The solution of a compound inequality is the common region or intersection region of two inequalities.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
A sentence having two inequality statements connected by the words 'or' Or 'and' is referred to as a compound inequality. The conjunction "and" denotes the simultaneous truth of both statements in the compound sentence.
For example, if in a compound inequality we get x > 3 and x > 5 so the final conclusion is x > 5.
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The perimeter of the triangle BAG is 43. AG= 16, AB=x+4, and BG= 2x+2. What is the value of x?
Answer:
x=7
isosceles triangle
Step-by-step explanation:
To find the perimeter we just add all the sides so we do that for this too
(X+4)+(2x+2)+(16)
And we set it equal to 43 since that is perimeter
(X+4)+(2x+2)+(16)=43
Combine like terms
3x+22=43
-22. -22
3x=21
/3. /3
x=7
And if we fill in the x we find BG and AG are equal so this is an Isosceles triangle
Hopes this helps
Answer:
x = 7
Isosceles triangle
Step-by-step explanation:
The perimeter of a two-dimensional shape is the distance all the way around the outside.
Given values of triangle BAG:
Perimeter = 43AG = 16AB = x + 4BG = 2x + 2Therefore:
⇒ AG + AB + BG = perimeter
⇒ 16 + x + 4 + 2x + 2 = 43
⇒ x + 2x + 16 + 4 + 2 = 43
⇒ 3x + 22 = 43
⇒ 3x + 22 - 22 = 43 - 22
⇒ 3x = 21
⇒ 3x ÷ 3 = 21 ÷ 3
⇒ x = 7
Substitute the found value of x into the expressions for AB and BG to find their lengths:
⇒ AB = x + 4
⇒ AB = 7 + 4
⇒ AB = 11
⇒ BG = 2x + 2
⇒ BG = 2(7) + 2
⇒ BG = 14 + 2
⇒ BG = 16
As sides BG and AG are both 16 units in length, the triangle is an isosceles triangle (as it has two sides of equal length).
Susan buys candy that costs $4 per pound. She will buy more than 6 pounds of candy. What are the possible amounts she will spend on candy?
The possible amounts Susan will spend on candy is $25 and above.
What are the possible amounts that will be spent on candy?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this situation, since Susan will buy more than 6 pounds of candy, the same expression will be illustrated by x.
x > ($4 × 6)
x > $24
In this case, she'll have to spend $25 or more.
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Suppose you have a treatment that you suspect may alter performance on a certain task. You compare the mean of your sample to the norm. Further, suppose you use az-test for means and your result is statistically significant (z=2.70,p<0.05, one-taifed). Glven your statistically significant result, indicate which (if anyl of the following statements is true. Check each statement that is true. In other words, you may check none, one, several, or all of the statements. You have absoluidy disproved the null hypothesis ghat is, there is no ditference between the population means). You have found the protablity of the null hypothesis being true.
All of the assertions are false. A statistically significant finding does not necessarily imply that the null hypothesis has been proven incorrect, nor does it indicate how likely it is to be true.
What is a norm defined as?Generally speaking, the word "norm" describes something that is customary, typical, anticipated, or standard. Norms are established definitions of beneficial attitudes and actions that ought to be commonplace, or "the norm," whenever a group is working together. They apply to cooperation and collaboration.
What Is a Z-Test?When the variances are known and the sample size is large, a z-test is a statistical test that is used to assess whether two population means differ from one another.
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Use Pythagoras' theorem to work out the height of the equilateral
triangle below.
Give your answer in centimetres (cm) to 1 d.p.
N
10 cm
allowed
M
10 cm
10 cm
You select three cards from a deck of cards without replacement. The first card is a king, then queen, and lastly a jack. What is the probability you select those three cards in that order? Round answer to nearest hundredth and include percent sign.
10. The total cost of shipping toys from a specific company is $5 plus $2.50 times the number of toys purchased
Answer:y=2.50x+5
Step-by-step explanation:
y=2.50x+5
that's all i can do with the information provided
Marvin and Alicia are putting new carpet in there living room. The carpet cost $4.15 per square foot and $97 to have it stalled. Their total bill is $1, 789.50 how many square feet 9s their living room
There are 407.83 square feet living room.
What is linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Given that;
The carpet cost $4.15 per square foot and $97 to have it stalled.
And, Their total bill is $1, 789.50.
Now,
Let number of square feet living room = x
So, We can formulate;
⇒ 4.15x + 97 = 1,789.50
Solve for x as;
⇒ 4.15x = 1,789.50 - 97
⇒ 4.15x = 1,692.5
⇒ x = 1,692.5 / 4.15
⇒ x = 407.83 square feet
Thus, There are 407.83 square feet living room.
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A taxi charges a flat 1.23 plus an additional 0.76 per mile. Brent has only 14.91 to spend on the ride. How many miles can Brent travel?
Will be reported by all 53 of my account if not a good answer
Answer:
18 miles
Step-by-step explanation:
To determine how many miles Brent can travel, we need to first determine the cost of the base fare and then subtract that from the total amount of money Brent has. The base fare is $1.23, so we can subtract that from the total amount of money Brent has to find out how much money he has left for the per-mile charge:
14.91 - 1.23 = 13.68
Now that we know how much money Brent has left for the per-mile charge, we can divide that amount by the per-mile charge to find out how many miles Brent can travel:
13.68 / 0.76 = 18 miles
Therefore, Brent can travel a maximum of 18 miles given the amount of money he has available to spend on the ride.
hi!!! i’d appreciate it sm if someone could do 25 and 26 i’m thing to turn my work in tomorrow and these are the last ones i need, i’ll mark u brainliest when it pops up :) thank you
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.
[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-1)}}} \implies \cfrac{-4}{2 +1} \implies \cfrac{ -4 }{ 3 } \implies - \cfrac{ 4 }{ 3 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{- \cfrac{ 4 }{ 3 }}(x-\stackrel{x_1}{(-1)}) \implies y -3 = - \cfrac{ 4 }{ 3 } ( x +1) \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y-3)=3\left( - \cfrac{ 4 }{ 3 } ( x +1) \right)}\implies 3y-9=-4(x+1)\implies 3y-9=-4x-4 \\\\\\ 3y=-4x+5\implies \text{\LARGE 4}x+3y=5[/tex]
Please help and please explain this question step by step
Answer + Step-by-step explanation:
In the attach pdf
What is the equation in slope-intercept form of the line that passes through the point (3,4) and is parallel to the line represented by y=3x−2?
y=3x+7y
y=3x−5y
y=−3x+5y
y=−3x−7
The equation of the line in slope intercept form that passes through the point (3,4) and is parallel to the line represented by y=3x−2 is y = 3x - 5.
How to find equation of a line?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the line that passes through the point (3,4) and is parallel to the line represented by y = 3x − 2.
Parallel line have the same slope. Therefore, the slope of the line is 3.
Let's find the y-intercept using (3, 4).
y = 3x + b
4 = 3(3) + b
4 - 9 = b
b = -5
Therefore, the equation is y = 3x - 5
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Draw a rectangle that has a golden ratio of its sides. Label the rectangle’s sides. Show how it has a golden ratio of the sides.
The golden ratio can be found using the following formula if we take x as the width, and y as the length of the rectangle:
[tex]\frac{y}{x} =\frac{x+y}{y} =1.618[/tex]
What is the golden ratio?
The golden ratio is a unique proportion between two values where the ratio of the two values equals the ratio of their sum to the bigger of the two values.
If we take a square of sides A,B,C,D.
Locate the midpoint of any one side of the square by bisecting it.
Connecting the midpoint (say) P to a corner of the opposite side.
Placing the compass on point P, and the width set to match the distance of P to one of the opposite sides, we draw an arc.
By extending the line where P sits, we see that the arc intersects at a point. say Q.
Extending the opposite line to P, we see that the point Q drawing parallel to the side, we see that it intersects at another point R.
Now, the rectangle AQRD is a golden ratio rectangle.
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Sort 3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5 using quicksort with median-of-three partitioning and a cutoff of 3. The three elements are not pre-sorted when choosing pivot and pivot moved to end in each step. Show all steps.
Using quicksort with median-of-three partitioning and a cutoff of 3. we will get 1, 1, 3, 2, 3, 4, 5, 5, 5, 6, 9.
The Original input is 3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5.
We get on the basis of the median after sorting the first, middle, and final elements 3, 1, 4, 1, 5, 5, 2, 6, 5, 3, 9.
As a result, we select pivot = 5. It also provides after the pivot is removed or hidden 3, 1, 4, 1, 5, 3, 2, 6, 5, 5, 9.
It is necessary to swap the two fives. However, in the subsequent swap, p and q cross. turn is traded back with the p:
3, 1, 4, 1, 5, 3, 2, 5, 5, 6, 9
It is now time to quickly sort the first eight elements of the array in a recursive fashion:3, 1, 4, 1, 5, 3, 2, 5,
and after sorting the three relevant elements, we get 1, 1, 4, 3, 5, 3, 2, 5.
As a result, we select the pivot value of 3, and after hiding this pivot once more, we get:
1, 1, 4, 2, 5, 3, 3, 5
A switch takes place between 4 and 3: 1, 1, 3, 2, 5, 4, 3, 5
Now, because the next swap crosses the pointer, the pivot needed to be swapped: 1, 1, 3, 2, 3, 4, 5,
and the following is the result: 1, 1, 3, 2, 3, 4, 5, 5, 5, 6, 9
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Find the 10th term of the geometric sequence whose common ratio is 1/3 and whose first term is 7.
The 10th term of the geometric sequence whose common ratio is 1/3 and whose first term is 7 is [tex]\frac{7}{19683}[/tex].
What is geometric sequence?
A unique kind of sequence is a geometric sequence. Every term in the series (apart from the first term) is multiplied by a fixed amount to determine the following term. In other words, we multiply the current phrase in the geometric sequence by a constant term (called the common ratio), and then divide the current term in the geometric sequence by the same common ratio to discover the previous term in the geometric sequence.
nth term of geometric series
a(n) = a(1) * r^(n-1)
You are given a(1) = 7, r = 1/3 and n = 10.
a(10) = 7 * 1/3^(10-1)
[tex]7\left(\frac{1}{3}\right)^{10-1}$$[/tex]
Apply exponent rule: [tex]$\left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}$[/tex]
[tex]$$\begin{aligned}& \left(\frac{1}{3}\right)^{10-1}=\frac{1^{10-1}}{3^{10-1}} \\& =7 \times \frac{1^{10-1}}{3^{10-1}}\end{aligned}$$[/tex]
[tex]$$\begin{aligned}& 1^{10-1}=1 \\& =7 \times \frac{1}{3^{10-1}} \\& 3^{10-1}=19683 \\& =7 \times \frac{1}{19683}\end{aligned}$$[/tex]
Convert element to fraction: [tex]$\quad 7=\frac{7}{1}$[/tex]
[tex]=\frac{7}{1} \times \frac{1}{19683}$$[/tex]
Apply the fraction rule: [tex]$\frac{a}{b} \times \frac{c}{d}=\frac{a \times c}{b \times d}$[/tex]
[tex]=\frac{7 \times 1}{1 \times 19683}$$[/tex]
Multiply the numbers: [tex]$7 \times 1=7$[/tex]
[tex]=\frac{7}{1 \times 19683}$$[/tex]
Multiply the numbers: [tex]$1 \times 19683=19683$[/tex]
[tex]=\frac{7}{19683}[/tex]
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PLEASE HELP IT IS CALCULUS
Consider the equation below. (If an answer does not exist, enter DNE.)
f(x)= 3cos^2 -6sin(x) , 0<_x<_ 2pi
(a) Find the interval on which f is increasing. (Enter your answer using interval notation.)
Find the interval on which f is decreasing. (Enter your answer using interval notation.)
(b) Find the local minimum and maximum values of f.
(c) Find the inflection points.
(x, y)
(smaller x-value):
(x, y)
(larger x-value):
Find the interval on which f is concave up.(Enter your answer using interval notation.)
Find the jnterval on which f is concave down. (Enter your answer using interval notation.)
A)the interval on which f is increasing is x ∈ (π/2, 3π/2), The interval on which f is decreasing x∈ ( 0, π/2), (3π/2,2π)
B) local minimum = -6
local maximum = 6
C) Inflection points are (π/6,-3/4), (5π/6,-3/4).
Local minimum and maximum values are what?Local maxima are points in an interval where the values of the function at those points are never greater than the values of the function nearby. Local minima, on the other hand, are locations where the values of the function nearby are higher than the values of the function itself.
Inflection points are what?A point of inflection is the location where a curve changes from sloping up or down to sloping down or up; also known as concave upward or concave downward. Points of inflection are studied in calculus and geometry. In business, the point of inflection is the turning point of a business due to a significant change.
f(x) = 3cos^2 -6sin(x)
f'(x) = 6cosx d(cosx)/dx -6cosx
f'(x) = 6cosx( -sinx) - 6cosx
f'(x) = -6cosx ( sin x +1)
f"(x) = -6d (cosx)/dx (sinx +1) + -6cosx d ( sin x +1)/dx
f"(x) = -6 ([tex]cos^{2}x - sin^{2}x[/tex]) + 6sinx
a).the interval on which f is increasing is
f'(x)>0
-6cosx ( sin x +1) >0
6cosx ( sin x +1) <0
x ∈ (π/2, 3π/2)
The interval on which f is decreasing
f'(x)<0
-6cosx ( sin x +1) <0
6cosx ( sin x +1) >0
x∈ ( 0, π/2), (3π/2,2π)
since the function is decreasing till x = π/2
so x = π/2 is local minimum (x,y) = ( π/2, -6)
it increasing till 3π/2 and then decreasing
x = 3π/2 is local maximum values (x,y) = ( 3π/2, 6)
local minimum = -6
local maximum = 6
c). inflection points. f"(x) = 0
f"(x) = -6 ([tex]cos^{2}x - sin^{2}x[/tex]) + 6sinx = 0
-6 (1-2sin^{2}x) + 6sinx = 0
2[tex]sin^{2}x[/tex] + 2sinx -sinx -1 = 0
sinx = 1/2,-1
x = (π/6,5π/6)
concave up f"(x) >0
-6 (1-2sin^{2}x) + 6sinx > 0
x ∈ (π/6,5π/6)
concave down f"(x) <0
(2sinx -1)(sinx+1) <0
x ∈ (0,π/6) (5π/6,3π/2),(3π/2, 2π)
Inflection points are (π/6,-3/4), (5π/6,-3/4).
A)the interval on which f is increasing is x ∈ (π/2, 3π/2), The interval on which f is decreasing x∈ ( 0, π/2), (3π/2,2π)
B) local minimum = -6
local maximum = 6
C) Inflection points are (π/6,-3/4), (5π/6,-3/4).
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Here is a data set:
1 2 3 3 4 4 4 4 5 5 6 7
What happens to the mean and standard deviation of the data set when the 7 is changed to a 70?
The mean of the dataset increases and the standard deviation of the data set increases when the 7 is changed to a 70
How to determine the effect of changing a data element?From the question, we have the following parameters that can be used in our computation:
Dataset: 1 2 3 3 4 4 4 4 5 5 6 7
As a general rule:
When a data item is changed (increased), the mean is increasedWhen a data item is changed (increased), the standard deviation is increasedWhen a data item is changed (decreased), the mean is decreasedWhen a data item is changed (decreased), the standard deviation is decreasedTo prove the above statements, the mean and the standard deviations are calculated using online calculators
So, we have
Original dataset
1, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 7
Mean = 4
Standard deviation = 1.58
New dataset
1, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 70
Mean = 9.25
Standard deviation = 18.36
This means that changing 7 to 70 would increase the mean and the standard deviation
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What is the correct answer to this problem? g(x)=x2+6 find g(-3)=
Answer:
15
Step-by-step explanation:
A function and a quadrant are given. Find the other five function values. Give exact answers.
The other five function values are sin(Ф)= -4/5, tan(Ф)= 4/3, cot(Ф)= 3/4, sec(Ф)= -5/3 and csc(Ф)= -5/4.
what is trigonometry?Trigonometry is a field of mathematics that examines correlations between triangle side lengths and angles (from the Ancient Greek words "trigonon" and "metron"). The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research. Trigonometry has a wide variety of identities. With the intention of simplifying an expression, finding a more practical form of an expression, or solving an equation, these trigonometric identities are frequently employed to rewrite trigonometrical expressions.Since x is in IIIrd quadrant sin and cos will be negative but tan will be positive
given cos x= -3/5
We know that
sin²x + cos²x=1
sin²x+(-3/5)²=1
sin²x+9/25=1
sin²x=1-9/25
sin²x=16/25
sinx= ±√16/25
sinx= ±4/5
since, x is in IIIrd quadrant.
As sinx is negative IIIrd quadrant,
∴sinx= -4/5
tanx=sinx/cosx
=-4/5÷-3/5
=4/3
cotx=1/tanx
=1/4/3
=3/4
cosecx=1/sinx
=1/-4/5
=-5/4
secx=1/cosx
=1/-3/5
=-5/3
Hence, The other five function values are sin(Ф)= -4/5, tan(Ф)= 4/3, cot(Ф)= 3/4, sec(Ф)= -5/3 and csc(Ф)= -5/4.
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what's the answer my friend needs help
The image by rotation of the triangle ABC with vertices A(x, y) = (8, - 9), B(x, y) = (5, - 4), C(x, y) = (7, - 1) is represented by vertices A'(x, y) = (- 9, - 8), B'(x, y) = (- 4, - 5) and C'(x, y) = (- 1, - 7). The transformation rule is R'(x, y) = (x · cos θ - y · sin θ, x · sin θ + y · cos θ).
How to find the transformation rule and image of a given figure
In this problem we have the case of triangle set on a Cartesian plane and that must be rotated 90° clockwise, the image can be found by using the following transformation rule:
R'(x, y) = (x · cos θ - y · sin θ, x · sin θ + y · cos θ)
Where:
x, y - Coordinates of the original point.
θ - Angle of rotation, in degrees.
If we know that A(x, y) = (8, - 9), B(x, y) = (5, - 4), C(x, y) = (7, - 1) and θ = - 90°, then the image of the triangle is:
A'(x, y) = (8 · cos (- 90°) - (- 9) · sin (- 90°), 8 · sin (- 90°) + (- 9) · cos (- 90°))
A'(x, y) = (- 9, - 8)
B'(x, y) = (5 · cos (- 90°) - (- 4) · sin (- 90°), 5 · sin (- 90°) + (- 4) · cos (- 90°))
B'(x, y) = (- 4, - 5)
C'(x, y) = (7 · cos (- 90°) - (- 1) · sin (- 90°), 7 · sin (- 90°) + (- 1) · cos (- 90°))
C'(x, y) = (- 1, - 7)
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x^2+y^2+4x+6y-12=0 identify the radius and the center
Answer:
Center = (-2, -3)
Radius = 5
Step-by-step explanation:
help meeeeeeeeeee pleaseee
(a) 794g of the initial sample will be left in the sample after 25 years. (b) Time taken to decay to half of its original amount is 3.39 years.
Isotopes(200g) are atoms that have the same number of protons in their nucleus, but a different number of neutrons. This means that they have the same atomic number, but a different atomic mass. Because of this, isotopes have different physical and chemical properties. Isotopes can be stable, meaning that they do not undergo radioactive decay, or they can be unstable, meaning that they will undergo radioactive decay over time.
(a) Substituting 25 for t in the expression, we get:
[tex]A(25) = 200e^{0.0541 \times 25}[/tex]
[tex]= 200e^{1.3525}[/tex]
Thus, after 25 years, there will be
[tex]200e^{1.3525} = 2003.97[/tex]
794 g of the initial sample left in the sample.
(b) We want to find t such that
[tex]A(t) = 200e^{0.0541}[/tex]
= 100.
Solving for t, we get:
[tex]= 200e^{0.0541} \times t=100[/tex]
Dividing both sides by 200 and applying the natural logarithm to both sides, we get:
0.0541 × t = ln(0.5)
Therefore,
[tex]t = \frac{ln(0.5)}{0.0541}[/tex]
= 3.39 years.
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Answer…………………………………….
Math probability question
Answer:
9.
[tex] \frac{1}{6} [/tex]
10.
[tex] \frac{1}{3} [/tex]
Lucas mixed together 4/12 quarts of iced tea and 2/14 quarts of lemonade to make punch for a party. He filled glasses with 3/8 quart of punch. How many glasses of punch was Lucas able to fill?
On solving the provided question, we got that 18 no. of glasses of punch was Lucas able to fill
What is mathematical operation?a mathematical procedure. The most frequent operations are add, subtract, multiply, and divide . However, there are numerous others, including squaring, taking the square root, logarithms, etc. If it's not a number, it's probably an operation.
9/2= quarts of iced tea
9/4= quarts of lemonade
After mixing,
punch for a party = 9/2 + 9/4 = 27/4
He fills 3/8 = quart of punch
No. of glasses of punch was Lucas able to fill = 27/4 X 8/3 = 18
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Suppose f(x)=x^(2) and g(x)=(3x)^(2). Which statement best compares the graph of g(x) with the graph of f(x) ?
A. The graph of g(x) is horizontally compressed by a factor of 3 .
B. The graph of g(x) is shifted 3 units to the right.
C. The graph of g(x) is vertically stretched by a factor of 3 .
D. The graph of g(x) is horizontally stretched by a factor of 3 .
x3+y3+z3=k
Solve in simplest form
Answer:
No answer
Step-by-step explanation:
Answer:
x3+y3+z3=k
Let x=a, y=b, and z=c.
Then, a3+b3+c3=k
This is a Diophantine equation, which has no general solution. To find particular solutions, we must use trial and error.
Step-by-step explanation:
Help! Write the slope-intercept form given the graph. PLEASE I NEED A ANSWER
The linear equation written in the slope-intercept form is:
y = (-3/5)*x
The correct option is C.
How to write the line on the graph?A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
Here we can see that the line crosses through the poin (0, 0), so the y-intercept is 0.
b = 0
y = a*x + 0
y = a*x
To find the value of a, we can use another point on the graph.
We can see that the linear equation passes through (5, - 3), replacing these values:
-3 = a*5
-3/5 = a
Then the linear equation is just:
y = (-3/5)*x
The correct option is C.
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Find the difference (7/8x-8)-(1/8x-12
The expressions are given to solve and reduce the answer to their simplest form.The x is 1/8.
Find the difference (7/8x-8)-(1/8x-2 ?We move all terms to the left:
7/8x-8-(1/8x-2)=0
Domain of the equation: 8x!=0
x!=0/8
x!=0
x∈R
Domain of the equation: 8x-2)!=0
x∈R
We get rid of parentheses
7/8x-1/8x+2-8=0
We multiply all the terms by the denominator
2*8x-8*8x+7-1=0
We add all the numbers together, and all the variables
2*8x-8*8x+6=0
By multiply elements
16x-64x+6=0
We add all the numbers together, and all the variables
-48x+6=0
We move all terms containing x to the left, all other terms to the right
-48x=-6
x=-6/-48
x = 1/8
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Given a function value of an acute angle, find the other five trigonometric function values
The other five trigonometric function values are cos(∅) = 11/61, tan(∅) = 60/11, sec(∅) = 61/11, csc(∅) = 61/60 and cot(∅) = 11/60
How to determine the other five trigonometric function valuesFrom the question, we have the following parameters that can be used in our computation:
sin(∅) = 60/61
The cosine of the angle can be calculated using
sin²(∅) + cos²(∅) = 1
Substitute the known values in the above equation, so, we have the following representation
(60/61)² + cos²(∅) = 1
This gives
cos²(∅) = 1 - (60/61)²
Evaluate the like terms
cos²(∅) = 121/3721
Take the square root of both sides
cos(∅) = 11/61
The tangent of the angle can be calculated using
tan(∅) = sin(∅)/cos(∅)
Substitute the known values in the above equation, so, we have the following representation
tan(∅) = (60/61)/(11/61)
Evaluate
tan(∅) = 60/11
The other ratios of the angle are calculated as follows
sec(∅) = 1/cos(∅) = 61/11
csc(∅) = 1/sin(∅) = 61/60
cot(∅) = 1/tan(∅) = 11/60
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The following is an incomplete flowchart proving that the opposite angles of parallelogram JKLM are congruent:
- Parallelogram JKLM is shown where segment JM is parallel to segment KL and segment JK is parallel to segment ML. - Extend segment JM beyond point M and draw point P, by Construction. - An arrow is drawn from this statement to angle MLK is congruent to angle PML, Alternate Interior Angles Theorem. An arrow is drawn from this statement to angle PML is congruent to angle KJM, numbered blank 1.
- An arrow is drawn from this statement to angle MLK is congruent to angle KJM, Transitive Property of Equality. - Extend segment JK beyond point J and draw point Q. - An arrow is drawn from this statement to angle JML is congruent to angle QJM, Alternate Interior Angles Theorem. - An arrow is drawn from this statement to angle QJM is congruent to angle LKJ, numbered blank 2. - An arrow is drawn from this statement to angle JML is congruent to angle LKJ, Transitive Property of Equality. - Two arrows are drawn from this previous statement and the statement angle MLK is congruent to angle KJM, Transitive Property of Equality to opposite angles of parallelogram JKLM are congruent.
Which reasons can be used to fill in the numbered blank spaces?
1Alternate Interior Angles Theorem 2Alternate Interior Angles Theorem
1Corresponding Angles Theorem 2Corresponding Angles Theorem 1Same-Side Interior Angles Theorem 2Alternate Interior Angles Theorem
1Same-Side Interior Angles Theorem 2Corresponding Angles Theorem
The reason (B) Corresponding Angles Theorem can be used to fill in the blanks in the given question.
What is a parallelogram?A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry.
A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.
So, extend segments JM and JK beyond points M and J, respectively, and draw points P and Q.
It is assumed that a parallelogram with segments JM parallel to segments KL and JK parallel to segments ML is presented.
Draw point P and extend segment JM past point M through construction.
Through construction also Continue segment JK draws point Q after point J.
Consequently, the Alternate Interior Angles Theorem ∠MLK≅∠PML and ∠JML≅∠QJM (1)
Then, the corresponding angles theorem ∠PML≅∠KJM and ∠QJM≅∠LKJ is applied (2)
Equations (1) and (2) and the transitive property of equality are used to create:
∠MLK≅∠KJM and ∠JML≅∠LKJ
As a result, the supplied parallelogram JKLM's opposite angles are congruent. So it was proved.
Therefore, the reason (B) Corresponding Angles Theorem can be used to fill in the blanks in the given question.
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Correct question:
The following is an incomplete flowchart proving that the opposite angles of parallelogram JKLM are congruent:
Parallelogram JKLM is shown where segment JM is parallel to segment KL and segment JK is parallel to segment ML. Extend segment JM beyond point M and draw point P, by Construction. An arrow is drawn from this statement to angle MLK is congruent to angle PML, Alternate Interior Angles Theorem. An arrow is drawn from this statement to angle PML is congruent to angle KJM, numbered blank 1. An arrow is drawn from this statement to angle MLK is congruent to angle KJM, Transitive Property of Equality. Extend segment JK beyond point J and draw point Q. An arrow is drawn from this statement to angle JML is congruent to angle QJM, Alternate Interior Angles Theorem. An arrow is drawn from this statement to angle QJM is congruent to angle LKJ, numbered blank 2. An arrow is drawn from this statement to angle JML is congruent to angle LKJ, Transitive Property of Equality. Two arrows are drawn from this previous statement and the statement angle MLK is congruent to angle KJM, Transitive Property of Equality to opposite angles of parallelogram JKLM are congruent.
Which reasons can be used to fill in the numbered blank spaces?
a. Alternate Interior Angles Theorem
b. Corresponding Angles Theorem
c. Same-Side Interior Angles Theorem
d. Same-Side Interior Angles Theorem