The slope of the scenario is calculated as: -250.
How to Find the Slope Value?Slope (m) = change in y / change in x = (y2 - y1)/((x2 - x1).
Given the points:
(4, 7,000) = (x1, y1)
(6, 6,500) = (x2, y2)
Plug in the values
Slope (m) = (6,500 - 7,000) / (6 - 4)
Slope (m) = (-500) / (2)
Slope (m) = -250
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would really appreciate help thank you!
Answer:
(2, 2) ⇒ (-2, 2)
(-5, 6) ⇒ (-6, -5)
(2, 6) ⇒ (-6, 2)
(-5, 2) ⇒ (-2, -5)
Step-by-step explanation:
The new coordinates can be found using the transformation function for figures rotated 90° about the origin.
TransformationRotation 90° (counterclockwise) about the origin can be described by ...
(x, y) ⇒ (-y, x)
ApplicationThe end points of the diagonal that comes closest to the origin will be transformed to ...
(2, 2) ⇒ (-2, 2)
(-5, 6) ⇒ (-6, -5)
The other diagonal end points will be on the same horizontal and vertical lines as these.
(2, 6) ⇒ (-6, 2)
(-5, 2) ⇒ (-2, -5)
(3x^{4} +3x^{3}+5x^{2})-(x^{4}-6x^{3}+5x^{2} )
Answer: x^{3}(2x+9)
Step-by-step explanation:
Eliminate redundant parentheses:
(3x^{4}+3x^{3}+5x^{2})-1(x^{4}-6x^{3}+5x^{2})
3x^{4}+3x^{3}+5x^{2}-1(x^{4}-6x^{3}+5x^{2})
Distribute:
^{4}+3x^{3}+5x^{2}{-1(x^{4}-6x^{3}+5x^{2})}
3x^{4}+3x^{3}+5x^{2}
Combine like terms UNTIL YOU FIND ONE FACTOR
answer the last question that is blank
The solutions to the given quadratic equation are as follows:
x = 1.10, x = 10.9.
What is a quadratic function?A quadratic function is given according to the following rule:
[tex]y = ax^2 + bx + c[/tex]
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]In which:
[tex]\Delta = b^2 - 4ac[/tex]
For this problem, the equation in item D is:
-x² + 12x - 12 = 0
x² - 12x + 12 = 0
Hence the coefficients are:
a = 1, b = -12, c = 12.
Then the solutions to the equation are found as follows:
Delta = (-12)² - 4 x 1 x 12 = 96x1 = 0.5(12 + sqrt(96)) = 10.9x2 = 0.5(12 - sqrt(96)) = 1.10The solutions are:
x = 1.10, x = 10.9.
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At an airport screening, every 4th passenger will be selected to have their hands swabbed to screen for traces of explosives. Which sampling method is being used
The sampling method used is classified as Systematic.
How are sampling strategies classified?Samples may be classified as:
Convenient: Drawn from a conveniently available pool.Random: All the options into a hat and drawn some of them.Systematic: Every kth element is taken. Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.Stratified: Also divides the population into groups. Then, a equal proportion of each group is surveyed.In this problem, every 4th element is taken, which is a systematic sample with k = 4.
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You have $30 to buy muffins. However, at the shop you can buy 1 muffin for $4. (a) Write an inequality from the above information. (b) Solve this inequality to find the number of muffins you can buy. (c) How much money will you have left over?
Answer:
Let m be the number of muffins.
a) 4m <= 30
b) m <= 7.5, so the maximum number of muffins to buy is 7.
c) $4 × 7 = $28, so $2 will be left over.
the area of a piece of land is 4.08km^2. it is bought at a piece of $6000 per square km. calculate the total cost of the land, giving our answer to the nearest $100
Answer:
22480.000
Step-by-step explanation:
Cost of 1km²=6000
So,
Cost of 4.08km²=6000x4.08
=22480.000
I don't know what nearest $100 means tho maybe nearest hundredth but I'm not sure.
The total cost nearest 100 is = $22500.
What is area?Modern mathematics heavily relies on the concept of area. The area is the quantity that shows the amount of space occupied by a two-dimensional figure or shape or planar lamina in the plane. Simply put, the area is the amount of cloth or other material with the specified thickness needed to build a model of the form or the quantity of paint required to cover the shape's surface in a single layer, or "coat," of paint.
According to the given Information:Cost of 1km2 = 6000
So,
Cost of 4.08km2 = 6000 * 4.08
= 22480.000
Rounding off to 100;
Cost = 22500.00
Hence,
Total cost of the land nearest 100 is = $22500.
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Word Problem On Division
1. a cup can hold 2/9 ( fraction) litres of water. how many cups of water can be filled with 3 litre bottle?
Applying the knowledge of fractions, the number of cups of water that will fill a bottle of 3 liters is calculated as: 13.5 cups.
What are Fractions?Fractions are numbers that indicate a part of whole numbers. For example, 2/9 of a liter means 2/9 of a part of 1 liter.
What is a Proportion?In math, a proportion is simply and equation that sets to ratios equal to each other.
To solve the problem given, create a proportion then use cross product to find the wanted value, which is the number of cups of water that can be filled into a 3-liter bottle.
Let x represent the cups of water we are looking for.
1 cup = 2/9 liter
x = 3 liters
We would have:
(1)(3) = (2/9)(x)
3 = 2x/9
(3)(9) = 2x
27/2 = x
x = 13.5
The number of cups of water to fill a 3-liter bottle is: 13.5.
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Elsa went to Malacca with three friends. The total amount spent by them is RMx. If Elsa spent RM 145, and the amount spent by each of her three friends did not exceed RM 110 per person, which of the following cannot be the value of x.
The total amount spent by Elsa and her friends must not exceed RM 475; 475 ≤ x
InequalityTotal amount spent = RMxAmount spent by Elsa = RM 145Amount spent by each of her three friends = RM 110Elsa + 3(her friends) ≤ Total
145 + 3(110) ≤ x
145 + 330 < x
475 ≤ x
Therefore, the total amount spent by Elsa and her friends must not exceed RM 475; 475 ≤ x
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Una estrategia de cálculo mental con
números decimales consiste en buscar
parejas de números cuya suma sea un
número entero. Aplica esta estrategia para
calcular mentalmente:
a. 15,75 + 1,2 + 0,25
b. (–1,8) + 2,45 + (–0,20)
c. 3,5 + 11,8 + 12,5
d. 7,38 – 1,5 + 2,62
Esta estrategia se puede aplicar sumando 15,75 + 0,25, –1,8 + –0,20, 3,5 + 12,5 y 2,62 + 7,38 antes de sumar el tercer número dado en cada caso.
¿En qué consiste está estrategia?La estrategia propuesta consiste en sumar dos números decimales que den como resultado un número entero antes de sumar el tercer número decima. Por ejemplo si teneos 1,4 + 0,6 + 1,2, se debe sumar primero 1,4 + 0,6 lo que es igual a 2 antes de sumar el 1,2.
¿Por qué utilizar esta estrategia?Este estrategia es beneficiosa porque facilita sumar números decimales.
¿Cómo aplicar está estrategia?15,75 + 1,2 + 0,25 = 16 (0,25+15,75) + 1,2 = 17,2 (–1,8) + 2,45 + (–0,20) = -2 (-1,8-0,20) + 2,45 = 0,453,5 + 11,8 + 12,5 = 16 (12,5+3,5) +11,8 = 27.87,38 – 1,5 + 2,62 = 10 (7,38+2,62) + 2,62 = 12,62Aprenda más sobre números decimales en: https://brainly.com/question/24620232
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A student is constructing a pair of perpendicular lines using a compass and ruler. Here are her first steps:
Step 1: The student draws her first line and labels it l. She marks a point A (not on the first line) for the second line to pass through.
Step 2: She puts the compass point on A and draws an arc that intersects l at two points. She labels the points B and C.
Step 3: Without changing the compass setting, she puts the compass point on B and draws a large arc.
What should be her next step?
The next step she should take is to use her ruler to join the given point to the point where the arcs intersect.
Steps in constructing perpendicular linesPlace your compass on the given point Draw an arc across the line on each side of the given point. Do not adjust the compass width when drawing the second arcFrom each arc on the line, draw another arc on the opposite side of the line from the given point. The two new arcs will intersect.Use your ruler to join the given point to the point where the arcs intersect.Use your compass and ruler to draw a perpendicular line from each given point to the line segmentFrom this, we can deduce that her next step is to use her ruler to join the given point to the point where the arcs intersect
Thus, the next step she should take is to use her ruler to join the given point to the point where the arcs intersect.
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what is the solution to this equation 7x-3(x-6)=30
Hi there,
please see below for solution steps :
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⨠ use the distributive property
[tex]\sf{7x-3(x-6)=30}[/tex]
[tex]\sf{7x-3x+18=30}[/tex]
⨠ combine like terms
[tex]\sf{4x+18=30}[/tex]
⨠ subtract both sides by 18
[tex]\sf{4x=30-18}[/tex]
[tex]\sf{4x=12}[/tex]
⨠ divide both sides by 4
[tex]\boxed{\sf x=3}[/tex]
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Trigonometry Question:
Find all solutions on the interval [0,2π)
12sin^2(x)+cos(x)-6=0
Recall the Pythagorean identity,
[tex]\sin^2(x) + \cos^2(x) = 1[/tex]
Use it to rewrite the equation in terms of cos only.
[tex]12 (1 - \cos^2(x)) + \cos(x) - 6 = 0[/tex]
[tex]-12 \cos^2(x) + \cos(x) + 6 = 0[/tex]
Factorize the left side.
[tex]-(3\cos(x) + 2) (4\cos(x) - 3) = 0[/tex]
Solve the two cases for [tex]\cos(x)[/tex].
[tex]3 \cos(x) + 2 = 0 \text{ or } 4\cos(x) - 3 = 0[/tex]
[tex]\cos(x) = -\dfrac23 \text{ or } \cos(x) = \dfrac34[/tex]
From the first equation, we get one family of solutions:
[tex]\cos(x) = -\dfrac23[/tex]
[tex]x = \cos^{-1}\left(-\dfrac23\right) + 2n\pi \text{ or } x = -\cos^{-1}\left(-\dfrac23\right) + 2n\pi[/tex]
From the second equation, we get another family:
[tex]\cos(x) = \dfrac34[/tex]
[tex]x = \cos^{-1}\left(\dfrac34\right) + 2n\pi \text{ or } x = -\cos^{-1}\left(\dfrac34\right) + 2n\pi[/tex]
where [tex]n[/tex] is an integer.
We get solutions in the given domain for
[tex]n = 0 \implies \boxed{x = \cos^{-1}\left(-\dfrac23\right)} \text{ or } \boxed{x = \cos^{-1}\left(\dfrac34\right)}[/tex]
[tex]n=1 \implies \boxed{x = 2\pi - \cos^{-1}\left(-\dfrac23\right)} \text{ or } \boxed{x = 2\pi - \cos^{-1}\left(\dfrac34\right)}[/tex]
Find using appropriate Properties:
6/7 x -2/3 + 3/5 + 5/8 x -6/7
The simplified form of the expression is given as 83x/56 -(97/105)
Finding the value of unknown variablesAlphabets are usually represented as unknown variables in a equation or expression.
Given the following expression shown below
6/7 x -2/3 + 3/5 + 5/8 x -6/7
Collect the like terms to have;
6/7 x+ 5/8 x -2/3 + 3/5 -6/7
Simplify
48x+35x/56 - (70-63 + 90)/105
The final expression will be given as;
83x/56 -(97/105)
Hence the simplified form of the expression is given as 83x/56 -(97/105)
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The graph of a linear relation passes through the point (-3,-5) and has a slope of 3.
Determine an equation for this linear relation in slope intercept form.
Answer:
y = 3x + 4
Step-by-step explanation:
Substituting into point-slope form and converting to slope-intercept form,
[tex]y+5=3(x+3) \\ \\ y+5=3x+9 \\ \\ \boxed{y=3x+4}[/tex]
what is a real world example of a rational function, and how could you graph it and put it in a table?
An example of the real world example of a rational function would be when a person would decide to share a cookie with their friend. Each of them would get half of the cookie each.
What is a rational function?This is the term that is used to refer to the fraction that is represented by the use of a rational fraction. That is there is denominator and a numerator.
The denominator must have a variable and this variable has to be of degree 1. Hence the real world example of a rational function would be when a person would decide to share a cookie with their friend. Each of them would get half of the cookie each.
How to graph a real world situationFirst you have to know if it is an inequality or not. Then you have to assign x and y variables to numbers. From here you form an equation. This equation is plotted on a graph.
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I need help finding the quotient of this equation in simplified form.
by breaking it down u can write it as
15p^-4/_20p^-12 * q^-6/q^-3
15/-20=-3/4
using law of indices we have
-3/4p^-4+12 * q^-6+3
-3/4p^8q^-3
the answer is the first own
Select the correct answer. What is the value of the limit lim x 2 (x^2+3x+1/x^3+x+1) ? A. B. 1 C. D.
So by direct evaluation we can see that the limit when x tends to 2 is equal to 1.
How to get the value of the limit?
Here we want to get the limit:
[tex]\lim_{x \to \ 2} \frac{x^2 + 3x + 1}{x^3 + x + 1}[/tex]
First, we can try to evaluate directly in x = 2 and see if it does not generate any problem, we will get:
[tex]\lim_{x \to \ 2} \frac{x^2 + 3x + 1}{x^3 + x + 1} = \frac{2^2 + 3*2 + 1}{2^3 + 2 + 1} = 1[/tex]
So by direct evaluation we can see that the limit when x tends to 2 is equal to 1.
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Which graph shows the solution to this system of in
y>-1/3x+1
y> 2x-3
Answer:
Step-by-step explanation:
the graph is down below
What will be the length of the diagonal of a rectangle of sides 6 m and 8 m?
Answer:
The length of the diagonal of a rectangle is 10m
Step-by-step explanation:
There is a visual below,
The diagonal of a rectangle has formed 2 right triangles.
This diagonal is called hypotenuse side length of a triangle
To find the hypotenuse, we can use the Pythagorean Theorem
a² + b² = c²
we are given the length of a and b, where a = 6 and b = 8
(6)² + (8)² = c²
36 + 64 = c²
100 = c²
√100 = c
10 = c
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35 Points + Brainest
Answer:
5/12a + 1/3b
Step-by-step explanation:
2/3a + 1/6b + (-1/6a) + 3/18b + (-1/12a)
[2/3a + (-1/6a) + (-1/12a)] + [3/18b + 1/6b]
5/12a + 1/3b
Find the value of n in this equation.
Answer:
D. 9=========================
GivenTriangle with:
Base of n² -3,Midsegment of 39.To findThe value of n.SolutionAs per definition of midsegment, it is connecting the midpoints of two sides and its length is half the length of the opposite side of the triangle.
So we have:
(n² - 3)/2 = 39Solve it for n:
n² - 3 = 78n² = 81n = √81n = 9Correct choice is D.
william bougght canned goods at 2.40 per can.he wants to increase the price per can so that he makes a 25% profit. what will the selling price per can be?
Answer:
The answer is 3
Step-by-step explanation:
25% of 2.40 equals 0.6
so 3 will be the total price and he will get 0.6 profit.
William bought canned goods at 2.40 per can. he wants to increase the price per can so that he makes a 25% profit, the selling price per can be, 3.00
What is the percentage?The percentage is a mathematical term, which means a number or a ratio which is represented in fractions of 100. We use the '%' symbol to represent the percentage.
Formula for percentage;
Percentage = (present quantity/whole quantity)×100
Given that,
William bought canned goods at 2.40
He wants to increase the price per can so that he makes a 25% profit
The selling price per can be =?
Percentage = Amount he wants to increase/previous amount×100
25 = x/2.40×100
x = 0.60
new selling price = 2.40+0.60
= 3.00
Therefore, The new selling price is 3.00 per can
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write the expression as the sine or cosine of an angle
The expression, written as the sine of an angle is sin (7π/10)
Trigonometry IdentitiesFrom the question, we are to write the given expression as the sine or cosine of an angle.
The given expression is
sin(π/5)cos(π/2) + sin(π/2)cos(π/5)
Let A = π/5
and
B = π/2
Thus, we get
sinA cosB + sinB cosA
From the given information, we have that
sin(A ± B) = sinA cos B ± cosA sinB
∴ sin(A + B) = sinA cos B + cosA sinB
Now,
sinA cosB + sinB cosA = sinA cosB + cosA sin B
∴ sinA cosB + sinB cosA = sin (A + B)
Put A = π/5
and
B = π/2
sinπ/5 cosπ/2 + sinπ/2 cosπ/5 = sin (π/5 + π/2)
sinπ/5 cosπ/2 + sinπ/2 cosπ/5 = sin (7π/10)
Hence, the expression, written as the sine of an angle is sin (7π/10)
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Use a right-hand sum with 4
intervals to approximate the area
under f(x) = 4 - x² between
x = 0 and x = 2.
Answer:
17 / 4
Step-by-step explanation:
To find the right sum, you need to....
Step #1: Find Δx
Step #2: Find [tex]x_k[/tex]
Step #3 Make the right-hand sum equation: ∑[tex]^n_{k=1}f(x_k)[/tex]Δx
Step #4: Solve the right-hand sum equation
I NEED HELP WITH THIS ASAP! Find x and y
Answer: D
Step-by-step explanation: a^2+b^2=c^2
so use y value for b2 and 6 square root 3 as a and check with it.
In the expansion of (3a + 4b)8, which of the following are possible variable terms? Explain your reasoning.
a2b3; a7b; ab8; b8; a4b4; a6b2; a3b4; a8
pls help
The terms b⁸, a⁶ · b², a⁴ · b⁴, a⁷ · b and a⁸ are part of the expansion of (3 · a + 4 · b)⁸.
How to find the missing terms of a power polynomials
In this case, we have to expand a power binomial by means of the Pascal's triangle, which offers a useful and quick resource to expand expressions of this kind, now we proceed to present the result of this approach:
(3 · a + 4 · b)⁸ = 6 561 · a⁸ + 69 984 · a⁷ · b + 326 592 · a⁶ · b² + 870 912 · a⁵ · b³ + 1 451 520 · a⁴ · b⁴ + 1 548 288 · a³ · b⁵ + 1 032 192 · a² · b⁶ + 393 216 · a · b⁷ + 65 536 · b⁸
Such combinations of products between variables a and b are also supported by the theorem of the binomial. Finally, the terms b⁸, a⁶ · b², a⁴ · b⁴, a⁷ · b and a⁸ are part of the expansion of (3 · a + 4 · b)⁸.
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4. Which of the following can be used
to support the idea that the set of
polynomials is closed under
multiplication?
A (5x-1)(3x² +4x)
B
(9x³-5)(2x-17)
(10x0.5-8)(5x0.5 +4)
D(2x¹5x¹)(7x-2x5)
The option that can be used to support the idea that the set of polynomials is closed under multiplication is; Option C: (10x^(0.5) - 8)(5x^(0.5) + 4)
What is the Closure property under multiplication?When multiplying polynomials, the variables' exponents are added, according to the rules of exponents. It is pertinent to note that the exponents in polynomials are whole numbers. The whole numbers are closed under addition, which guarantees that the new exponents will be whole numbers. Thus, we can also say that the polynomials are closed under multiplication.
Now, looking at the options, we can say that option C is the only polynomial that is closed under multiplication because its' variables and exponents will not change;
(10x^(0.5) - 8)(5x^(0.5) + 4)
The output will retain the same thing.
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HELPPPP (x-y)^3-(y-x)^2
Answer:
(x-y)(x-y)(x-y)= x²-yx+x²-yx-yx+y²-yx+y²
2x²-4yx+2y²
(y-x)(y-x)= y²-yx-yx+x²
y²-2yx+x²
-(y²-2yx+x²) = -y²+2yx-x²
2x²-4yx+2y²-y²+2yx-x²= x²-2yx+y²
or
(x−y−1)(x−y)² ≡ x³−x²+3xy²+2xy−y³−y²−3yx³
complete the remainder of the table for the given function rule.
Answer:
following the (x,y) coordinate system,
(0,4) ; (1,1) ; (2,-2)
Step-by-step explanation:
youre given the value of the x variable in the table, so all you need to do is substitute x and follow pedmas!! hope this helps<3
In quadrilateral qrst, angle r s t measures (5x 15)°. angle tqr measures (4x 3)°. circle p is inscribed with quadrilateral q r s t. what is the measure of angle rst?
The measure of the angle rst is [tex]105^{o}[/tex].
What is the inscribed quadrilateral theorem?According to the theorem, a quadrilateral can be inscribed by a circle if and only if its opposing angles are supplementary. A quadrilateral that may be encircled by a circle is known as a cyclic quadrilateral.
The sum opposite angles of a quadrilateral is 180 degrees.
We can see that the angles rst and angle tqr are opposite angles of quadrilateral qrst, hence supplementary angles.
Therefore,
<RST + <TQR = 180
5x+15 + 4x+ 3 = 180
9x + 18 = 180
9x = 180 - 18
9x = 162
x = 162/9
x = 18
Since <RST = 5x+15
<RST = 5(18) + 15
<RST = 90 + 15
<RST = 105degrees
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