Answers
The rate of change of the relationship is 6/5
Rate of change of a lineThe rate of change of a line is also known as the slope of the line. The formula for calculating the slope of a line is expressed as:
Slope =y2-y1/x2-x1
Given the coordinate points (-3,-2) and (2, 4). On substituting;
Slope = 4-(-2)/2-(-3)
Slope =4+2/2+3
Slope = 6/5
Hence the rate of change of the relationship is 6/5
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Related Questions
The figures below are similar.
12 yd
30 yd
What are a) the ratio of the perimeters and b) the ratio of the areas of the larger figure to the
smaller figure? The figures are not drawn to scale.
Answers
Answer:
a) 2.5
b) 6.25
Step-by-step explanation:
For similar figures, the ratio of any corresponding linear dimensions is the same. The ratio of areas is the square of that.
ApplicationThe ratio of linear dimensions, larger to smaller, is ...
(30 yd)/(12 yd) = 2.5
a) PerimeterPerimeter is a linear dimension, the sum of side lengths. The ratio of perimeters is 2.5.
b) AreaThe ratio of areas, larger to smaller, is the square of the scale factor for side lengths:
(2.5)² = 6.25
The ratio of the areas of the larger to smaller figure is 6.25.
Ab and cd with m as the midpoint of both ab and cd. ab = 6.4 cm and cd = 4.0 cm. a, b and c are not collinear.
Answers
From the straight line AB and CD with point M as midpoint of both lines, AM = BM = 3.2 cm and CM = DM = 2 cm
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
m as the midpoint of both ab and cd, hence:
AM = BM = AB/2 = 6.4/2 = 3.2 cm
CM = DM = CD/2 = 4/2 = 2 cm
From the straight line AB and CD with point M as midpoint of both lines, AM = BM = 3.2 cm and CM = DM = 2 cm
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Class A has 13 pupils and class B has 16 pupils.
Both classes sit the same maths test.
The mean score for class A is 20.
The mean score for class B is 45.
What is the mean score (rounded to 2 DP) in the maths test across both classes?
Answers
Answer:
ok so we can just add 20 + 45 then divide by 2
20+45=65/2=32.5
32.5
Hope This Helps!!!
A study on the latest fad diet claimed that the amounts of weight lost by all people on this diet had a mean of 23.4 pounds and a standard deviation of 6.8 pounds.
Step 2 of 2 : If a sampling distribution is created using samples of the amounts of weight lost by 63 people on this diet, what would be the standard deviation of the sampling distribution of sample means? Round to two decimal places, if necessary.
Answers
Using the Central Limit Theorem, the standard deviation of the sampling distribution of sample means would be of 0.86.
What does the Central Limit Theorem state?It states that the standard deviation of the sampling distribution of sample means is given by:
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.The parameters for this problem are given as follows:
[tex]\sigma = 6.8, n = 63[/tex].
Hence:
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]s = \frac{6.8}{\sqrt{63}}[/tex]
s = 0.86.
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give the meaning of each expression.
16^5
y^4
7a^3
Answers
Answer:
16 to the power of 5
y to the power of 4
(7a) to the power of 3 or 7 times a to the power of 3
aimee has 20 apples and wants to have the same amount of apples in each bag but ends up with more than one bag of apples and each bag to contain more than one apple
work out all the possibilities for all of the number of apples that she could use for each bag
Answers
Answer:
There are 4 possibilities: 2, 4, 5 or 10 apples in each bag.===========
Let the number of apples in each bag is x, then the number of bags is 20/x.
Since the number of apples in each bag is greater than one and number of bags is greater than one, we have the following conditions:
x > 1 , 20/x > 1 ⇒ x < 20,x is factor of 20.The factors of 20 between 1 and 20 are:
2, 4, 5, 10The possibilities are:
If x = 2, then the number of bags is 20/2 = 10;If x = 4, then the number of bags is 20/4 = 5;If x = 5, then the number of bags is 20/5 = 4;If x = 10, then the number of bags is 20/10 = 2.Using mod, find the remainder of 3^51 when divided by 7. Please show steps on how to use modulu, am a bit confused.
Answers
Answer:
[tex]6[/tex]
Step-by-step explanation:
The gist of modular arithmetic in a nutshell: the numbers [tex]a[/tex] and [tex]b[/tex] are considered to be congruent by their modulus [tex]m[/tex] if [tex]m[/tex] is a divisor of their difference.
In mathematics: [tex]a \equiv_{m} b \Leftrightarrow (a - b) \vdots m[/tex]
Exemplifying this: [tex]6 \equiv_{7} -1[/tex] because [tex]6 - (-1) = 6 + 1 = 7[/tex], [tex]7 \vdots 7[/tex].
Let us have following equivalences: [tex]a \equiv_{m} b[/tex] and [tex]c \equiv_{m} d[/tex], then: [tex](a - b) \vdots m[/tex] and [tex](c - d) \vdots m[/tex] by definition.
Properties:
1. [tex]a + c \equiv_{m} b + d \Leftrightarrow ((a + c) - (b + d)) \vdots m \Leftrightarrow (a + c - b - d) \vdots m \Leftrightarrow ((a - b) + (c - d)) \vdots m[/tex].
2. [tex]a - c \equiv_{m} b - d \Leftrightarrow ((a - c) - (b - d)) \vdots m \Leftrightarrow (a - c - b + d) \vdots m \Leftrightarrow ((a - b) - (c - d)) \vdots m[/tex].
3. [tex]ac \equiv_{m} bd \Leftrightarrow (ac - bd) \vdots m \Leftrightarrow (ac - bc - bd + bc) \vdots m \Leftrightarrow (c(a - b) + b(c - d)) \vdots m[/tex].
4. What if we have [tex]a \equiv_{m} b[/tex] twice? If we abide by property 3, we can come to the conclusion that [tex]a^2 \equiv_m b^2[/tex]. It is fair enough that there is room for the equivalence [tex]a^n \equiv_{m} b^n[/tex].
[tex]3^{51} = (3^3)^\frac{51}{3} = 27^{17} \equiv_{7} (-1)^{17} \equiv_{7} -1 \equiv_{7} 6[/tex].
We used property 4.
Keep in mind that any remainder cannot be a negative number.
Therefore, the remainder equals [tex]6[/tex].
Under his cell phone plan, Elijah pays a flat cost of $46.50 per month and $4 per
gigabyte. He wants to keep his bill at $58.50 per month. How many gigabytes of data
can he use while staying within his budget?
Answers
Answer:
3
Step-by-step explanation:
Start with the amount that he wants to pay with gigabytes and subtract the amount of his bill without gigabytes.
58.50-46.50=12
Then divide that amount by the price of each gigabyte to determine how many gigabytes he can use while staying in budget.
12/4=3
Answer: 3
Inequalities help us to compare two unequal expressions. The gigabytes of data that Elijah should use while staying within his budget is 3 gigabytes.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
Given that Elijah pays a flat cost of $46.50 per month and $4 per gigabyte. He wants to keep his bill at $58.50 per month. Therefore, we can write the inequality for this condition as,
$46.50 + $4(x) ≤ $58.50
46.50 + 4x ≤ 58.50
4x ≤ 58.50 - 46.50
4x ≤ 12
x ≤ 12/4
x ≤ 3
Hence, the gigabytes of data that Elijah should use while staying within his budget is 3 gigabytes.
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The circle below is centered at (4,-1) and has a radius of 3. What is it’s equation?
Answers
Answer:
(x - 4)^2 + (y + 1)^2=9
Step-by-step explanation:
The equation of a circle can be written using a kinda of fill-in-the-blank method if you know the coordinates of the center and the radius.
If the center is (h,k) and the radius is r, then fill in those given numbers into:
(x-h)^2 + (y-k)^2 =r^2
The center of your circle is (4, -1).
Fill in 4 for the h, -1 for the k and 3 for the r.
(x-4)^2+(y- -1)^2= 3^2
Simplify.
(x-4)^2+(y+1)^2=9
seperate 90 into two parts so that one part is four times the other
Answers
Answer:
18 and 72
Step-by-step explanation:
the smaller part can be assigned as x while the larger will be 4x. Both numbers need to add up to 90, giving the equation: 4x+x = 90
Solve:
4x+x = 90
5x = 90
x = 18
4x = 72
The following are the ages (years) of 5 people in a room:
13
,
12
,
13
,
15
,
12
A person enters the room.
The mean age of the 6 people is now 20.
What is the age of the person who entered the room?
Answers
Answer:
55
Step-by-step explanation:
To find the average you add up all numbers given then divide by the amount of numbers there were. The mean, or average, of the original 5 people was 13 since their ages added was 65, which you divide by 5 for 13. The new mean once the 6th person entered the room was 20. So, you do 6 [number of people] times 20 [average] to get 120. Taking 65 [added amount of original ages of the 5 people] away from 120 [the new added up ages of all 6 people], you get 55. This means 55 would be the 6th person's age.
Sorry if the explanation is confusing!
Call the total ages of the 6 people, x
To calculate the mean age of 6 people, we take the total age (x) and divide by the amount of people (6)
So, x : 6 = 20
-> The total ages of the 6 people are 20 x 6 = 120
We can calculate the 6th person's age by taking 120 and minus the total age of the other 5
-> 120 - (13+12+13+15+12) = 55
So, the 6th person's age is 55.
If an artist combines 6 L of 33% by volume solution and 4 L of 60% by volume solution, what's the percent by volume of the resulting solution
Answers
The percent by volume of the resulting solution is 10L by 93 percent
How to determine the volumeThe resulting solution = sum of the volumes of both solutions
Resulting solution = 6L × 33 percent + 4L × 60 percent
Resulting solution = 10 L × 93 percent
This is so because both solutions add up to form the resulting solution
Thus, the percent by volume of the resulting solution is 10L by 93 percent
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Which function has zeros at x = -2 and x = 5?
O f(x) = x2 + 2x - 10
• f(x) = x2 - 2x - 10
O f(x) = X2 + 3x - 10
® f(x) = x2 - 3x - 10
Answers
Answer:
f(x)=x²-3x-10
Step-by-step explanation:
[tex]f(x) = x {}^{2} - 3x - 10 \\ to \: find \: x \: intercept \:o r \: zero \: substitute \: f(x) = 0\: \\ 0 = x {}^{2} - 3x - 10 \\ x {}^{2} - 3x - 10 = 0 \\ x {}^{2} + 2x - 5x - 10 = 0 \\ x(x + 2) - 5x - 10 = 0 \\ x(x + 2) - 5(x + 2) = 0 \\ (x + 2).(x - 5) = 0 \\ x + 2 = 0 \\ x - 5 = 0 \\ x = - 2 \\ x = 5[/tex]
therefore the zeros of the equation are x₁=-2,x₂=5
If sin= 7/25 what are the other primary trig ratios?
Answers
Answer:
cos=24/25
tan=7/24
Step-by-step explanation:
sin=opposite/hypotenuse
therefore 7 is the opposite and 25 is the hypotenuse.
using pythagorean theorem we can find the adjacent. i.e hypotenuse squared= sum of adjacent squared and opposite squared.
h^2= a^2+ O^2
25 squared - 7 squared= 576
which is equal to 24 squared.
therefore adjacent=24
cos=adjacent/hypotenuse
cos=24/25
tan=opposite/adjacent
tan=7/24.
Answer:
[tex]\cos(\theta)= \dfrac{24}{25}[/tex]
[tex]\tan(\theta)=\dfrac{7}{24}[/tex]
Step-by-step explanation:
General outlineTrig ratio DefinitionsVisualizing the triangle for the problemApplying the Pythagorean TheoremIdentifying the other trig ratiosStep 1. Trig ratio definitionsDefinitions of primary trig functions
For a given acute angle in a right triangle :
Sine function: [tex]\sin(\theta)=\dfrac{\bold{opposite} \text{ side length}} {\bold{hypotenuse} \text{ length}}[/tex]Cosine function: [tex]\cos(\theta)=\dfrac{\bold{adjacent} \text{ side length}} {\bold{hypotenuse} \text{ length}}[/tex]Tangent function: [tex]\tan(\theta)=\dfrac{\bold{opposite} \text{ side length}} {\bold{adjacent} \text{ side length}}[/tex]...where the hypotenuse is the side across from the right angle, the opposite side is the side not touching the angle theta, and the adjacent side is the side touching the angle theta (but that isn't the hypotenuse).
We are already given the ratio for the Sine function, so we need to find the Cosine and Tangent function ratios. It will be helpful to visualize what this triangle looks like.
Step 2. Visualizing the triangle for the problemThe given equation states [tex]\sin(\theta)=\frac{7}{25}[/tex], so there is some right triangle, with a specific angle theta, that has a ratio of sides (opposite to hypotenuse) of 7 to 25. For ease, we'll consider the triangle that has actual side lengths of 7 and 25 for those sides. (See attached diagram)
Given that information, we can identify that the unknown side length is the adjacent side length. Since the triangle is a right triangle, this value can be found through the Pythagorean Theorem.
Step 3. The Pythagorean TheoremThe Pythagorean Theorem states that for any right triangle, [tex]a^2+b^2=c^2[/tex] where "c" is the length of the hypotenuse of the triangle, and "a" and "b" are the lengths of the other two sides of the triangle (often called "legs"). It does not matter which leg is chosen to be side "a" or side "b" due to the commutative property of addition, but "c" must be the hypotenuse.
[tex]a^2+b^2=c^2[/tex]
Substituting known values, and simplifying...
[tex]a^2+(7)^2=(25)^2[/tex]
[tex]a^2+49=625[/tex]
Subtracting 49 from both sides to begin to isolate "a", and simplifying...
[tex](a^2+49)-49=(625)-49[/tex]
[tex]a^2=576[/tex]
Applying the square root property to isolate "a", and simplifying/calculating...
[tex]\sqrt{a^2}=\pm \sqrt{576}[/tex]
[tex]a=\pm 24[/tex]
[tex]a=24[/tex] or [tex]a=-24[/tex]
Under the assumption that the triangle is an acute triangle, the adjacent side length is a positive value, so we reject the negative solution, deducing that the adjacent side length must be 24.
Side note: If there is more information in the context of the question that suggests that theta may be larger than 90°, then other factors will need to be taken into account.
Step 4. Identifying the other trig ratiosReturning to the trig ratio definitions, we can identify the requested cosine and tangent ratios
[tex]\cos(\theta)=\dfrac{\bold{adjacent} \text{ side length}} {\bold{hypotenuse} \text{ length}} = \dfrac{24}{25}[/tex]
[tex]\tan(\theta)=\dfrac{\bold{opposite} \text{ side length}} {\bold{adjacent} \text{ side length}}=\dfrac{7}{24}[/tex]
what is high common factor
Answers
Answer:
The highest number that divides each of the two or more numbers is the HCF or Highest Common Factor.
Step-by-step explanation:
Example: What is the HCF of {12,42,14}
Answer: The HCF is 2 as the biggest number they can all be divided by is 2. {12,42,14} = {2^2*3,2*3*7,2*7} The factors in each number is 2.
4,8,12,16
(2/5) power of 2 as a fraction.
Please help.
khan academy.
Answers
[tex]\Large\maltese\underline{\textsf{Our problem:}}[/tex]
What is [tex]\bf{\bigg(\dfrac{2}{5}\bigg)^2[/tex]?
[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]
When we have a fraction that is raised to a specific power, we raise both the numerator and the denominator to that power.
[tex]\bf{\dfrac{2^2}{5^2}}=\dfrac{4}{25}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\bf{Answer:}[/tex]
[tex]\bf{=\dfrac{4}{25}[/tex]
[tex]\boxed{\bf{aesthetic \not101}}[/tex]
Determine if each table below represents a linear function, quadratic function, or neither.
Answers
The table below is a quadratic function.
What is a quadratic function?A quadratic function is an Algebraic function with the power of its variable as 2.
This function normally has three algebraic terms, the x-square term, the x-term and the constant term.
Analysis:
The X-column values increases from -2 to 1, while the f(x) column which is the y-column increase from -9, until it gets to 1, where the value falls to -5.
A typical behavior of an inverted-v curve which is a quadratic curve.
If it were a linear function, as x values increase, y value would either keep increasing or decreasing, it does not change its orientation.
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Which statement regarding the diagram is true W, X,Z,Y
Answers
The statement that's true about the triangle is that WXY + YXZ = 180°.
How to illustrate the information?It should be noted that in the question, the options are related to a linear pair.
According to the linear pair, when a line cuts another line at a point, then the sum of the adjacent angles formed at the point will be 180°.
Therefore, WXY + YXZ = 180°.
The correct option is C.
The complete question is:
Which statement regarding the diagram is true?
m∠WXY = m∠YXZ
m∠WXY < m∠YZX
m∠WXY + m∠YXZ = 180°
m∠WXY + m∠XYZ = 180°
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X = square root=
Help me please thanks
Answers
The value of x will be equal to 33.94 units.
What is trigonometry?Trigonometry is the branch of mathematics that set up a relationship between the sides and angle of the right-angle triangles.
Given that:-
Given that the radius of the circle is 12 units which are PO = 12 and OR = 12, QR = x , ∠O = 60 So ∠Q = 30.
First, we will calculate the Length OQ by angle property in triangle OQR.
[tex]Sin 30=\dfrac{Perpendicular}{Hypotenuse}[/tex]
[tex]Sin 30 = \dfrac{12}{OQ-12}[/tex]
[tex]\dfrac{1}{2}=\dfrac{12}{OQ-12}[/tex]
OQ - 12 = 24
OQ = 36
Now applying the Pythagorean theorem in the triangle OQR.
H² = P² + B²
36² = 12² + x²
x² = 1296 - 144
x = √1152
x = 33.94
Therefore the value of x will be equal to 33.94 units.
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The 8 foot diameter circular table has a 4 foot wide extension. What is the total area with the extension? How does the area compare to the area of the 10 foot diameter table? Show your work. (3 points)
Answers
Answer: the total area with the extension S≈82,3 foot², S>S'.
Step-by-step explanation:
D₁=8 foot D₂=10 foot a wide extension = 4 foot.
1) Let the total area with the extension S is the area of the circular table S₁
plus a wide extension S₂.
Considere S₁:
[tex]R_1=\frac{D_1}{2} \\R_1=\frac{8}{2} \\R_1=4 foot.\\S_1=\pi* R_1^2\\S_1=\pi *4^2\\S_1=16*\pi \\S_1\approx50,3\ foot^2.\\[/tex]
[tex]S_2=8*4\\S_2=32 \ foot^2.[/tex]
[tex]S\approx50,3+32\\S\approx82,3 \ foot^2.[/tex]
2)\ Considere S':
[tex]R_2=\frac{D_2}{2} \\R_2=\frac{10}{2} \\R_2=5 \ foot.\\S'=\pi *R^2\\S'=\pi *5^2\\S'=25*\pi \\S'\approx78,5\ foot^2.[/tex]
S>S'.
Good luck an' have a nice day!
Please help! Consider the sequence {20, 17, 14, 11, 8, 5, 2...}.
Answers
Answer:
c.) 38
Step-by-step explanation:
[tex]\sum\limits_{n=3}^6 a_n[/tex] means "summation of the all the elements starting from the 3rd element to the 6th element".
The 3rd element in the series is 14, and the 6th element is 5; we have to add these and all the elements between them together.
∴ [tex]\sum\limits_{n=3}^6 a_n[/tex] = 14 + 11 + 8 + 5
= 38
Find the probability. Leave your answer in simplest fraction form.
You roll a six-sided die. The die shows an even number or a number
greater than three.
Answers
Answer:
5/6
Step-by-step explanation:
The numbers on a six-sided die are as shown:
1, 2, 3, 4, 5, 6
The even numbers are:
2, 4, 6
The numbers greater than 3 are:
3, 4, 5, 6
Both lists together are:
2, 3, 4, 5, 6
Because 5 out of 6 numbers satisfy these conditions, the probability of satisfying these conditions is 5/6.
Using the following image, solve for SR. Look at the image closely.
What would SR be? Giving Brainly!
Answers
Step-by-step explanation:
I assume
SR = 2x + 23
RQ = x + 21
if that is true, then the situation is completely simple :
14 = (2x + 23) + (x + 21) = 3x + 44
3x = -30
x = -10
SR = 2×-10 + 23 = -20 + 23 = 3
RQ = -10 + 21 = 11
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:x = -10 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex] \qquad \tt \rightarrow \: SR + RQ = SQ[/tex]
[tex]\qquad \tt \rightarrow \: 2x + 23 + x + 21 = 14[/tex]
[tex]\qquad \tt \rightarrow \: 3x + 44 = 14[/tex]
[tex]\qquad \tt \rightarrow \: 3x = 14 - 44[/tex]
[tex]\qquad \tt \rightarrow \: 3x = - 30[/tex]
[tex]\qquad \tt \rightarrow \: x = - 10[/tex]
Now,
[tex] \qquad \tt \rightarrow \: SR = 2x + 23 [/tex]
[tex] \qquad \tt \rightarrow \: SR = 2(-10) + 23 [/tex]
[tex] \qquad \tt \rightarrow \: SR =-20+ 23 [/tex]
[tex] \qquad \tt \rightarrow \: SR = 3 \:\: units [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
The curved sides of large storage tanks at a refinery need to be painted. What is the approximate area of each tank that will be painted?
OA. 9,500 ft²
OB. 1,144 ft²
OC. 4,574 ft²
OD. 2,287 ft²
Answers
Deepak wrote out the steps to his solution of the equation startfraction 5 over 2 minus 3 x minus 5 plus 4 x equals negative startfraction 7 over 4 endfraction – 3x – 5 4x = –.
Answers
The solution is x=3/4
How can we solve given equation?
First, we will solve like terms. Then shift constant to other side and keep x on the same side to get the value of x.
We can solve given equation as shown below:
5/2-3x-5+4x=-7/4
(5-10)/2+x=-7/4
-5/2+x=-7/4
x=5/2-7/4
x= (10-7)/4
x=3/4
Hence, the solution is x=3/4.
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Area=
Help me please!! Thank u so much
Answers
Our base of the triangle: 13 units
Our height of the triangle: 12 units
Because the formula requires multiplying base times height, we can do 13 x 12. 13 x 12 = 156. However, we are not done. We now must multiply our answer (156) by 1/2 or divide it by 2. I would recommend to divide it by 2 because it is easier that way. 156 divided by 2 gives us 78. Therefore, by using the formula bh/2, we will find that our result is 78 units squared. If you need to better understand this, let me know and I will gladly assist you.
Answer:
area = 78
Step-by-step explanation:
Area of triangle = 1/2 x base x perpendicular height
⇒ 1/2 x 13 x 12
⇒ 78 units²
An airplane flies with a constant speed of 600 miles how far can it travel in 135 minutes
Answers
An airplane flying at a constant speed of 600 miles per hour, will travel 1350 miles in 135 minutes.
The average speed of any object is the ratio of the total distance the object travels, and the total time taken by the object to cover that distance.
Thus, Average speed = Total Distance/Time taken.
In the question, we are asked the distance traveled by airplane in 135 minutes at the constant speed of 600 miles per hour.
First, we need to convert the time from minutes to hours as our speed is given in miles per hour.
To convert minutes to hours, we divide it by 60.
Thus, the time = 135/60 hours = 2.25 hours.
Now, we substitute the speed = 600 miles per hour, and time = 2.25 hours in the formula:
Average speed = Total Distance/Time taken
or, 600 = Distance/2.25,
or, Distance = 600*2.25 miles,
or, Distance = 1350 miles.
Thus, an airplane flying at a constant speed of 600 miles per hour, will travel 1350 miles in 135 minutes.
The question is incomplete. The complete question is:
"An airplane flies with a constant speed of 600 miles per hour. How far can it travel in 135 minutes".
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Answer:
We know,
Distance,d = speed × time
Converting time into hours divide the value by 60 so, 135 minutes = 2.25 hoursd = 600 × 2.25
d = 1350km
Hence, the airplane can travel 1350km in 135 minutes with a speed of 600 miles.
What is the value of x?
Answers
Answer: 5
Step-by-step explanation:
By the inscribed angle theorem.
[tex]\frac{9}{15}=\frac{2x-1}{3x}\\\\27x=30x-15\\\\-3x=-15\\\\x=5[/tex]
Please answer this question fast (Lines and angles ch...class9)
Answers
The angle of y in the triangle is 30 degrees.
How to find angles in a triangle?∠O = 180 - 30 - 70 (angles in a triangle)
∠O = 180 - 100(angles in a triangle)
∠O = 80°
Using vertically opposite angle principle and sum of angle in a triangle,
80 + y + 70 = 180
180 - 150 = y
y = 30 degrees
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For which value of k is the value of k(k-2)(k+1) negative
Answers
Answer:
[tex](-\infty, -1)\ \cup\ (0, 2)[/tex]
Step-by-step explanation:
So if you expand out the two binomials (k-2)(k+1), you'll get: [tex]k^2+k-2k-2[/tex]. which simplifies to: [tex]k^2-k-2[/tex]. Multiplying this by the k gives you: [tex]k^3-k^2-2k[/tex]. As you can see the degree is odd, this means that this polynomial will have two opposite end behaviors. And as you can see the leading coefficient is positive, meaning that this function will go towards positive infinity as k goes towards positive infinity. Also we if look at the original equation given, it's in factored form, with the zeroes as k=0, k=2, and k=-1. So given this we can draw a simple graph to see when the value of the equation is negative. If you look at the graph I drew you'll see that it's negative from (-infinity, -1) and then negative from (0, 2)