallel to given line containing C is
y = 8/9x + 64 / 9
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PLEASE HELP ASAP this stuff doesn’t make sense ;-;
The system of Inequality for the given graph is;
2x + 3y ≥ 12
3x - 5y ≥ 15
How to Interpret Inequality graph?
Inequalities that use < or > symbols are always plotted with a dashed line while Inequalities that use ≤ or ≥ symbols are always plotted with a solid line.
Now, if the shaded portion is above a dashed line, the the symbol is > but if it is shaded above a solid line, then the symbol is ≥. In this question, a solid line is used for both equations and shaded above the lines and so we will use ≥.
Equation of Line 1;
x-intercept = 6
y intercept = 4
Slope = -2/3
Thus, using the general equation of slope of line, the equation of this inequality is; 2x + 3y ≥ 12
Similarly, the equation of the second line will be;
3x - 5y ≥ 15
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9. A teacher assigns 4 points for a correct
answer, -1 points for an incorrect answer,
and 0 points for leaving the question
unanswered. What is the score for a
student who had 23 correct answers, 2
incorrect answers, and 1 unanswered
questions?
Answer:
90
Step-by-step explanation:
4 x 23 = 92
2 x (-1) = -2
1 x 0 = 0
92 + (-2) + 0 = 90
Skippy got his first paycheck and his gross pay was $1200. He noticed he paid the federal
government $180, FICA $91.44, and a state tax of $60.
a) How much did he pay in taxes?
b) What percentage of his gross income went to taxes?
c) What is his net pay?
The arithemetic mean of 3,15, and my number is 40. What is my number?
_
Average of given n numbers X1,X2,.........,Xn is x= £xi/n
Let the my number be x
Given:- The average of 3,15,x is 40
£xi/n =40
3+15+x/3=40
Multiplying 3 both side
18+x=120
x=120-18
x=102
Hence, my number is 102
Grand canyon tours offers air and ground scenic tours of the grand canyon. tickets for the 7-1/2 hr tour cost $169 for an adult and $129 for a child, and each tour group is limited to 19 people. on three recent fully booked tours, total receipts were $2931 for the first tour, $3011 for the second tour, and $2771 for the third tour. determine how many adults and how many children were in each tour. hint: use method of question 2 to find the number of adults and children in each tour (3 tours).
Using a system of equations, the number of people on each tour is given as follows:
First tour: 12 adults and 7 children.Second tour: 14 adults and 5 children.Third tour: 8 adults, 11 children.What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the context of the given problem.
For this problem, the variables are described as follows:
Variable x: number of adults in the tour.Variable y: number of children in the tour.All the tours were fully booked, hence the following equation is used in all cases:
x + y = 19.
Four the first tour, considering the values of the ticket and the total receipts, the following equation is built:
169x + 129y = 2931.
Using a calculator, the solution is:
x = 12, y = 7 -> 12 adults and 7 children.
For the second tour, the equation is:
169x + 129y = 3011.
Hence:
x = 14, y = 5 -> 14 adults and 5 children.
For the third tour, the equation is:
169x + 129y = 2771.
The solution is:
x = 8, y = 11 -> 8 adults, 11 children.
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Long division synthetic remainder theorem and factor theorem
[tex](4n^3 - 18n + 21 - 8n^2) ÷ (2n - 6)[/tex]
answer step by step:
hope this helps
Find the solutions to x² = 12. O A. x = +2√/6 OB. x = +2√3 O C. x = +6√2 O D. x = ±3√2
The solution for the expression x² = 12 will be x = ±2√3.
The expression is given in the form of square of a variable x which is equal to 12. This expression does not form a perfect square as the constant term is not a perfect square number. A perfect square is a number which is expressed as the square of whole number, or a number multiplied by itself twice. Here, we are given that x² = 12. We take square root of the expression on both the sides then,
√x² = √12
x = √(2×2×3)
x = ±2√3
We use the sign '±' because any number which when expressed in variable form comes out of the square root then it can be positive or negative,
Thus, the value of x is ±2√3.
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Sam creates a dot pattern using a rule. He starts with 2 dots and adds 2 dots for each term. The dot pattern continues for 50 terms. The first four terms in his dot pattern are shown below.
Answer:
That means the sum of the first 99 positive integers is 49(100) + 50 = 4900 + 50 = 4950. 2.
Converting Units of Measure I - Item 35100
Ellie needs 24 cups of milk for a large recipe. How many gallons does she need?
2 c = 1 pint
(pt)
2 pt = 1
quart (qt)
4 qt = 1
gallon (gal)
Ellie needs 1.5 gallon of milk (that is 24 cups).
we are given 2 cup = 1 pint
we have 24 cup which will be equal to 24/2 i.e. 12 pint.
we are given 2 pint = 1 quart
we have 12 pint which will be equal to 12/2 i.e. 6 quart
we are given 4 quart = 1 gallon
we have 6 quart which will be equal to 6/4 i.e. 1.5 gallon.
Hence, we know 24 cups of milk is equivalent to 1.5 gallon of milk
what are conversions in maths?
By multiplying or dividing a number, a conversion factor can be used to change one set of units to another. When a conversion is required, the right conversion factor to an equivalent value must be applied. For instance, 12 inches equals 1 foot when converting between inches and feet.
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In the circle below, P is the center. If < APB measures 56 °, find the measure of < ACB.
Given the shown figure
since
The Central Angle Is Twice The Inscribed Angle
where
a= mACB
2a = mAPB=56
then
[tex]2a=56[/tex][tex]a=\frac{56}{2}[/tex][tex]a=28[/tex]a= mACB=28
Correct answer
option b
28
cami invested $6000 dollars into an account that ears 10% intrest compound annually. write an explicit equation for how much money she wil have after t years
Answer:
Below in bold.
Step-by-step explanation:
10% = 0.10 as a decimal fraction.
After t years:
Amount = 6000(1 + 0.10)^t
8th grade Mathematics
According to the trend line equations, which plants are growing at the same rate per day?
1 and 2
1 and 4
2 and 3
2 and 4
I appreciate you answers so much!
Have a great day! :)
The plant are growing at the same rate per day is given by equation 1[tex]y=\frac{3}{2}x +\frac{3}{2}[/tex] and equation 4 [tex]y = \frac{3}{2}x+1[/tex] i.e because they have same slope(rate of change )
What is rate of change ?The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one item by the equal amount of change in another.
The plant are growing at the same rate per day is given by equation 1[tex]y=\frac{3}{2}x +\frac{3}{2}[/tex] and equation 4 i.e [tex]y = \frac{3}{2}x+1[/tex]
because they have same slope(rate of change )
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Determine whether the graph represents a linear or non linear function and explain
Answer:
Non-linear
Step-by-step explanation:
Because the line is not straight.
7. You bought a Gatorade and 4 bags of apples for $5.50. Write the equation that determines how much
each bag of apples was if the Gatorade cost $2.50.
Answer: (5.50-2.50)/4 = 0.75. each bag of apples is $0.75
Step-by-step explanation:
first, you subtract $5.50 by $2.50 to get $3, the cost of the 4 bags of apples altogether ($5.50 - $2.50 = $3)
then you divide $3 by 4 to get the cost of each bag of apples. (3/4 = 75)
so each bag of apples is $0.75
i hope this helps!
Find the odd one out
7142
2168
3248
7426
3211
8547
9455
9273
1. Given the sequence: {5, 7, 9, 11, ...}
Which explicit formula generates this sequence?
What’s the answer
Given that each term has a common difference, this is an arithmetic sequence as per the explicit formula that generates this sequence.
Arithmetic Sequence formula.In this instance, the next word in the sequence is obtained by adding 2 to the previous term. To put it another way, a n = a 1 + d (n – 1) This is the arithmetic sequence’s formula.
How are explicit formulas handled?Firstly, we have to find the initial phrase in a given series. Thereafter we have to find the shared difference between the following phrases in the sequence. For an explicit rule, replace the general form with the first term and common difference.
What in mathematics is an arithmetic sequence?The distance between succeeding terms in an arithmetic series is always the same.
The difference between consecutive terms in the sequence 3, 5, 7, 9…, for instance, is an example of an arithmetic sequence.
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Write down the order of rotational symmetry of this regular heptagon.
The order of the rotational pentagon is 6.
What is order of a polygon?The amount of times a form may be turned in a full circle without losing its appearance is known as its order of rotational symmetry. The only time the triangle appears the same after being rotated a full 360 degrees is when it returns to its original beginning position. It only has one rotational symmetry order, which is the initial position. A form can only have one rotational symmetry order.
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suppose that 75% of the applicants for a certain industrial job possess advanced training in computer programming. applicants are interviewed sequentially and are selected at random from the pool. find the probability that the first applicant with advanced training in programming is found on the third interview. (round your answer to four decimal places.)
The probability that the first applicant with advanced training in programming is found on the third interview is 0.0469
Let X denote the number interviewed until 1 has advanced training and follows a geometric distribution with parameter 75%, so
Geometric distribution is: (1-75%)
=0.75
The density function of geometric distribution is,
[tex]P(X=x)=p(1-p)^{x-1}[/tex], for all x = 1,2,3,....
Now, we calculate the probability that the first applicant with advanced training in programming is found on the third interview:
P(X=3) =[tex]0.75(1-0.75)^{3-1}[/tex]
=[tex]0.75(1-0.75)^{2}[/tex]
=0.75×0.0625
=0.0469
Hence, the required probability is 0.0469
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Write a rule to describe the transformation.
E(-1-3), F(0,1), G(3,-2)
E'(-1.5,-4.5), F'(0,1.5), G' (4.5.-3)
Answer:
x= x1.5 y = x1.5
E' = E dilated by 1.5
Step-by-step explanation:
-1 x 1.5 =-1.5 -3 x 1.5 = -4.5 (-1.5,-4.5)
0 x 1.5 =0 1 x 1.5 = 1.5 (0,1.5)
3 x 1.5 = 4.5 -2 x 1.5 =-2 (4.5.-3)
Zoe downloaded a trial game to her computer. She has at most 60 free minutes to
play the game. It takes 5 minutes to set up her character, and the instructions say
each level takes 8 minutes.
How many levels L is she estimated to complete on the free trial?
Show work or explain. Write your answer as an inequality. (here are inequality symbols you can
copy and paste < > ≤ ≥)
Answer:
6 levels
Step-by-step explanation:
60 - 5 (to set up the character)
55 total minutes
8(l) = 55
L = 55/8
L = 6.875
.˙. they can finish 6 levels
which rational is qvuivalent to 0.86
The rational equivalent to 0.86 can be written as 43/50.
A rational number may be defined as the number which can be expressed in the form of p/q where p and q are integers, and the term q cannot be equal to zero. It can be either positive or negative or both. We can also say that any fraction which does not have zero in the denominator is called a rational number. Zero can also be regarded as a rational number as it can also be represented as a fraction. For example, 0/2, 0/5. In order to write 0.86 as a rational number, we have to convert it in fraction form. In fraction form it can be written as
0.86 = 86/100
This is also a rational number, but we simplify it further and we get
86/100 = 43/50 which is a rational number.
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please help. urgent!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
From the given linear equation graph, we can tell that the equation of the line in slope intercept form is; y = 1.2x + 3
How to Interpret Linear Equation Graph?
The general form of equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
From the given graph, we see that;
y - intercept = 3
x - intercept = -2.5
Now, we can find the slope by taking two coordinates;
(-2.5, 0) and (0, 3)
Slope = (3 - 0)/(0 - (-2.5))
Slope = 3/2.5
Slope = 1.2
Thus, the equation of the line is;
y = 1.2x + 3
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All of the following are equivalent fractions except
04/12
07/21
O 5/20
O9/27
Answer:
05/20 is not an equivalent fraction
Step-by-step explanation:
1) Write each fraction in its simplest form. To do this divide the numerator by the denominator.
04/12 becomes 1/3
07/21 becomes 1/3
05/20 becomes 1/4
09/27 becomes 1/3
2) all the fractions simplify to the same number except 05/20. So, we can conclude that 05/20 is not an equivalent fraction
Find the equation of the line.
Use exact numbers.
Answer:
y = (1/2)x + -3
Step-by-step explanation:
Point 1: (0, -3); Point 2: (6, 0)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 0 - (-3) 0 + 3 3 1
m = ------------- = ------------ = ---------- = -------- = --------
x₂ - x₁ 6 - 0 6 6 2
y - y₁ = m(x - x₁)
y - (-3) = (1/2)(x - 0)
y + 3 = (1/2)x
- 3 -3
----------------------------------
y = (1/2)x - 3
I hope this helps!
Answer: y=0.5x-3
Step-by-step explanation:
[tex]\displaystyle\\(0,-3)\ \ \ \ (6,0)\\ \frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} \\\\x_1=0\ \ \ \ x_2=6\ \ \ \ \ y_1=-3\ \ \ \ \ y_2=0\\\\\frac{x-0}{6-0} =\frac{y-(-3)}{0-(-3)}\\\\\frac{x}{6} =\frac{y+3}{0+3} \\\\\frac{x}{6} =\frac{y+3}{3}[/tex]
Multiply both parts of the equation by 3:
[tex]\displaystyle\\\frac{x}{2} =y+3\\\\0.5x=y+3\\\\0.5x-3=y+3-3\\\\0,5x-3=y\\\\Thus,\ y=0.5x-3[/tex]
Multiply −14y(7y − 5).
−98y2 + 70y
−98y2 + 70
−98y2 − 5
98y2 − 70y
Answer:
[tex]-98y^2+70y[/tex]
Step-by-step explanation:
Expand the equation [tex]-14y(7y-5)[/tex], we get
[tex](-14y*7)-(-14y*5)[/tex]
Which is equal t0:o
[tex]-98y^2+70y[/tex]
The product of given monomial by binomial is -98y²+70y.
Given that, -14y(7y - 5).
What is product of polynomials?To multiply two polynomials: multiply each term in one polynomial by each term in the other polynomial. Add those answers together, and simplify if needed.
Using distributive property, multiply given monomial by binomial. That is,
-14y(7y - 5)=-14y×7y - (-14y)(5)
= -98y²+70y
Therefore, the product of given monomial by binomial is -98y²+70y.
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Find the distance between points S(-2,4) and T(3,9). Round your answer to the nearest tenth.
Answer:
d^2=(x2-x1)^2+(y2-y1)^2
d^2=[3-(-2)]^2+(9-4)^2
d^2=(5)^2+(5)^2
d^2=25+25
d^2=50
d= [tex]\sqrt{50}[/tex]
d=7.07 units
a. If p is an even number, then p + 12 is even.
Answer:
True???
Step-by-step explanation:
Is this a true or false question?
P+12=even number
Examples...
12+12=24
16+12=28
66+12=78
Answer:
YES
Step-by-step explanation:
even + even = even
always and forever
Solve for x -
[tex]\sf 6+4x+3=6x-21[/tex]
Answer:
x = 15
Step-by-step explanation:
Let's start by copying down the equation.
6 + 4x + 3 = 6x - 21
Let's simplify this equation and we get,
4x + 9 = 6x - 21
Now, we can add 21 to both sides to isolate 6x on one side. Then, we get...
4x + 30 = 6x
Now, we minus 4x from both sides to get rid of it.
Then we get...
2x = 30
Thus, x = 15
6 + 4x + 3 = 6x - 21
We minus (4x+3) on both side.
6 + 4x + 3 - (4x+3) = 6x - 21 - (4x + 3)
6 = 2x - 24
2x = 30
x = 15.
Recheck : 6 + 60 + 3 = 90 - 21
69 = 69 (nice.)
If f(x)=2(x)^2 + 5 square root (x-2), complete the following statement
The domain for f(x) is all real numbers _____ than or equal to 2.
Answer:
Greater.
Step-by-step explanation:
The in the function , the square root term has to give a real number if is to be real. This can only happen if because if then will give a complex number and therefore will not be real.
Thus, the domain for f(x) is all real numbers greater than or equal to 2.
Answer:
The domain for f(x) is all real numbers greater than or equal to 2.
Step-by-step explanation:
Given function:
[tex]f(x)=2x^2+5 \sqrt{x-2}[/tex]
The domain of a function is the set of all possible input values (x-values).
As the square root of a negative number cannot be taken:
[tex]\implies x-2\geq 0[/tex]
Therefore:
[tex]\implies x-2+2\geq 0+2[/tex]
[tex]\implies x\geq 2[/tex]
Therefore, the domain of the given function is greater than or equal to 2.