The variable 'm' represent the slope.
What is slope?The slope is defined as the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run.
Given:
y= mx + b
The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line.
The net change in y coordinate is Δy, while the net change in the x coordinate is Δx.
So the change in y coordinate with respect to the change in x coordinate can be written as,
m = Δy/Δx
where, m is the slope
The slope of a line can be calculated from the equation of the line. The general slope of a line formula is given as,
y = mx + b
where,
m is the slope, such that m = tan θ = Δy/Δx
θ is the angle made by the line with the positive x-axis
Δy is the net change in y-axis
Δx is the net change in x-axis
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1. What is the sum or difference?
4x^10 - 9x^10 (1 point)
(A). -5x^10
(B). -5x^20
(C). -36x^20
(D). -36x^20
2. What is the sum or difference?
6y^5 - 9y^5 (1 point)
(A). -3y^10
(B). 15y^5
(C). -54y^5
(D). -3y^5
3. Write the Polynomial in standard form. Then name the Polynomial based on its degree and number of terms.
2 - 11x^2 - 8x + 6x^2 (1 point)
(A). -5x^2 - 8x + 2; quadratic trinomial
(B). -5x^2 - 8x; quadratic binomial
(C). -6x^2 - 8x - 2; cubic polynomial
(D). 6x^2 - 8x + 2; cubic trinomial
4. A biologist studied the populations of white-sided jackrabbits and black-tailed jackrabbits over a 5-year period. The biologist modeled the populations, in thousands, with the following polynomials where x is time, in years.
White-sided jackrabbits: 5.5x^2 - 9.2x + 6.9
Black-tailed jackrabbits: 5.5x^2 + 9.9x + 1.3 (1 point)
(A). 11x^2 + 0.7x + 8.2
(B). 11x^2 - 0.7x + 8.2
(C). 11x^2 - 0.7x - 8.2
(D). -11x^2 + 0.7x - 8.2
Someone please help! Unit 3 Lesson 9, Polynomials and Factoring!
Solving question 1 : What is the sum or difference?
[tex] 4x^{10} - 9x^{10} \\\\
(4-9)x^{10} \\\\
-5x^{10} [/tex]
Hence, option A is correct i.e. [tex] -5x^{10} [/tex].
Solving question 2 : What is the sum or difference?
[tex] 6x^{5} - 9x^{5} \\\\
(6-9)x^{5} \\\\
-3x^{5} [/tex]
Hence, option D is correct i.e. [tex] -3x^{5} [/tex].
Solving question 3 : Write the Polynomial in standard form.
2 - 11x² - 8x + 6x²
We can combine like terms, and rewriting it in decreasing power of x's.
⇒ - 11x² + 6x² - 8x + 2
⇒ (-11 + 6)x² - 8x + 2
⇒ -5x² - 8x + 2
Hence, option A is correct i.e. -5x² - 8x + 2; quadratic trinomial.
Solving question 4 :
White-sided jackrabbits: 5.5x² - 9.2x + 6.9
Black-tailed jackrabbits: 5.5x² + 9.9x + 1.3
Total population = White-sided jackrabbits + Black-tailed jackrabbits
Total population = (5.5x² - 9.2x + 6.9 ) + (5.5x² + 9.9x + 1.3)
Total population = (5.5 + 5.5)x² + (9.9 - 9.2)x + (6.9 + 1.3 )
Total population = 11x² + 0.7x + 8.2
Hence, option A is correct i.e. 11x² + 0.7x + 8.2
I need the answer to question number 12
Katherine is landscaping her home with juniper trees and pansies. She wants to arrange 15 pansies around each of 8 trees. Each tree costs $20.75 and a six-pack of pansies costs $2.50. Explain how to write an expression to find Katherine’s final cost.
Answer:
Look below
Step-by-step explanation:
The total cost of the trees must be added to the total cost of the pansies. The tree cost is the cost of one tree times eight. The pansy cost is the cost for 15 pansies multiplied by 8 trees, then divided by the number of pansies in a pack: 20.75(8) + 2.50(15)(8) ÷ 6.
For customers purchasing a refrigerator at a certain appliance store, let A be the event that the refrigerator was manufactured in the U.S., B be the event that the refrigerator had an icemaker, and C be the event that the customer purchased an extended warranty. Relevant probabilities are below.
P(A) = 0.80 P(B | A) = 0.94 P(B | A' ) = 0.79
P(C | A ∩ B) = 0.76 P(C | A ∩ B' ) = 0.56
P(C | A' ∩ B) = 0.68 P(C | A' ∩ B' ) = 0.33
(c) Compute P(B ∩ C).,
Milena's take-home pay is $1200 a month. She spends 12% of her take-home pay on her cable bill. How much is Milena's monthly cable bill?
Answer:
$144
Step-by-step explanation:
Just did test
Which of the following fractions is not in simplest form?
3/4
7/10
9/12
4/15
Simplify completely. square root of 18y^10
Simplify the rational expression. state any restrictions on the variable. n^4-11n^2+30/n^4-7n^2+10
To simplify the given rational expression, we factor both the numerator and the denominator, cancel out the common factor, and express the result as (n^2 - 6) / (n^2 - 2), with restrictions on n that it can't equate to the square roots of 5 or 2.
Explanation:The question involves simplifying the rational expression n^4 - 11n^2 + 30 divided by n^4 - 7n^2 + 10, and stating any restrictions on the variable. To simplify this, we first factor both the numerator and the denominator.
Numerator: (n^2 - 5)(n^2 - 6)
Denominator: (n^2 - 5)(n^2 - 2)
After factoring, we can cancel out the common factor (n^2 - 5) from both the numerator and the denominator. This leaves us with (n^2 - 6) / (n^2 - 2).
However, we must state the restrictions on the variable n. The original denominator cannot be equal to zero, thus n^2 cannot be equal to 5 or 2, leading to restrictions of n != sqrt(5) and n != sqrt(2).
What is the median for the data set? 252, 210, 264, 278, 208, 295, 248, 257, 284, 271
A basket contains 4 green marbles and 8 blue marbles. a marble is drawn without replacement. then another marble is drawn. what is the probability that both marbles will be green?
Final answer:
The probability of drawing two green marbles consecutively without replacement from a basket of 4 green marbles and 8 blue marbles is 0.1, or 10%.
Explanation:
The question involves calculating the probability of drawing two green marbles in succession without replacement from a basket containing 4 green marbles and 8 blue marbles. For the first draw, the probability of drawing a green marble is 4 out of 12, which reduces to 1/3 or about 0.3333. Once that marble is drawn, there are 3 green marbles left and 7 blue marbles, making a total of 10.
Therefore, the probability of drawing another green marble is 3 out of 10, or 0.3. To find the probability of both events happening consecutively, we multiply the two individual probabilities: (1/3) * (3/10) = 1/10 or 0.1. Hence, the probability that both marbles will be green is 0.1, or 10%.
The monthly list of expenditures on your credit card statement can be very helpful at tax time to find items for which you are entitled to tax deductions. true or false
Answer:
true
Step-by-step explanation:
Which table identifies points on the line defined by the equations y-5x=-9
The equation y - 5x = -9 defines a line that none of the given points (1,5), (2,10), (3,7), and (4,14) lie on, as substituting their x-values in the equation doesn't yield the corresponding y-values.
Explanation:The question involves identifying points on a line described by the equation y - 5x = -9. To verify which points belong to this line, we can substitute the x-values of the given points into the equation and see if the resulting y-values match those in the points. We solve for y in the equation to get y as a function of x (dependence of y on x): y = 5x - 9.
Now, let's examine the points (1,5), (2,10), (3,7), and (4,14) to see if they satisfy this equation:
For (1,5): y = 5(1) - 9 = -4 which does not equal 5, so (1,5) is not on the line. For (2,10): y = 5(2) - 9 = 1 which does not equal 10, so (2,10) is not on the line. For (3,7): y = 5(3) - 9 = 6 which does not equal 7, so (3,7) is not on the line. For (4,14): y = 5(4) - 9 = 11 which does not equal 14, so (4,14) is not on the line.
None of these points lie on the line defined by y = 5x - 9. For a point to be on the line, plugging its x-coordinate into the equation must result in its corresponding y-coordinate.
Find all solutions in the interval [0, 2π).
2 sin2x = sin x
x = pi divided by three. , two pi divided by three.
x = pi divided by two. , three pi divided by two. , pi divided by three. , two pi divided by three.
x = 0, π, pi divided by six , five pi divided by six
x = pi divided by six , five pi divided by six
Final answer:
The solutions to the equation 2sin^2x = sinx in the interval [0, 2π) are x = 0, π, π/6, 5π/6 and x = π/6, 5π/6.
Explanation:
The given equation is: 2sin^2x = sinx.
To solve this equation, we can first factor out sinx:
sinx(2sinx - 1) = 0.
Setting each factor equal to zero, we get two equations:
sinx = 02sinx - 1 = 0Solving for x, we find:
x = 0, π, π/6, 5π/6x = π/6, 5π/6someone help me please!
Answer:
hudadagra what does a say im sorry for putting this in answer but it wont let me comment.
Step-by-step explanation:
i cant see the pic
HELP ASAP PLEASE!!!!
The pressure P (in pounds per square foot), in a pipe varies over time. Ten times an hour, the pressure oscillates from a low of 40 to a high of 280 and then back to a low of 40. The pressure at time t = 0 is 40. Let the function P = f(t) denote the pressure in pipe at time t minutes. Find the formula for the function P=f(t),
To model the pressure function in the pipe that oscillates between 40 and 280 ten times an hour, we can use a sine function. The formula is P = f(t) = 120 sin(π/3 t) + 160.
Explanation:The pressure in the pipe oscillates between 40 and 280 ten times an hour, this is a trigonometric function scenario. Assuming the oscillation is sinusoidal, we can use a sine function to model the pressure in the pipe. The oscillation's period is 6 minutes because the pressure changes happen 10 times per hour. Thus, the function modelling this pressure will be of the form
P = a sin(b(t - c)) + d.
Given that the middle value of the pressure (between the max of 280 and the minimum of 40) is 160, this makes
'd' = 160.
The amplitude 'a' is half the total swing of the pressure which is 120.
To find 'b', we use the fact that the period of a sinusoid in this form is (2π/b).
As our period is 6 minutes, that makes 'b' = π/3.
The pressure is at a minima at t=0 so the phase shift 'c' = 0
Hence the formula P = f(t) = 120 sin(π/3 t) + 160.
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Graph the information presented in the table. Use that graph to predict the week that revenue will equal expenses for this small company.
Note: Revenue and Expenses are drawn on the vertical axis and Month is on the horizontal axis.
Week 6
Week 7
Week 5
Week 8
Answer:
Step-by-step explanation:
We plot the points on a graph with months on x-axis and Revenue/expenses on y-axis.
A straight line shows the decrease in expenses and another line showing increase in revenue.
The point of intersection shows the common point where the revenue and expenses become equal. This point of intersection we get at 6.5 months as shown in the graph attached.
Answer:
Week 7
Step-by-step explanation:
You can solve this problem by graphing the revenue and the expenses and it's asking on which week the lines intersect.
7 eighty percent of all california drivers wear seat belts. if three drivers are pulled over, what is the probability that all would be wearing their seat belts? worksheet
It rained 2/8 inch in one hour. If rained 4/8 inch in the next hour.find the total amount of rain.wrote in simplest form
Use common sense to determine whether the given event is impossible; possible, but very unlikely; or possible and likely. A solar eclipse occurs on your birthday.
9m2-6/5m+c is a perfect square what is the value of c
The expression given to us is:
[tex] 9m^2-\frac{6}{5}m+c [/tex]
If the above expression is a perfect square then the middle term will have to be 2 times the square root of the first term times the square root of the last term. Thus:
[tex] -\frac{6}{5}m=2\times 3m\times \sqrt{c} [/tex]
[tex] \therefore \sqrt{c}=-\frac{1}{5} [/tex]
Thus, [tex] c=\frac{1}{25} [/tex]
Thus, for 9m^2-(6/5)m+c to be a perfect square, the value of c must be equal to [tex] \frac{1}{25} [/tex] or 1/25
Which transformation could not map trapezoid 1 to trapezoid 8?
reflection
translation
rotation
Answer:
A rotation
Explanation:
A reflection across the y-axis would map trapezoid 1 to trapezoid 8.
A horizontal translation would also map trapezoid 1 to trapezoid 8.
However, a rotation would map trapezoid 1 to trapezoid 7; it would not map it to trapezoid 8.
Answer: The answer is (c) rotation.
Step-by-step explanation: We are given a figure where 8 trapezoid are drawn on the coordinate plane. We are to select from the given option the transformation that will not map trapezoid 1 to trapezoid 8.
We can easily check that by reflecting and translating that both these transformations will definitely map trapezoid 1 to trapezoid 8.
Only the rotation will not work here. If we rotate trapezoid 1 by 180° taking origin as the centre of rotation, the the image will be opposite of trapezoid 8. Therefore, rotation will not map trapezoid 1 to trapezoid 8.
Thus, (c) is the correct option.
Sal bought 35 feet of window trim at a hardware store. The trim cost $1.75 per foot, including sales tax. If Sal paid with a $100.00 bill, how much change should he have received?
The correct answer is:
$38.75
Explanation:
35 feet of trim at $1.75 per foot would give us a cost of
35(1.75) = 61.25.
Paying with a $100 bill, he would receive
100-61.25 = $38.75 in change.
PLEASE HELP WILL GIVE 20 POINTS MARK BRAIN~LEST 5 STAR RATTING FOR ONE QUESTION
Using the following equation, find the center and radius of the circle by completing the square.
x2 + y2 + 6x − 6y + 2 = 0
center: (−3, 3), r = 4
center: (3, −3) r = 4
center: (3, −3), r = 16
center: (−3, 3), r = 16
what is the midpoint of a segment in the complex plane with endpoints at 6 -2i and -4 + 6i
Answer:
Midpoint of a segment in the complex plane with endpoints at 6 -2i and -4 + 6i is:
1+2i
Step-by-step explanation:
The midpoint of a segment in the complex plane with endpoints at 6 -2i and -4 + 6i is:
[tex]\dfrac{6-2i-4+6i}{2} \\\\=\dfrac{2+4i}{2}\\ \\=1+2i[/tex]
Hence, midpoint of a segment in the complex plane with endpoints at 6 -2i and -4 + 6i is:
1+2i
Answer: 2 + 4 i
Step-by-step explanation:
Hi, to solve this we have to apply the next expression:
(a1 +a2)/ 2 + (b1 +b2 )/2 i=
Where a is the real part, and b is the imaginary part (with i)
For example, for our case:
6 -2i , 6 is the real part (2) and -2 is the imaginary part (b)
Replacing with the values given
(6 -4) /2+ (-2 +6) /2 i = 2 + 4 i
Feel free to ask for more if needed or if you did not understand something.
if 10% of x is 20, what is 23% of x?
HELP PLEASE! FAST!!
1.Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle B?
2. Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle A?
3. Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle C?
IF YOU DO NOT KNOW, DO NOT ANSWER JUST FOR POINTS. YOU WILL BE REPORTED.
(1) The measure of angle B is [tex]140^o.[/tex]
(2) The measure of angle A is [tex]65^o.[/tex]
(3) The measure of angle C is [tex]80.5^o.[/tex]
(1) The quadrilateral [tex]\(ABCD\)[/tex] is inscribed in a circle. For any quadrilateral inscribed in a circle, the opposite angles are supplementary (i.e., their sum is [tex]\(180^\circ\)).[/tex]
In the first image:
[tex]- \( \angle DAB = x^\circ \)\\ - \( \angle DCB = (4x - 20)^\circ \)[/tex]
Since these two angles are opposite angles of the inscribed quadrilateral, we have:
[tex]\[ x + (4x - 20) = 180 \][/tex]
Solving for [tex]\(x\):[/tex]
[tex]\[ 5x - 20 = 180 \][/tex]
[tex]\[ 5x = 200 \][/tex]
[tex]\[ x = 40 \][/tex]
Therefore, [tex]\( \angle B = (4x - 20) = 4(40) - 20 = 160 - 20 = 140^\circ \).[/tex]
(2) In the second image:
[tex]- \( \angle ADC = x^\circ \)\\ - \( \angle ABC = 148^\circ \)[/tex]
These are opposite angles of the inscribed quadrilateral. Thus:
[tex]\[ x + 148 = 180 \][/tex]
Solving for [tex]\(x\):[/tex]
[tex]\[ x = 180 - 148 = 32 \][/tex]
Therefore, [tex]\( \angle A = (2x + 1) = 2(32) + 1 = 64 + 1 = 65^\circ \).[/tex]
(3) In the third image:
[tex]- \( \angle DAB = (x + 15)^\circ \)\\ - \( \angle DCB = (x + 10)^\circ \)\\ - \( \angle BCD = (x + 24)^\circ \)[/tex]
Using the property that opposite angles are supplementary:
Opposite angles are [tex]\( (x + 15) \)[/tex] and [tex]\( (x + 24) \),[/tex] thus:
[tex]\[ (x + 15) + (x + 24) = 180 \][/tex]
Solving for [tex]\(x\):[/tex]
[tex]\[ 2x + 39 = 180 \][/tex]
[tex]\[ 2x = 141 \][/tex]
[tex]\[ x = 70.5 \][/tex]
Therefore, the measure of angle C is [tex]\( (x + 10) = 70.5 + 10 = 80.5^\circ \).[/tex]
How long will it take the ball to reach the ground
WILL GIVE BRAINLIEST FOR CORRECT ANSWER
7. Find the value of x. Round to the nearest tenth. The diagram is not drawn to scale.
Answer:
x = 8.4 cm
Step-by-step explanation:
Here we have to use the tan ratio to find the value of x.
tan = opposite/adjacent
tan 35 = x/12
Multiplying both sides by 12, we get
x = 12 tan 35 [tan 35 = 0.7]
x = 12*0.7
x = 8.4
Therefore, the value of x = 8.4 cm
Hope this will helpful.
Thank you.