Answers
A point P on the line segment starting at A and ending at B can be parameterized by
[tex]p(t) = (1-t)(-2,-4) + t (6,1)[/tex]
with [tex]0\le t\le1[/tex].
If AP/PB = 3/2, then point P is 3/5 of the length of AB from A, and 2/5 of the length of AB from B. So the coordinates of P are obtained at [tex]t=\frac35[/tex], and we find
[tex]p\left(\dfrac35\right) = \left(1-\dfrac35\right)(-2,-4) + \dfrac35 (6,1) = \boxed{\left(\dfrac{14}5, -1\right)}[/tex]
Related Questions
Write the correct equation for the following statement.
The quotient of x and seven is twelve
Answers
Answer:
Step-by-step explanation:
x/7=12
MATHEMATICAL PHRASES_____5. the quatient of y and seven is eight_____6. thrice a number is eighteen_____7. the sum of twice a number and five is nine_____8. a number decreased by seven is twenty-eight
Answers
Explanation
Part A: The quotient of y and seven is eight.
Answer: y/7 =8
Part B: Thrice a number is eighteen
Answer: 3x = 18
Part C: The sum of twice a number and five is nine
Answer: 2x+5 =9
Part D: A number decreased by seven is twenty- eight
Answer: x-7 =28
Find the variance and standard deviation of the set of data to the nearest tenth (one decimal place){4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 9}
Answers
Hello there. To solve this question, we'll need to remember how to find the variance and standard deviation of a data set.
First, given a data set with values:
[tex]\mleft\lbrace x_1,x_2,x_{3,\ldots}\mright\rbrace[/tex]The variance can be calculated by the formula:
[tex]\sum ^{}_{}\frac{(x_i-\mu)^2}{n}[/tex]In this case, μ is the arithmetic mean of the data set and x_i is the i-th element of the data set.
The data set given is:
{4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 9}
To calculate the mean, we add every term and divide by the number of terms:
[tex]\frac{4+5+5+5+5+5+6+6+6+6+7+7+7+7+8+9}{16}=\frac{98}{16}=6.125[/tex]Now, we calculate the square of the difference between every term and mean.
Notice we have some repeated terms, we rewrite the sum like this:
[tex]\frac{(4-6.125)^2+5\cdot(5-6.125)^2+4\cdot(6-6.125)^2+4\cdot(7-6.125)^2+(8-6.125)^2+(9-6.125)^2}{16}[/tex]Adding the terms and calculating the squares, we have:
[tex]\begin{gathered} \frac{(-2.125)^2+5\cdot(-1.125)^2+4\cdot(-0.125)^2+4\cdot(0.875)^2+(1.875)^2+(2.875)^2}{16} \\ \\ \frac{4.515625+6.328125+0.0625+3.0625+3.515625+8.265625}{16} \\ \\ \frac{25.75}{16}\text{ = }1.609 \end{gathered}[/tex]This is the variance of the values of this data set. We can round it up to the nearest tenth as 1.6
The standard deviation is the square root of the variance.
Then, we calculate:
[tex]\sigma\text{ = }\sqrt[]{1.6}=1.268[/tex]Again, rounding it to the nearest tenth, we have 1.3;
The final answer is: The variance of this data set is 1.6 and its standard deviation is 1.3.
Solving the second question:
We apply the same formula. First, find the mean of the values:
[tex]\mu\text{ = }\frac{4.3+6.4+2.9+3.1+8.7+2.8+3.6+1.9+7.2}{9}=4.54[/tex]Now, as every term is different from each other, we apply the formula and get the following:
[tex]\frac{(4.3-4.54)^2+(6.4-4.54)^2+(2.9-4.54)^2+(3.1-4.54)^2+(8.7-4.54)^2+(2.8-4.54)^2+(3.6-4.54)^2+(1.9-4.54)^2+(7.2-4.54)^2}{9}[/tex]Calculating the difference, squaring it, adding the values and dividing by 9, we get:
Variance is approximately equal to 4.84
The Standard deviation is the square root of the variance, namely 2.2
This diagram shows a pre-image A ABC, and its image, A A"B'C", after a series of transformations. Select from the drop-down menus to correctly complete the statements. C A A A ABC is X Choose. B to becomeA ABC'. Then A A'BC' is C C Choose.. to become A A"B"C" . Because the transformations are Choose... the pre- image and image are Choose..
Answers
The pre-image ABC in order to become the reflection at A'B'C' is reflected across the x-axis.
The pre-image ABC in order to become A"B"C" both are CONGRUENT, because the image and pre-image are BOTH RIGID.
**Please note that the rules for the transformation from ABC to A"B"C" were not provided**
50 points again!!!!!!!!!!!!!
Answers
Answer:
Step-by-step explanation:
f(x)=|5x|
f(2)= |5(2)| Substitute 2 for x
f(2)= 10 Answer
Answer:
f(2) = | 5 • 2 | = | 10 | = 10
Step-by-step explanation:
Replace x with 2 then solve with the absolute value
The table and graph show the population or Oregon
Answers
From the given table, it is found that:
a. The average population decline was of 2,250 deer a year.
b. The population would have reached 225 thousand deer during the years of 2017 and 2018.
What is the average rate of change of a function?The average rate of change of a function is given by the change in the output divided by the change in the input of the function. Hence, over an interval [a,b], the average rate of change is given as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
In 1984 and 2018, the populations are given as follows:
1984: 250 thousand.2018: 173.5 thousand.Hence the rate of change is given as follows:
r = (173.5 - 250)/34 = -2.25.
(2.25 thousand = 2,250).
For item b, the following linear function is built:
y = 230.5 - 1.45x.
The amount would be of 225 when:
230.5 - 1.45x = 225
1.45x = 5.5.
x = 5.5/1.45
x = 3.79.
Hence between the years of 2017 and 2018.
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Alicia has 10 paintings and wants to hang them side by side on the wall. How many ways can she hang the paintings?
Answers
The total number of ways she can hang the painting is 720 after applying the concept of permutation and combination.
What are permutation and combination?The variety of possible arrangements of a set is its permutation however order is important in permutations but not in combinations.
It is given that:
Alicia wants to place her ten paintings side by side on the wall.
We can get the factorial of 6 and use that knowledge to calculate how many ways there are to multiply 6 by multiplying it by all positive integers that are more than or equal to that number, in this case, 6.
Alicia can arrange her six paintings:
6! = 6x5x4x3x2x1
6! = 720
Thus, the total number of ways she can hang the painting is 720 after applying the concept of permutation and combination.
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A city has a population of 250,000 people. Suppose that each year the population grows by 6%. What will the population be after 5 years?Use the calculator provided and round your answer to the nearest whole number.
Answers
The population after 5 years is approximately 337,465 people
Explanation:The population of the city is 250,000
Annual growth rate is 6%
The population after t years is:
[tex]P=P_oe^{rt}[/tex]After 5 years, t = 5 and the population becomes:
[tex]\begin{gathered} P=250000e^{\frac{6}{100}\times5} \\ \\ =250000e^{0.3} \\ \\ \approx337465 \end{gathered}[/tex]The population after 5 years is approximately 337,465 people
i need help with this pls
Answers
Hello!
What is an x-intercept:
⇒ value of x when the value of y equals '0'
[tex]8x + 5y=25\\8x+5(0)=25\\8x=25\\\\x=\dfrac{25}{8}[/tex]
x-intercept is 25/8
What is a y-intercept:
⇒ value of y when the value of x equals '0'
[tex]8x+5y=25\\8(0)+5y=25\\5y=25\\y=5[/tex]
y-intercept is 5
Hope that helps!
What is the measure of a?
In the figure below, C D bisects ∠A C B
AB=B C
∠ B E C=90° and
∠D C E=42°
Find the measure of ∠A
Answers
The measure of "a" in the above-given right-angled triangle is 32°
What is a triangle?Note that a triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same.
Key properties of a right-angled triangle to note are:
One angle is always 90° or a right angle.The side opposite angle of 90° is the hypotenuse.The hypotenuse is always the longest side.The sum of the other two interior angles is equal to 90°.The other two sides adjacent to the right angle are called base and perpendicular.The Sum of all three interior angles is equal to 180°To solve for "a" recall the following. It is given that:
AB = BC
∠BEC=90°
∠DCE=42°
Because CD bisects ∠ACB, Hence,
∠ACD = ∠DCB = x.............................1
∠DCE= ∠BCE + ∠DCB .....................2
= ∠BCE + x = 42° ................................3
To find ∠A, we use deductive reasoning to state:
∠A +∠E +∠ACD + ∠DCB + ∠BCE = 180° (Sum of Interior Angles)
Recall equation 1 hence, replacing ∠ACD with ∠DCB we have:
∠A +∠E +∠DCB + ∠DCB + ∠BCE = 180°
Recall equation 2, where ∠DCB = x, hence
∠A +∠E +x + x + ∠BCE = 180°
Recall equation three where 3 where ∠BCE + x = 42°, hence
∠A +∠E +x + (x + ∠BCE) = 180°
⇒ ∠A +∠E + x + 42° = 180°
Recall that ∠E = 90° so
⇒ ∠A +90° + x + 42° = 180° (Collect like terms)
⇒ ∠A + x = 180° - 90° - 42° = 48°; Hence
∠A + x = 48°...........................4
Recall that in Δ ABC
AB = BC (given)
Hence, ABC is an Isosceles triangle. Since this is true, then
⇒ ∠A = ∠ACB = 2x ...........................5 (Two angles opposite the equal sides are equal)
Substituting 2x in equation 5 into equation 4, we have
2x + x = 48°
3x = 48
x = 48/3
x = 16°
Recall that
∠A = 2x...........equation 5, hence,
∠A = 2 * 16
∠A = 32°
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. If g= 12 and h = 19, what is the value of3h(h-g)?A. 13B. 43C. 252D. 399
Answers
Solution
For this case we have the following:
g = 12 and h=19
And we want to find 3h(h-g)
If we replace we got:
3*19 (19-12) =57*7=399
Then the answer would be:
D. 399
Henry purchased compact disks for $112. The compact discs cost $16 each.Which of the following equations could you use to find how many compact disks, x, Henry purchased?$16 = $112xO $112 = $16xXO $112=16$112 = x - $16
Answers
Problem
Henry purchased compact disks for $112. The compact discs cost $16 each.
Which of the following equations could you use to find how many compact disks, x, Henry purchased?
Solution
We can set up the following notation:
x= number of disks
total cost = (number of disks)* (unitary price)
Total cost = $112
number of disks =x
unitary price = $16
Replacing we got:
112 = x*16
For this case the correct equation would be given by:
$112 = $16x
A committee of 6 is to be chosen from the 28 students in a class. If there are 10 males and 18 females in the class, in how many ways can this be done if there must be at least three females on the committee? A: 339864B: 816720C: 3060D: 18564
Answers
Hello! First, let's write some important information contained in the exercise:
committee = 6 students
class: 28 students:
- 10 males
- 18 females
Let's consider the rule: At least three females must be on the committee, so we have some cases, look:
_F_ * _F_ * _F_ * __ * __ * __
1st option:
3 females and 3 males
_F_ * _F_ * _F_ * _M_ * _M_ * _M_
2nd option:4 females and 2 males
_F_ * _F_ * _F_ * _F_ * _M_ * _M_
3rd option:5 females and 1 male
_F_ * _F_ * _F_ * _F_ * _F_ * _M_
4th option:6 females and 0 male
_F_ * _F_ * _F_ * _F_ * _F_ * _F_
Now, we have to use the formula below and find the number of possible combinations:
[tex]C_{n,p}=\frac{n!}{p!\cdot(n-p)!}[/tex]Let's calculate each option below:
1st:3 females:
[tex]C_{18,3}=\frac{18!}{3!\cdot(18-3)!}=\frac{18\cdot17\cdot16\cdot15!}{3\cdot2\cdot1\cdot15!}=\frac{4896}{6}=816[/tex]3 males:
[tex]C_{10,3}=\frac{10!}{3!\cdot(10-3)!}=\frac{10\cdot9\cdot8\cdot7!}{3\cdot2\cdot1\cdot7!}=\frac{720}{6}=120[/tex]3 females and 3 males: 816 * 120 = 97920
2nd option:4 females:
[tex]C_{18,4}=\frac{18!}{4!\cdot(18-4)!}=\frac{18\cdot17\cdot16\cdot15\cdot14!}{4\cdot3\cdot2\cdot1\cdot14!}=\frac{73440}{24}=3060[/tex]2 males:
[tex]C2=\frac{10!}{2!\cdot(10-2)!}=\frac{10\cdot9\cdot8!}{2\cdot1\cdot8!}=\frac{90}{2}=45[/tex]4 females and 2 males: 3060* 45 = 137700
3rd option:5 females:
[tex]C_{18,5}=\frac{18!}{5!\cdot(18-5)!}=\frac{18\cdot17\cdot16\cdot15\cdot14\cdot13!}{5\cdot4\cdot3\cdot2\cdot1\cdot13!}=\frac{1028160}{120}=8568[/tex]1 male:
[tex]C_{10,1}=\frac{10!}{1!\cdot(10-1)!}=\frac{10!}{1\cdot9!}=\frac{3628800}{362880}=10[/tex]5 females and 1 male = 8568 * 10 = 85680
4th option:6 females and 0 male:
[tex]C_{18,6}=\frac{18!}{6!\cdot(18-6)!}=\frac{18\cdot17\cdot16\cdot15\cdot14\cdot13\cdot12!}{6\cdot5\cdot4\cdot3\cdot2\cdot1\cdot12!}=\frac{13366080}{720}=18564[/tex][tex]C_{10,0}=\frac{10!}{0!\cdot(10-0)!}=\frac{10!}{10!}=1[/tex]6 females and 0 male: 18564 * 1 = 18564
To finish the exercise, we have to sum the four options:
97920 + 137700 + 85680 + 18564 = 339864
So, right answer A: 339864.
The line of best fit is given as y = 9 - 3x. Find the value of y when x = -3.091827
Answers
Solution
We are given the equation
[tex]y=9-3x[/tex]We want to find y when x = -3. We only need to put x = -3
[tex]\begin{gathered} y=9-3x \\ y=9-3(-3) \\ y=9+9 \\ y=18 \end{gathered}[/tex]Therefore, the answer is
[tex]\begin{equation*} 18 \end{equation*}[/tex]A manufacturer knows that their items have a lengths that are skewed right, with a mean of 17.6 inches, andstandard deviation of 3.3 inches.If 37 items are chosen at random, what is the probability that their mean length is greater than 18.9 inches?(Round answer to four decimal places)Question Help: D VideoSubmit Question
Answers
The probability is 0.9999
Explanation:Given that the mean is 17.6 inches
standard deviation is 3.3/37 = 0.089
We have:
z(18.9)
[tex]z=\frac{x-\mu}{\sigma}[/tex][tex]\frac{18.9-17.6}{0.089}=14.6067[/tex]Now, we have
P(x > 18.9) = P(z > 14.6067)
= 0.9999
z(0.394) = 0.6532
400 in savings for 20 years compounded 5% monthly
Answers
Answer:1,086
Step-by-step explanation: Initial Deposit
$400
Contributions
$0
Investment Time Span
20
Estimated Rate of Return
5.00%
can somebody please help me with this question
Answers
Answer:
U'(12, 15)
Step-by-step explanation:
Given point U(4, 5) is part of figure STUVW that is dilated by a factor of 3 about the origin, you want the coordinates of U'.
DilationDilation about the origin multiplies each coordinate value by the scale factor:
U' = 3U
U' = 3(4, 5) = (12, 15)
The coordinates of U' are (12, 15).
The two plots below show the heights of some sixth graders and some seventh graders:Sixth Graders+52 53 54 55 56 57Height (inches)Seventh Graders52 53 54 55 56 57Height (inches)The mean absolute deviation (MAD) for the first set of data is 1.2 and the MAD for the second set of data is 1.0. Approximately how manytimes the variability in the heights of the seventh graders is the variability in the heights of the sixth graders? (Round all values to the tenthsplace.)
Answers
From the information given,
MAD for the heights of some sixth graders = 1.2
MAD for the heights of some seventh graders = 1
Number of times = MAD of data1/MAD of data 2 = 1.2/1
The answer is 1.2
I need help finding the area I have a huge test tomorrow and I’m nervous.
Answers
The given figure can be divided into a rectangle and a triangle
The rectangle has the dimensions 10 m by 12 m
so, the area of the rectangle = 10 x 12 = 120 square meters
Now, we will find the area of the triangle:
Base = 12 - 10 1/4 = 1 3/4 m
Height = 15 - 10 = 5 m
Area = 1/2 x base x height =
[tex]\frac{1}{2}\cdot1\frac{3}{4}\cdot5=\frac{1}{2}\cdot\frac{7}{4}\cdot5=\frac{35}{8}=4\frac{3}{8}m^2[/tex]So, the total area =
[tex]120+4\frac{3}{8}=124\frac{3}{8}m^2[/tex]Find all X such that -13 < 5x - 3 ≤ 17.
Answers
Answer:
-5 < x < 17/5
Step-by-step explanation:
add three onto all sides -10 < 5x < 17
then divide all sides by -5 < x < 17/5
<1 is in a triangle work <4 and a 53° angle . what is the sum of the measures of these two angles
Answers
In the small triangle
There are a right angle and an acute angle of measure 53 degrees
Since the sum of the angles of a triangle is 180 degrees
Then 90 + 53 + < 1 = 180 degrees
Then 143 + < 1 = 180
Subtract 143 from both sides
Then < 1 = 37 degrees
Since <2 is an exterior angle of the small triangle
Then its measure = the sum of <1 and 90 degrees
Then < 2 = 37 + 90 = 127 degrees
In the triangle of angles 2, n3 and 30
< 2 + < 3 + 30 = 180
127 + < 3 + 30 = 180
Add 127 and 30
157 + <3 = 180
<3 = 23
The answer is < 2 = 127 degrees and < 3 = 23 degrees
Colleen truman earns 5% commission on all sales in june her sales totaled 54,000$ how much did she earn in commission?
Answers
The amount earned as commission in the month of June is $2700
How to determine the amount earned as commission?From the question, we have the following parameters that can be used in our computation:
Commission percentage = 5%
Total sales in the month of June = $54000
The amount earned as commission in the month of June is then calculated as
Amount = Commission percentage x Total sales in the month of June
Substitute the known values in the above equation
So, we have
Amount = 5% x 54000
Evaluate
Amount = 2700
Hence, the commission amount is $2700
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One batch of pink paint uses 2 cups of red paint and 7 cups of white paint. Mai made a
large amount of pink paint using 14 cups of red paint.
a. How many batches of pink paint did she make?
Answers
Answer:
7
Step-by-step explanation:
14/2=7
Step by step explanation
1 batch=2cups of red and 7 cups white
14 cups of red paint = 7 batches
Type the correct answer in type the answer in the box.Consider functions fand g.f(x)=(x+1)^3g(x) = 3sqrtx + 1Evaluate the function composition.(fg)(-64) = _
Answers
f(x) = (x + 1)^3
g(x) = cubic root x + 1
f(g)(x) =
[tex]\begin{gathered} f(g(x))\text{ = (3}\sqrt[]{x}+2)^3 \\ f(g(x))\text{ = x + 6(3}\sqrt[]{x})^2\text{ + 12(3}\sqrt[]{x})\text{ + 8} \\ f(g(-64))\text{ = -64 + 6(3}\sqrt[]{-64})^2\text{ + 12(3}\sqrt[]{-64})\text{ + 8} \\ f(g(-64))\text{ = -64 + 6(16) - 48 + 8} \\ f(g(-64))\text{ = -64 + 96 - 48 + 8} \\ f(g(-64))\text{ = 104 - 112} \\ f(g(-64))\text{ = -8} \end{gathered}[/tex]result
f(g(-64)) = -8
dentashboard/home
Town policy requires that a certain number of trees be planted for every tree that is cut down.
For example, if 8 trees are cut down, 48 trees will be planted. A homeowner is going to cut down
5 trees on his property.
Solve Problems with Ratios and Unit Rates-Instruction-Level F
How many trees will be planted when 5 are cut down?
Trees Planted
Trees Cut Down
48
8
5
Answers
This can be solved using ratio and proportions.
What is ratio?
A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the proportion of lemons to oranges is 6:8 (or 3:4), while the proportion of oranges to overall fruit is 8:14. (or 4:7). A ratio's numbers can be any quantity, such as a count of persons or things, or measures of lengths, weights, time, and so forth. In most situations, both numbers must be positive. A ratio in mathematics illustrates how many times one number contains another.
First, we find the ratio of trees planted to trees cut
= 48/8 = 6
So, no. of trees to be planted when 5 trees are cut = 5x6 = 30
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In an office building, 42 offices are currently being rented. This represents 30% of the total units. How many offices are there in the building?
Answers
Let the total number of offices in the building be x.
We can represent the information provided in the question mathematically as:
[tex]30\text{ \% of x = 42}[/tex]Solving for x:
[tex]\begin{gathered} \frac{30}{100}\text{ }\times\text{ x = 42} \\ \frac{30x}{100}\text{ = 42} \\ \end{gathered}[/tex]Cross-Multiply:
[tex]\begin{gathered} 30x\text{ = 4200} \\ \text{Divide both sides by 30} \\ \frac{30x}{30}\text{ = }\frac{4200}{30} \\ x\text{ = 140} \end{gathered}[/tex]Hence, there are 140 offices in the building.
Answer: 140 offices
When do you know you can stop the long division process when converting a fraction to a decimal number?
Answers
Division stops after a certain number of steps as the remainder becomes zero and When division continues as there is a remainder after every step.
What is Division?a division is a process of splitting a specific amount into equal parts.
We can stop the long division process when converting a fraction to a decimal number.
There can be two situations in converting fractions to decimals:
When division stops after a certain number of steps as the remainder becomes zero.
When division continues as there is a remainder after every step.
Hence When division stops after a certain number of steps as the remainder becomes zero and When division continues as there is a remainder after every step.
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2.2.30QuesticFind a quadratic function that includes the set of values below.(0,6), (2,8), (3,0)The equation of the parabola is y=0
Answers
The form of quadratic is:
[tex]y=ax^2+bx+c[/tex]Since (0,6) is given, we know c = 6, thus we have:
[tex]\begin{gathered} y=ax^2+bx+c \\ ax^2+bx+6 \end{gathered}[/tex]Point 2 is (2,8), replace x and y and find equation:
[tex]\begin{gathered} y=ax^2+bx+6 \\ 8=a(2)^2+b(2)+6 \\ 8-6=4a+2b \\ 4a+2b=2 \end{gathered}[/tex]Putting point 2 (3,0), we have:
[tex]\begin{gathered} y=ax^2+bx+6 \\ 0=a(3)^2+b(3)+6 \\ 9a+3b=-6 \end{gathered}[/tex]Solving the 2 simulatenous equations for a and b, we get:
a = -3
b = 7
Now u have all the values, a, b, and c.
Just put it in the general form of parabola :
[tex]y=-3x^2+7x+6[/tex]y = -3x^2 + 7x + 6
Find the vertex of the function given below.
y = 3x² + 6x +1
A. (1,7)
B. (-1,-2)
C. (-4,9)
D. (-1,-1)
Answers
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{3}x^2\stackrel{\stackrel{b}{\downarrow }}{+6}x\stackrel{\stackrel{c}{\downarrow }}{+1} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 6}{2(3)}~~~~ ,~~~~ 1-\cfrac{ (6)^2}{4(3)}\right) \implies \left( - \cfrac{ 6 }{ 6 }~~,~~1 - \cfrac{ 36 }{ 12 } \right) \\\\\\ (-1~~,~~1-3)\implies {\Large \begin{array}{llll} (-1~~,~~-2) \end{array}}[/tex]
Two motorcycle dealers sell the same motorcycle for the same original price. Dealer A advertises that the motorcycle is on sale for 7.5% off the original price. Dealer B advertises that it is reducing the motorcycle’s price by $599. When Bonnie compares the sale prices of the motorcycles in both dealers, she concludes that the sale prices are equal.
Let p represent the motorcycle’s original price.
Which equation models this situation?
0.075p = p − 599
0.925p = p + 599
0.075(p−599) = p
0.925p =
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Answers
Considering the definition of an equation, the equation 0.925p= p - 599 models the following situation: the sale prices of the motorcycles in both dealers are equal.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values appear in addition to certain known data.
The solution of a equation means determining the value that satisfies it and the equality is true. To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.Equation in this caseBeing "p" the motorcycle’s original price, you know that:
Dealer A advertises that the motorcycle is on sale for 7.5% off the original price → Sale price A= 100%×p - 7.5%×p → Sale price A= (100% - 7.5%)× p → Sale price A= 92.5%p → Sale Price A= 0.925p (expressed as decimals)Dealer B advertises that it is reducing the motorcycle’s price by $599. → Sale price B=p - 599If the sale prices are equal, the equation in this case is:
Sale price A= Sale price B
0.925p= p - 599
Finally, the equation 0.925p= p - 599 represent the situation.
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