The water level of a river is 170 feet. The river recedes 4 feet each year. Ingrid claims that the equation that represents this scenario is y = 170x – 4. Is her equation correct? Explain
Sample Answer: No, Ingrid is incorrect. The initial value in the scenario is 170 feet, which represents the y − intercept. Receding 4 feet in the scenario represents the rate of change, which is the slope. In slope-intercept form, y = mx + b, where m represents slope and b represents the y−intercept, so the correct equation is y = −4x + 170.
Answer:
No, Ingrid is incorrect. The initial value in the scenario is 170 feet, which represents the y − intercept. Receding 4 feet in the scenario represents the rate of change, which is the slope. In slope-intercept form, y = mx + b, where m represents slope and b represents the y−intercept, so the correct equation is y = −4x + 170.
Step-by-step explanation:
Solve the equation 4(2y-6)+3=11. A.3. B.-3. C.4. D.5
PLEASE HELP
Natalie borrowed $1,800 from her mother to purchase a pre-owned car. She agrees to repay this amount by paying her mother $45 per week. This situation can be modeled by the function Which inequality represents the domain for this function?
The domain of the function is x ≤ 40, representing the maximum number of weeks Natalie can take to repay the loan.
Explanation:The situation can be modeled by the function f(x) = 1800 - 45x, where x represents the number of weeks. The domain of this function represents the possible values for x. Since Natalie borrowed $1800 and agrees to repay $45 per week, the maximum number of weeks she can take to repay the loan is given by:
Therefore, the inequality that represents the domain of the function is x ≤ 40. This means that Natalie can take up to 40 weeks to repay the loan without exceeding the borrowed amount.
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which point on the number line represents the product (5)(-2)(-1)
A ramp leading to the freeway overpass is 200 feet long and rises 37 feet. what is the measure of the angle formed between the ramp and the freeway?
A ramp leading to the freeway overpass is 200 feet long and rises 37 feet. The measure of the angle formed between the ramp and the freeway is
[tex]\mathbf{ \theta = sin^{-1} \Big ( \dfrac{37}{200} \Big)}[/tex]
From the information given:
The measure of the angle formed θ between the ramp and the freeway overpass can be determined by using the sine angle which is:
[tex]\mathbf{sin \theta = \dfrac{opposite}{hypotenuse}}[/tex]
[tex]\mathbf{sin \theta = \dfrac{37}{200}}[/tex]
[tex]\mathbf{ \theta = \dfrac{1}{sin} \Big( \dfrac{37}{200}\Big)}[/tex]
[tex]\mathbf{ \theta = sin ^{-1} \Big( \dfrac{37}{200}\Big)}[/tex]
Therefore, the measure of the angle formed between the ramp and the freeway is
[tex]\mathbf{ \theta = sin^{-1} \Big ( \dfrac{37}{200} \Big)}[/tex]
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Alyssa is jogging near Central Park. She runs along 65th Street for about 0.19 miles, turns right and runs along Central Park West for about 0.28 miles. She then turns right again and runs along Broadway until she reaches her starting point. How long is her total run to the nearest hundredth of a mile? 0.68 miles 0.81 miles 1.15 miles 1.44 miles
The total distance covered by her is 0.81 miles.
Given thatAlyssa is jogging near Central Park.
She runs along 65th Street for about 0.19 miles, turns right, and runs along Central Park West for about 0.28 miles.
She then turns right again and runs along Broadway until she reaches her starting point.
We have to determine
How long is her total run to the nearest hundredth of a mile?
According to the question
She runs along 65th Street for about 0.19 miles, turns right, and runs along Central Park West for about 0.28 miles.
Alyssa's route can be considered a right triangle with legs of length 0.19 and 0.28 (hundredths).
The total distance run is determined by using the Pythagoras theorem.
What is the Pythagorean theorem?Pythagorean theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Therefore,
The distance run by her is,
[tex]\rm x^2 = (0.19)^2 +(0.28)^2\\\\ x^2=0.0361 + 0.784\\ \\ x^2 = .1145\\ \\ x= \sqrt{.1145} \\\\ x= 0.34[/tex]
Therefore,
The total distance covered by her is,
= .34 + .19 + .28
= 0.81 miles
Hence, the total distance covered by her is 0.81 miles.
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how would the expression x^3+27 be rewritten using sum of cubes?
The expression x³ + 27 can be rewritten as (x + 3) (x² - 3x + 9).
The expression x³ + 27 can be rewritten using the formula for the sum of cubes, which is
a³ + b³ = (a + b) (a² - ab + b²)
In this case, we can recognize that 27 is equivalent to 3³
Therefore, we can set 'a' to be 'x' and 'b' to be '3' and apply the formula.
So, the expression x³ + 27 rewrites to:
x³ + 3³ = (x + 3)(x² - 3x + 9)
The expression x³+27 is rewritten as the sum of cubes by identifying a as x and b as 3, then applying the formula a³ + b³ = (a + b)(a² - ab + b²) to get (x + 3)(x² - 3x + 9).
The expression x³+27 can be rewritten using the sum of cubes formula. The sum of cubes formula is a³ + b³ = (a + b)(a² - ab + b²). In this case, x³ can be viewed as a^3 and 27 (which is 3³) as b³. Thus, to express x³ + 27 as a sum of cubes, we identify a as x and b as 3, and then apply the formula.
Using the sum of cubes formula:
Identify a = x and b = 3.
Substitute a and b into the sum of cubes formula: (x + 3)(x² - 3x + 9).
Simplify if necessary.
Therefore, x³ + 27 is rewritten as (x + 3)(x² - 3x + 9).
What is the point-slope form of a line with slope -4 that contains the point (-2, 3?
Answer:
y-3=-4(x+2)
Step-by-step explanation:
If y = f(x), and y = a f(x) is a vertical stretch or compression, a > 1 causes the graph to be stretched vertically by a factor of a.
A vertical stretch in the context of graphing functions occurs when the function is multiplied by a positive constant greater than 1, resulting in the graph being stretched vertically by that factor without affecting the y-intercept.
A vertical stretch occurs when we multiply the function by a positive constant greater than 1. For example, if we have y = a f(x) and a is greater than 1, this results in the graph being stretched vertically by a factor of a. This type of transformation doesn't affect the y-intercept since the behavior of the graph at x=0 remains unchanged. Multiplying the independent variable by a constant such as 1/2 would result in a horizontal stretching or compression, but this is different from the vertical stretching effect we are discussing here.
Additionally, suppose the vertical stretch factor is a natural number. In that case, we can think of the stretched function as being the sum of the original function added to itself repeatedly that number of times. This additive property also extends to the derivative, as the derivative of the vertically stretched function is the original derivative multiplied by the stretch factor. This is known as the vertical stretch property in the context of derivatives and calculus.
Find the measure of an angle whose measure is 20° less than the measure of its supplement.
The function f(x) = is reflected across the y-axis to create the function g(x). Which ordered pair is on g(x)?
Answer:
A
Step-by-step explanation:
does anyone know if this is correct or how to do this? (part a,b, and c)
Part A you would use 200-L ( since you have 400 feet total 200 feet would equal length plus width)
Part B 200 - 80 = 120
Part C 200-90 = 110
area = 90 x 110 = 9900 square feet
N is between m and p. If MN=3x, NP=x, and MP= 6x-6, find the numerical value of MN
Answer:
3
Step-by-step explanation:
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Convert 350 US dollars to British pound sterling .use 1 US dollar = 0.62 British pound sterling
The graph represents the system of inequalities .
The test point satisfies both of the inequalities in the system represented by the graph.
-2,3 -1,1 0,2 1,1
3x+2y is less than or equal to 3 and 3x+4y is greater than or equal to 2
3x+2y is less than or equal to 3 and 3x+4y is greater than 2
3x+2y is less than or equal to 3 and 3x+4y is less than 2
3x+2y is less than or equal to 3 and 3x+4y is less than or equal to 2
The solution is 3x+2y is less than or equal to 3 and 3x+4y is greater than or equal to 2
How to solve the inequality
Given the inequalities:
1. [tex]\( y < -\frac{3}{2}x + \frac{3}{2} \)[/tex]
2. [tex]\( y > -\frac{3}{4}x + \frac{1}{2} \)[/tex]
The inequality [tex]\( y < -\frac{3}{2}x + \frac{3}{2} \)[/tex] represents a dashed line with a slope of [tex]\( -\frac{3}{2} \)[/tex] and a y-intercept of [tex]\( \frac{3}{2} \)[/tex]. It does not include the points on the line (hence the dashed line).
3x + 4y = 2
The inequality [tex]\( y > -\frac{3}{4}x + \frac{1}{2} \)[/tex]
slope of [tex]\( -\frac{3}{4} \)[/tex]
y-intercept of [tex]\( \frac{1}{2} \)[/tex].
The region where both inequalities are simultaneously true
[tex]\( y > -\frac{3}{4}x + \frac{1}{2} \)[/tex]
and below the line
[tex]\( y < -\frac{3}{2}x + \frac{3}{2} \)[/tex]
This confirms the solution as the point (-2, 3) and the region it falls into on the graph.
In the figure below, m ROP = 125°.
Find the measure of each arc. For each arc, write two or more complete sentences explaining which theorem or postulate you used to find your answer. Include your equations and calculations in your final answer.
Answer: Hello!
In the figure, Q and P are on opposite ends of the circle, and the same is for R and S, which means that the line that connects Q and P, or R and S, divides the circle in two equal halves. From this, we know that the angle between QoP is 180°, and the same for the angle RoS = 180°.
We also know that the angle RoP = 125°, then the angle between Q and R is the same as the angle between Q and P minus the angle between R and P.
this is : QoR = QoP - RoP = 180° - 125° = 55°
then QoR and RoP are supplementary angles, wich means that the addition adds up to 180°.
And is easy to see that the angles SoQ and PoS are reflexes of RoP and QoR respectively, then:
SoQ = 125° and PoS = 55°, where this angles also are supplementary.
Suppose U={1,2,3,4,5,6,7,8,9,10} is the universal set G= {1,2,3,4,5,6,7}. What is G
Final answer:
The set G is a subset of the universal set U and contains the first seven natural numbers within U: {1,2,3,4,5,6,7}.
Explanation:
In mathematics, particularly in set theory, when we talk about the set G, we are referring to a collection of elements that are all part of a larger universal set, denoted by U. In your case, the universal set U is {1,2,3,4,5,6,7,8,9,10} and the set G is given as {1,2,3,4,5,6,7}. The set G contains the first seven natural numbers within the universal set.
Understanding the concept of the universal set and subsets is fundamental in set theory. The universal set is the set that contains all possible objects (usually numbers in this context) under consideration, and any other set is a subset if all its elements are also elements of the universal set. The subset G in your example is defined by explicitly listing its members, which are all part of the universal set U.
Part A: If (7 to the power of 2)x = 1, what is the value of x?
Part B: If (7to the power of 0)x = 1, what are the possible values of x?
If Mercury's mass is 3 × 10^23 kilograms, and Saturn's mass is 6 × 10^26 kilograms, which statement is true?
Answer:
Saturn has about 2,000 times more mass.
6x−3y=−6
solve for y
The solution to the equation is y = 2 + 2x.
We have,
To solve the equation 6x - 3y = -6 for y, we can isolate the term with y by performing the following steps:
Start with the equation: 6x - 3y = -6.
To isolate the term with y, subtract 6x from both sides of the equation:
6x - 3y - 6x = -6 - 6x.
This simplifies to: -3y = -6 - 6x.
Next, divide both sides of the equation by -3 to solve for y:
(-3y) / -3 = (-6 - 6x) / -3.
This simplifies to: y = 2 + 2x.
Therefore,
The solution to the equation is y = 2 + 2x.
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Two number cubes are rolled. If all numbers are equally likely, what is the probability that the sum is 8?
6/36 ≈ 17%
4/36 ≈ 11%
8/36 ≈ 22%
5/36 ≈ 14%
"Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one".
For the given situation,
The sample space for rolling two cubes,
s = { (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6) }
⇒[tex]n(s)=36[/tex]
The event is getting the sum 8,
[tex]e=[/tex] { [tex](2,6), (3,5), (4,4), (5,3), (6,2)[/tex] }
⇒[tex]n(e)=5[/tex]
The formula to find the probability of event, [tex]P(e)=\frac{n(e)}{n(s)}[/tex]
⇒[tex]P(e)=\frac{5}{6}[/tex]
⇒[tex]P(e)=13.8\%[/tex] ≈ [tex]14\%[/tex]
Hence we can conclude that the probability that the sum is 8 is 5/36 ≈ 14%.
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What's the possible answer
Philip buys the pizza shown below: A circular pizza is shown. The center is labeled as point A and a point on the circumference is marked B. What does AB represent?
The number of vertices in a prism is twice the number of vertices of one of the bases. How many vertices does one of the bases of a regular prism with 14 faces and 36 edges have? Euler’s formula: V + F = E + 2 12 13 17 24
The number of vertices will be 24. The correct option is D.
What is a prism?A prism is a polyhedron in geometry that has n parallelogram faces that connect the n-sided polygon basis, the second base, which is a translated duplicate of the first base, and the n faces. The bases are translated into all cross-sections that are parallel to them.
It is given that the number of vertices in a prism is twice the number of vertices of one of the bases. The number of the vertices of a regular prism with 14 faces and 36 edges is calculated as below:-
Use Euler's formula:-
V + F = E + 2
V + 14 = 36 + 2
V + 14 = 38
V = 38 - 14
V = 24
Therefore, the number of vertices will be 24. The correct option is D.
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Using Euler's formula, V + F = E + 2, with the given values for the faces (F = 14) and edges (E = 36), we determine there are 24 vertices in the prism. Considering a prism has twice as many vertices as one of its bases, it follows that one base has 12 vertices.
The question asks about the number of vertices on one of the bases of a regular prism that has 14 faces and 36 edges.
First, we use Euler's formula, which is V + F = E + 2, where V, F, and E represent the number of vertices, faces, and edges, respectively.
In this case, we have F = 14 and E = 36, so plugging these into Euler's formula gives us V + 14 = 36 + 2, therefore V = 24 vertices in total for the prism.
Since the prism has two congruent bases and the remainder of the faces are parallelograms connecting the bases, we can say that the number of vertices of the prism is twice the number of vertices of one of its bases.
So if V is 24, the number of vertices for one base is V/2, which is 12. That means each base of the prism has 12 vertices.
Ab¯¯¯¯¯ is congruent to cd¯¯¯¯¯. point p is the midpoint of ab¯¯¯¯¯, and point q is the midpoint of cd¯¯¯¯¯. which relationship must be true? ac¯¯¯¯¯≅pq¯¯¯¯¯ bc¯¯¯¯¯≅cq¯¯¯¯¯ pb¯¯¯¯¯≅cd¯¯¯¯¯ ap¯¯¯¯¯≅dq¯¯¯¯¯
The ordered pair(1,0) is a solution to the inequality y true or false?
Which of the following is a polynomial with roots 2, 3i, and −3i? f(x) = x3 − 2x2 + 6x − 9 f(x) = x3 − 6x2 + 9x − 18 f(x) = x3 − 6x2 + 18x − 2 f(x) = x3 − 2x2 + 9x − 18
Answer:
[tex]f(x)=x^3-2 x^2+9 x-18[/tex]
Step-by-step explanation:
The roots of the polynomial are [tex]2,3i,-3i[/tex].
This implies that [tex]x-2,x-3i,x+3i[/tex] are factors of the given polynomial.
The polynomial will have equation;
[tex]f(x)=(x-2)(x-3i)(x+3i)[/tex]
We expand using difference of two squares on the complex conjugates to get;
[tex]f(x)=(x-2)(x^2-(3i)^2)[/tex]
[tex]\Rightarrow f(x)=(x-2)(x^2-(-3)^2(i)^2)[/tex].
[tex]\Rightarrow f(x)=(x-2)(x^2-9(i)^2)[/tex].
Recall that;
[tex]\boxed{i^2=-1}[/tex]
[tex]\Rightarrow f(x)=(x-2)(x^2+9)[/tex].
Expand using the distributive property to get;
[tex]\Rightarrow f(x)=x^3+9x-2x^2-18[/tex].
We rewrite in standard form to obtain;
[tex]f(x)=x^3-2x^2+9 x-18[/tex]
Given rectangle ABCD, segment AC is a diagonal, segment BE is perpendicular to segment AC at E. Segment AE = 8 inches and segment CE = 5 inches. What is the length of segment BE?
what is the equation of the graphed line in point-slope form?
A. y+3=2(x+3)
B. y=2(x+3)
C. y+3=2x
D. y-3=2(x-3)
You are mailing a package that weighs 8 pounds, and sending it first class. The post office charges $0.44 for the first ounce, and charges $0.20 for each additional ounce. How much is the total cost to mail this package?
Final answer:
To calculate the mailing cost for an 8-pound package sent first class, convert to ounces, then apply the charges for the first ounce and each subsequent ounce. The total cost is $25.84.
Explanation:
The question involves calculating the total cost of mailing a package that weighs 8 pounds, first class, with specific charges for the first ounce and each additional ounce. To calculate the cost, we first need to convert the package's weight from pounds to ounces. There are 16 ounces in 1 pound, so an 8-pound package is equivalent to 8 x 16 = 128 ounces.
The post office charges $0.44 for the first ounce. Thereafter, it charges $0.20 for each additional ounce. The cost for the additional ounces is $0.20 x (128 - 1) = $25.40. Now, add the cost for the first ounce, so the total cost is $0.44 + $25.40 = $25.84.