A linear equation is an equation in which each term has at max one degree. The solution of the system of linear equations is (2,6).
What is a linear equation?A linear equation is an equation in which each term has at max one degree. Linear equations in variables x and y can be written in the form y=mx+c
Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.
Solving the second equation for x,
x + 5y = 32
x = 32 - 5y
Now, substitue the value of x in the first equation,
2(32 - 5y) + 5y = 34
64 - 10y + 5y = 34
-5y = -30
y = 6
Substitue the value of y in any one of the equation,
x + 5y = 32
x + 5(6) = 32
x = 2
Hence, the solution of the system of linear equations is (2,6).
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Which answer best describes the system of equations shown in the graph?
A. Consistent and dependent
B. Inconsistent
C. Not enough information
D. Consistent and independent
Thanks.
Answer:
A. Consistent and dependent
Answer:
D. Consistent and independent
Step-by-step explanation:
A. Consistent and dependent = two lines that overlap with each other so they have infinite solutions (ex. y = 4x and 4y = 16x equal the same thing)
B. Inconsistent = parallel lines that will NEVER meet each other, so no solution (y = 4x and y = 4x + 1 have the same slope so the steepness of the two lines is the same - they will NEVER have at least 1 point intersecting)
C. Not enough information - incorrect because there are two lines on a graph, and that is enough info to solve
D. Consistent and independent = two lines with EXACTLY ONE SOLUTION (ex. y = 4x + 3 and y = 2x + 2 have exactly one point that overlaps)
[tex]8a⁴ × (9a)⁴ [/tex]
find the value of it
8a⁴ × (9a)⁴
Hope you could get an idea from here.
Doubt clarification - use comment section.
Which expression has the greatest value when c = 7? 12 - 2C 0R C - 5
please show working
If c = 7, then
12 - 2c
= 12 - 2(7)
= 12 - 14
= -2
c - 5
= (7) - 5
= 2
=》+2 > -2.
So, c - 5 has greater value than 12 - 2c, if c = 7.
______
Hope it helps ⚜
a) Given that sin x =cos x , find the value of tan x .
b) Find the values of x in the interval 0≤x<360 for which sin x =cos x .
[tex](a)\\\\\text{Given that, sin x = cos x }\\\\\text{So,} ~ \tan x = \dfrac{\sin x}{\cos x} = \dfrac{\sin x}{\sin x} = 1\\\\\\(b)\\\\\text{Given that,}\\\\\sin x = \cos x\\\\\implies \dfrac{\sin x}{\cos x} =1\\\\\implies \tan x =1\\\\\implies x = n\pi + \dfrac{\pi} 4 \\\\\text{For interval}~ [0, 2\pi),}\\\\x= \dfrac{\pi}4, \dfrac{5\pi}4~~;[\text{When n = 0,1}]\\\\\text{In degrees,} ~ x= 45^{\circ} , 225^{\circ}[/tex]
What is the domain of the function
y = √x
Answer:
[tex]0\leq x<\infty[/tex]
Step-by-step explanation:
The function [tex]y=\sqrt{x}[/tex] is not defined for negative numbers in the domain as they produce non-real results. Therefore, all positive numbers including 0 are included in the domain, so the domain of the function would be [tex]0\leq x<\infty[/tex].
I've attached a diagram to help you visualize the domain.
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
8y - 6x = 56
Answer:
y = 3/4 + 7
Step-by-step explanation:
you must put the equation into the form of y = mx + b
add 6x to both sides and put it in front of the 56
8y = 6x + 56
y must be by itself by x does not so we divide everything by 8
y = 6/8x + 7
we must simplify the fraction 6/8
y = 3/4x + 7
What is the domain and range of this graph??
Answer: D: (-∞, ∞)
R: (-∞, ∞)
Step-by-step explanation:
Since the end points are arrows and have no set stopping point we can assume the answer is all real numbers, also known as infinity
Researchers claim that 90% of people are left handed. Suppose the researchers' claim is true. Mrs. Reyes has a Statistics class with 30 students. What is the probability that exactly 25 of them are left handed?
Answer:
10.23% to the nearest hundredth.
Step-by-step explanation:
This is a Binomial Probability Distribution.
If exactly 25 are left handed then exactly 5 are right handed.
So (probability that exactly 25 are left handed)
= 30C5*(0.1)^5(0.9)^25
= 0.1023047706
= 10.23%.
The probability that exactly 25 students out of 30 are left-handed, assuming the researchers' claim is true, is approximately 0.2031, or about 20.31%.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
This problem involves the binomial probability distribution, where we have a fixed number of trials (30 students in this case), and each trial has two possible outcomes (left-handed or not left-handed).
The probability of success (a student being left-handed) is 0.9, based on the researchers' claim.
The probability of a failure (a student not being left-handed) is 1 - 0.9 = 0.1.
We want to find the probability that exactly 25 students out of 30 are left-handed.
This can be calculated using the binomial probability formula:
[tex]P(X = k) = ^nC_ kp^k (1 - p)^{n-k}[/tex]
where:
n = 30 (the number of trials)
k = 25 (the number of successes we want)
p = 0.9 (the probability of success in each trial)
Plugging in the values, we get:
[tex]P(X = 25) = ^{30}C_ {25}~ 0.9^{25} ~0.1^5[/tex]
Using a calculator or statistical software, we can find that:
P(X = 25) ≈ 0.2031
Therefore,
The probability that exactly 25 students out of 30 are left-handed, assuming the researchers' claim is true, is approximately 0.2031, or about 20.31%.
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The midpoint of \overline{\text{AB}} AB is M(0, -3)M(0,−3). If the coordinates of AA are (2, -5)(2,−5), what are the coordinates of BB?
The formating kinda screwed up
Using the mid-point concept, it is found that the coordinates of B are (-2, -1).
The mid-point of two points is the mean of the coordinates of each point.In this problem:
The points are: A(2, -5) and B(x,y).The mid-point is (0, -3).Applying the concept for both the x and y-coordinates, we have that:
[tex]\frac{x + 2}{2} = 0[/tex]
[tex]x + 2 = 0[/tex]
[tex]x = -2[/tex]
[tex]\frac{-5 + y}{2} = -3[/tex]
[tex]-5 + y = -6[/tex]
[tex]y = -1[/tex]
The coordinates of B are (-2, -1).
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If there is a 30% chance of snow today and a 10% chance of snow tomorrow, what is the chance that it will not snow today and tomorrow? Write your answer as a percent.
Answer:
The weather forecast says that there is a "30% chance of rain," and we think we understand what it means. This quantitative statement is assumed to be unambiguous and to convey more information than does a qualitative statement like "It might rain tomorrow." Because the forecast is expressed as a single-event probability, however, it does not specify the class of events it refers to. Therefore, even numerical probabilities can be interpreted by members of the public in multiple, mutually contradictory ways. To find out whether the same statement about rain probability evokes various interpretations, we randomly surveyed pedestrians in five metropolises located in countries that have had different degrees of exposure to probabilistic forecasts--Amsterdam, Athens, Berlin, Milan, and New York. They were asked what a "30% chance of rain tomorrow" means both in a multiple-choice and a free-response format. Only in New York did a majority of them supply the standard meteorological interpretation, namely, that when the weather conditions are like today, in 3 out of 10 cases there will be (at least a trace of) rain the next day. In each of the European cities, this alternative was judged as the least appropriate. The preferred interpretation in Europe was that it will rain tomorrow "30% of the time," followed by "in 30% of the area." To improve risk communication with the public, experts need to specify the reference class, that is, the class of events to which a single-event probability refers.
In the figure, one exterior angle is drawn at each vertex of the triangle. Explain how to find the sum of the measures of these three exterior angles.
Explanation:
Here's one way:
At vertex A, draw the vertical angle to the given angle 4. That is, extend AC, rather than AB to show the exterior angle at that vertex.
Now, collapse triangle to one with zero area, so that vertices A, B, C lie on top of each other. You can do this using a dilation scale factor f such that f→0.
The result is that the exterior angles divide the circular space around point ABC into three parts that sum to 360°. Essentially, we have copied each of the exterior angles to the same vertex.
The sum of the measures of the exterior angles is 360°.
_____
Additional comment
This identical approach can be used to show the sum of exterior angles around any convex polygon is always 360°.
You have an object with a mass of 5 kg. If it has a velocity of 4.7 m/s, what distance will the object travel if 98 newtons are applied to stop it?
69,420 ------------------------------------------------------------------------
Test the following point in the inequality
-2x – 3y < 15 Test ( 6 , -10 ) Please help with this
Q7 AND Q8 solve in full steps
Answer:
Steps in the picture
Hope it helps
The US Constitution originally said that senators would be selected by state legislatures. Per the terms of the 17th Amendment, senators are now elected directly by the citizens of their respective states.
The party balance in the 115th Congress (2017–19) is 51 Republicans, 47 Democrats, and 2 independents, who caucus with the Democrats. As of January 2018, Republicans had control of the legislatures of 31 states; Democrats had control in 14; control was split in 4; and Nebraska was officially nonpartisan.
Develop an argument for or against repealing the 17th Amendment.
In your essay, you must:
articulate a defensible claim or thesis that responds to the prompt and establishes a line of reasoning.
use your knowledge of federalism, the constitutional position of the US Senate, partisan politics, checks and balances, voting rights, and the history of redistricting or gerr
Based on the provisions of the 17th Amendment, we can see that the provisions of the United States Constitution gave the people the right to vote for their senators who would represent their interests instead of the state legislature.
With this in mind, we can see that if the seat of a senator is unoccupied, then the governor of the state can make his appointment of a senator.
Based on the given data on the party balance of the US Senators, it is still not enough reason to repeal the 17th Amendment because giving the people the right to choose their representatives is still the core value of democracy which should never be tampered with.
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2(5 - 8x) -13 = 9(1 - x) -12
2 (5 - 8x) - 13 = 9 (1 - x) - 12
10 - 16x - 13 = 9 - 9x - 12
10 - 13 - 16x = 9 - 12 - 9x
- 3 - 16x = - 3 - 9x
- 3 + 3 = - 9x + 16x
0 = 7x
0/7 = x
0 = x
_____
Hope it helps ⚜
Answer:
x = 0Step-by-step explanation:
2(5 - 8x) - 13 = 9(1 - x) -12 => 10 - 16x - 13 = 9 - 9x - 12=> -3 - 16x = -3 - 9x=> 0 = 16x - 9x=> 0 = 7x => x = 0Conclusion:
Therefore, the answer is 'x = 0'
!! Hoped this helped !!
[tex]BrainiacUser1357[/tex]
let f(x)=5x+5 find f(-1)
I need your help with this. please help me
[tex]f(x) = 5x+5\\\\f(-1) = 5(-1) +5 = -5+5=0[/tex]
can someone help me with this
Answer 1 and 2 seriously please.
Answer:
Step-by-step explanation:
1
(x+3)+(x-1)+(x+1) = 90°
3x + 3 = 90°
3x = 90 - 3
3x = 87
x = 87/3
x = 29°
2
x + (x+104) = 180°
2x + 104 = 180°
2x = 180 - 104
2x = 76
x = 76/2
x = 38°
I NEED HELP PLEASE will give crown
Answer:
hey. use cymath. its easier and youll me able to answer more questions like this. it also shows you the whole process. here look:
Step-by-step explanation:
PLEASE HURRY. WILL GIVE BRAINLIEST. 100pts
Answer:
a - 4/11
b - 11/30
c - 9/25
Step-by-step explanation:
have a lovely day <3
Answer:
a b c
Step-by-step explanation:
hope it helps
what are integer solutions to the equality below-2 < x < 2
Answer:
-1, 0, 1
Step-by-step explanation:
Intengers are whole numbers. those 3 numbers are the only intengers between -2 and 2
(ii) A retailer paid Rs 40000 for an article after receiving a discount of 20% the marked price from the manufacturer. He sold the article to the customer at a discount of 10% on the marked price. If the rate of CGST is 6% and the sales are intra state, the price paid by the consumer is
(a) Rs 53760
(b) Rs 50400
(c) Rs 47700
(d) Rs 50880
if the answer is correct with explanation will mark you as BRAINLIST
Answer:
the answer is C
Step-by-step explanation:
40,000/.80 = 50,000
50,000 x .10 = 5,000
50,000 - 5,000 = 45,000
45,000 x .06 =2700
45,000 + 2,700 = 47,700
Use the diagram to answer the question that follows.
What is the image of C under the translation described by the translation rule (x, y) + (x +4,
y - 10)?
D
B
E
A
Answer:
B
Step-by-step explanation:
So we are at C:
We need to find the dilation:
First we add 4 to x (meaning we move the point C 4 points to the right)
Then we need to subtract 10 to y (meaning we move the point C 10 points downwards)
This will give you your point:
Which is B
Hope this helps!
Two skateboarders start a race at the same time skateboarder A travels at a steady rate of 15 feet per second skateboarder B travels at a steady rate of 22 feet per second after 4 minutes how much farther will skateboarder B have traveled?
Answer:
Step-by-step explanation:
Relative speed can play a major role in creating distance between two bodies. If the relative speed between two bodies is 0, then both the bodies are moving in the same direction with a similar speed. Thus, After 4 minutes, 1680 feet farther will Skateboarder B have traveled.
Skateboarder A travels at a steady rate of 15 feet per second.
Skateboarder B travels at a steady rate of 22 feet per second.
We need to determine that after 4 minutes, how much farther will Skateboarder B have traveled.
The formula for finding the distance travelled by anybody is represented below
Time is given that is 4 minutes which means 240 seconds.
Thus,
Distance travelled by skateboarder A
Distance travelled by skateboarder B.
Therefore, the separation of the distance between both the skateboarders is 5280 - 3600 = 1680.
Thus, After 4 minutes, 1680 feet farther will Skateboarder B have traveled.
3a + 5b - 4a + 2b = *
7a
23ab
a + b
-a + 7b
Answer:
-a + 7b
Step-by-step explanation:
This problem is asking you to simplify the equation.
In order to do this, we will combine like terms (like terms are terms that share the same variable and/or exponent).
So we will combine 3a and -4a to get -1a or just -a, and now we'll combine 5b and 2b to get 7b.
So all together we have -a + 7b.
Hope this helps you :)
[tex]\\ \sf\Rrightarrow 3a+5b-4a+2b[/tex]
[tex]\\ \sf\Rrightarrow 3a-4a+5b+2b[/tex]
[tex]\\ \sf\Rrightarrow (3-4)a+(5+2)b[/tex]
[tex]\\ \sf\Rrightarrow -a+7b[/tex]
[tex]\\ \sf\Rrightarrow 7b-a[/tex]
Given that f(x) = x² + 5x, evaluate f(-2).If g(x)=2x + 1, find g(a + h)- g(a).
[tex]\\ \sf\longmapsto f(x)=x^2+5x[/tex]
[tex]\\ \sf\longmapsto f(-2)=(-2)^2+5(-2)[/tex]
[tex]\\ \sf\longmapsto f(-2)=4-10[/tex]
[tex]\\ \sf\longmapsto f(-2)=-6[/tex]
.#2
[tex]\\ \sf\longmapsto g(x)=2x+1[/tex]
[tex]\\ \sf\longmapsto g(a)=2a+1[/tex]
[tex]\\ \sf\longmapsto g(a+h)=2(a+h)+1[/tex]
.Now
[tex]\\ \sf\longmapsto g(a+h)-g(a)[/tex]
[tex]\\ \sf\longmapsto 2(a+h)+1-2a-1[/tex]
[tex]\\ \sf\longmapsto 2a+2h+1-2a-1[/tex]
[tex]\\ \sf\longmapsto 2h[/tex]
[tex]41 \times 28 - 36 \div 32 + 17 \times 21 - 18 = [/tex]
answere please
Answer:
The answer is 1485.875.
Step-by-step explanation:
[tex]\large{\tt{\underline{\underline{\pink{SOLUTION:}}}}}[/tex]
To solve the above equation we will follow the BODMAS rule.
[tex]\blue\star[/tex] BODMAS is an order of mathematic operations.[tex]\blue\star[/tex] BODMAS rule is to be followed while solving expressions in mathematics.It stands for :
[tex]\purple\star[/tex] B = bracket[tex]\purple\star[/tex] O = order of power[tex]\purple\star[/tex] D = division[tex]\purple\star[/tex] M = multiplication[tex]\purple\star[/tex] A = addition[tex]\purple\star[/tex] S = subtractionSolving this question by bodmas rule :
[tex]\begin{gathered}\quad{\sf{ = 41 \times 28 - 36 \div 32 + 17 \times 21 - 18}}\\\\\quad{\sf{ = 41 \times 28 - \dfrac{36}{32} + 17 \times 21 - 18}}\\\\\quad{\sf{ = 41 \times 28 - 1.125+ 17 \times 21 - 18}}\\\\\quad{\sf{ = 1148 - 1.125+ 357 - 18}}\\\\\quad{\sf{ = (1148+ 357) - (1.125 + 18)}}\\\\\quad{\sf{ = (1505) - (19.125)}}\\\\\quad{\sf{ = 1505- 19.125}}\\\\\quad{\sf{ = 1485.875}}\end{gathered}[/tex]
Hence, the answer is 1485.875.
[tex]\rule{300}{2.5}[/tex]
Write an equivalent expression.
1. 8(y - 7)
2. -2x + 7
3. 3/5x + 2/5 + 3/5x
Answer:
8(y - 7) =8y-7-2x+7=7/2=3.5The equivalent expressions are;
1. 8 (y - 7) = 8y - 56
2. - 2 (x + 7) = - 2x - 14
3. 3/5x + 2/5 + 3/5x = (6x + 2) / 5
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expressions are;
1. 8 (y - 7)
2. - 2 (x + 7)
3. 3/5x + 2/5 + 3/5x
Now,
Solve all the expression as;
1. 8 (y - 7) = 8 × y - 8 × 7
= 8y - 56
Thus, 8 (y - 7) = 8y - 56
2. - 2 (x + 7) = - 2 × x - 2 × 7
= - 2x - 14
Thus, - 2 (x + 7) = - 2x - 14
3. 3/5x + 2/5 + 3/5x = 3/5x + 3/5x + 2/5
= (3x + 3x)/ 5 + 2/5
= 6x / 5 + 2/ 5
= (6x + 2) / 5
Thus, 3/5x + 2/5 + 3/5x = (6x + 2) / 5
Therefore, The equivalent expressions are;
1. 8 (y - 7) = 8y - 56
2. - 2 (x + 7) = - 2x - 14
3. 3/5x + 2/5 + 3/5x = (6x + 2) / 5
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2,826 rounded to the nearest tenth
Answer:
2,826
Step-by-step explanation:
A tenth is the first place value after the decimal point
In this case, 2,826.00
To round a number to the tenths place, we look at the hundredths place
If the number is 5 or more, we add 1 to the tenths place, and leave the numbers to the right 0's
If the number is 4 or less, we keep the number as it is in the tenths place, and leave the numbers to the right 0's
In this case, the hundredths place is a 0, which is less than 4, so we keep the 0 in the tenths place, and leave the to the right 0's.
Thus, our final answer is 2,826.
