What is the slope of the line that passes through the points (-4, 5) and (-7, 8)
Solve the following
simultaneous
equations using an
algebraic (not
graphical) method.
3x + 4y = 7
2x - 3y = 16
According to the substitution method, the value of x is 5 and the value of y is -2
Substitution method:
In math, substitution method, we have to substitute the value of a variable found by one equation in the second equation.
Given,
Here we have the equations:
3x + 4y = 7
2x - 3y = 16
Now, we have to solve this one by using an algebraic method.
Here we have to use the substitution method to solve this equations,
Suppose,
3x+4y=7 →(1)
and 2x-3y=16 →(2)
Taking equation (1), we have
=> 3x+4y = 7
⇒ 3x = -4y+7
⇒ x = (-4y+7)/3 →(3)
Putting x = (-4y+7)/3 in equation (2), we get
=> 2x - 3y = 16
=> 2((-4y+7)/3) - 3y = 16
⇒-8y + 14 - 9y = 48
⇒ - 17y + 14 = 48
⇒ - 17y = 48 - 14
⇒ - 17y = 34
⇒y=-2→(4)
Now, Putting y=-2 in equation (3), we get
=> x = (-4y+7)/3
=> x = (-4(-2)+7)/3
⇒ x = (8 + 7)3
⇒ x = 15/3
⇒ x = 5
∴ x = 5 and y = -2
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please help with working if u just type random words I will report to the Moderator please this is for my o levels
Answer:
the answer for this is just a coincidence 18: 18 sets of equipment
19: 100 tickets
Step-by-step explanation:
this is the answer :)
1. Given f(x) = -3x - 2, find the following.
f(3)=
f(-1)=
f(-2)=
Answer:
f(3)=-11
f(-1)=1
f(-2)=4
Explanation:
For each question you would replace the x in the main equation (f(x)=-3x-2) for the number given within f(x).
Therefore,
f(3)=-3(3)-2
=-9-2
=-11
f(-1)=-3(-1)-2
=3-2
=1
f(-2)=-3(-2)-2
=6-2
=4
f(x) = -x + 5; g(x) = 2f(x)
Answer:
∴ g(x) = -2x + 10
Step-by-step explanation:
Since f(x) = -x + 5,
g(x) = 2[f(x)]
= 2(-x + 5)
= -2x + 10
the speed of a lazy river current is 5 mph. if a boat travels 20 miles downstream at the same time that it takes to travel 10 miles upstream, find the speed of the boat on still water.
The speed of boat in still water is 15 m per hour.
What is speed?
The speed of an object, also known as v in kinematics, is the size of the change in that object's position over time or the size of the change in that object's motion per unit of time, making it a scalar quantity. The instantaneous speed is indeed the upper limit of a average speed as that of the length of the interval approaches zero. The average speed of the object in a period of time is equal to the distance travelled by object divided by duration of the period. Velocity and speed are not the same thing.
The dimensions of speed are time divided by distance.
Given, speed of lazy river current = 5
distance covered = 20 miles downstream
and 10 miles upstream
Let x be the speed in still water
(x+5)T = 20
(X-5)T= 10
2(X-5) = (X+5)
X = 15
Therefore, speed of the boat in still water is 15 m per hour
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Answer these questions please.
Answer:
Tan A = Opposite/ Adjacent
Tan A = 40/9
option D
Step-by-step explanation:
On the second page, last question
Tan is given by a formula opposite divided by the adjacent
Based on the position of the angle, our opposite will be 40 and the adjacent, 9 leaving us with and equation
tan A = 40/9
value 26 - 19
the value of negitive and positive
The value of the final result when 19 is subtracted from 26 will be positive value (7).
According to the question,
We have the following expression:
26-19
Now, we have to find whether the value of this expression will be positive or negative.
We know that when two integers are of different signs then the smaller one is subtracted from the larger one but in the final result the sign remains that of the larger integer.
In this case, 26 is greater than 19 and it is positive.
So, the result will also be positive.
26-19
7
Hence, the value of the final result when 19 is subtracted from 26 will be positive (7).
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ƒ(x) = −x² + 9x – 17
Find f(-5)
What is the factored form of the expression over the complex numbers? 121x2+36y2.
The expression is (11x+i6y)(11x-i6y).
Given:
[tex]121x^{2} +36y^{2}[/tex]
[tex]121x^{2} +36y^{2} = (11x)^{2} +(6y)^{2}[/tex]
[tex]= (11x)^{2} -(-1)(6y)^{2}[/tex]
[tex]=(11x)^{2} -i^{2} (6y)^{2}[/tex]
[tex]=(11x)^{2} -(i6y)^{2}[/tex]
Formula:
[tex]a^{2} -b^{2} = (a+b)(a-b)[/tex]
[tex]121x^{2} -36y^{2}=(11x+i6y)(11x-i6y)[/tex]
#123
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Expression's factored form over complex numbers (11x + 6iy) (11x-6iy).
Given expression;
[tex]121x^2 + 36y^2[/tex]
Factored form of the expression over the complex numbers;
[tex]121x^2 + 36y^2[/tex] = [tex](11x)^2 + (6y)^2[/tex]
= [tex](11x)^2 -(-1)(6y)^2[/tex]
= [tex](11x)^2 - i^2(6y)^2[/tex]
= [tex](11x)^2 - (6iy)^2[/tex]
= (11x + 6iy) (11x-6iy)
Expression's factored form over complex numbers (11x + 6iy) (11x-6iy).
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Help mee someoneeeeee
Length of KM using distance formula is √53.
Define distance.Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage. In math, what is a distance? The length of the line segment connecting the two sites is used to measure distance between them. The shortest line segment between a point and a line will have a length equal to the distance between them.
Given,
Coordinates of K = (8,-4)
Coordinates of M = (1,-2)
Distance formula:
D = √(x₂ - x₁)² + (y₂ - y₁)²
D = √(8-1)² + (-4+2)²
D = √49 + 4
D = √53
Length of KM using distance formula is √53.
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if 45% of an item is $36 what is the original price
Answer:
$80 original price
Step-by-step explanation:
If 45% of an item is $36 what is the original price?
40% = 0.4
36/0.4 = $80 original price
Answer:
$80
Step-by-step explanation:
45/100=36/x
Cross multiply
45x=100(36)
45x=3600
/45. /45
x=80
Hopes this helps please mark brainliest
Could someone explain how to solve these?
Answer:
Yes
Step-by-step explanation:
I will do question 4 so you understand: What there asking is for you to simplify.
This is how you do so.
step 1 find the numbers that have the same letter
Step 2 If you find one for example 7y and 3y you add them which is 10y
Step 3: Any letters that are by them selves and the question doesn't give you a value ignore!
Hope this helps!!
The sum of three times a and four is the same as 5
times a.
Answer: 2
Step-by-step explanation:
Equation: 3a + 4 = 5a
-5a+3a+4 = 5a-5a
-2a+4 = 0
-2a+4-4 = 0-4
-2a = -4
a = 2
Done!
Bro please help this question is pain
Answer:
tttttttttttttttttttttttttttttttttttttttttt
Step-by-step explanation:
tttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttt
Diane walks 5,000 steps each day for exercise. Over the next year, her goal is to increase the number of steps she walks each day by 10. Let f (r) represent the number of steps Diane plans to walk on day z since beginning her goal. What does f (100) = 6,000 represent? Select from the drop-down menus to complete the sentence correctly.
Di-ane plans to walk 6000 steps on day 100.
Given, Di-ane walks 5000 steps each day. She keeps her goal to increase the 10 number of steps. The increase has been modelled using the function.
A re-lation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a re-lationship between inputs in which each input is connected to precisely one output.
We have to write what does f(100)=6000 represent.
As given in question the function represents the number of steps. and x represent the day.
100 represents the number 100th day, f(100)=6000 represents that Di-ane walks 6000 steps on the 100th day.
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What is the mean for this data?
Thank you for helping.
Answer:
5
Step-by-step explanation:
add the numbers up
1+2+5+5+6+6+7+8=40
divide it by 8 (because there are 8 numbers)
40/8=5
Which value of m makes this equation true?
Answer:
m = -27/13
Step-by-step explanation:
Given equation,
→ (2m - 27)/3 = 5m
Now the value of m will be,
→ (2m - 27)/3 = 5m
→ 2m - 27 = 5m × 3
→ 2m - 15m = 27
→ -13m = 27
→ [ m = -27/13 ]
Hence, value of m is -27/13.
Simplify pls will mark brainliest
The simplified expression can be given as 3y^7
What is exponent?
We we multiply same number multiple times then it we write it in forms of exponent. an exponent shows how many times a multiplied to itself
We are given an expression 3y^3/ y^-4
We multiply numerator and denominator by y^4 to simplify the expression
In the numerator the term gets added and in the denominator +4 and -4 get subtracted getting 0 in the exponent.
And anything raised to 0 is 1
Hence, We get, 3y^7
This is the simplified expression
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Solve this using elimination
-4x+6y=24
2x+y=8
What are the coordinates of (9,4) after the following translation? *
(x, y) (x - 2, y + 1)
(7,5)
(11,5)
(7,3)
(11,3)
The coordinates of (9,4) after the following translation (x, y) (x - 2, y + 1) is (7,5)
What does a coordinate in mathematics mean?
A group of numbers used to express the divisions of two reference axes' positions along the horizontal and vertical axes of a coordinate plane. frequently represented as the union of x-values and y-values (x,y).
Given that
x = x-2
y = y+1
After this we can convert this (9,4) coordinate in the following translation
9-2 = 7
4+1 = 5
Hence now new coordinate after the translation is (7,5)
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find the area of mirror.
Answer:
8.5
Step-by-step explanation:
the distance between points X and Y. In other words, to view an image of yourself in a plane mirror, you will need an amount of mirror equal to one-half of your height. A 6-foot tall man needs 3-feet of mirror (positioned properly) in order to view his entire image.
Anne worked out at the gym for
an hour. She spent 25 minutes on the
treadmill, 20 minutes lifting weights,
and the rest of the time stretching.
What percent of the time did Anne
spend stretching?
Answer:
Anny consumed 25% time in stretching
Total time taken by anny in gym = 1 hour.
Time spent by anny on the treadmill= 25 minutes.
Time spent by anny in lifting weights= 20 minutes.
And remaining time anny spent on streching,
we have to find what percent did anny spend on streching.
Therefore anny consumed 25% time in streching.
Answer is 25%.
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Please answer these and tell me if mine is correct
The value of a company’s stock is represented by the expression x^2 – 2y and the company’s purchases are modeled by 2x + 5y. The company’s goal is to maintain a stock value of at least $7,000, while keeping the purchases below $1,000. Which system of inequalities represents this scenario?
x^2 – 2y > 7000
2x + 5y < 1000
x^2 – 2y ≥ 7000
2x + 5y < 1000
x^2 – 2y > 7000
2x + 5y ≤ 1000
x^2 – 2y ≤ 7000
2x + 5y ≤ 1000
The system of inequalities that represents this scenario is;
x² - 2y ≥ 7000
2x + 5y < 1000
How to express a system of Inequalities?We are given that;
Value of company's stock = x² - 2y
Now, purchases by the company is modeled by; 2x + 5y
We are now told that the company’s goal is to maintain a stock value of at least $7,000. This means the stock value must be greater than or equal to $7000. Thus, this inequality is;
x² - 2y ≥ 7000
Now, we are told that the purchases must be kept below $1000. This means less than $1000 and as such the inequality is;
2x + 5y < 1000
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Can we use 1 2bh for equilateral triangle?.
An equilateral triangle is not a right triangle for which the formula A = 1/2 bh applies. where A is the area, b is the length of the base, and h is the height. This formula does not work because all sides and angles of an equilateral triangle are equal.
What is equilateral triangle ?In geometry, a triangle with all sides equal is called an equilateral triangle. Splitting the word equilateral, here 'equi' means equal and 'lateral' means side. An equilateral triangle is also called a regular polygon with three equal sides. In this article, you will learn about equilateral triangles, properties of equilateral triangles, and formulas for equilateral triangles. An equilateral triangle is a triangle with all three equal sides and equal angles. An equilateral triangle is also called an equilateral triangle because each angle has a value of 60 degrees. Equilateral triangles are considered regular polygons or equilateral triangles because they have equal angles and equal sides.Triangles are classified into three different types based on their sides. An isosceles triangle, a scalene triangle, and an equilateral triangle. Equilateral triangles are different from isosceles and scalene triangles.Hence, An equilateral triangle is not a right triangle for which the formula A = 1/2 bh applies. where A is the area, b is the length of the base, and h is the height. This formula does not work because all sides and angles of an equilateral triangle are equal.
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Make
x
the subject of the formula:
x/y - z = w
Making x the subject of the formula x/y -z=w is
x = y(w+z)
What is subject of a formula?The subject of a formula is the variable which is expressed in terms of the other variable. For example the volume of a cylinder is V = πr^2h.
where V is the volume and r is the radius and h is the height . In the formula V is expressed in term of other variables like radius and height. Therefore V is said to be the subject of the formula
Relating the explanation with the formula x/y -z= w, here w is the subject and we need to make x the subject.
We achieve this by evacuating other variables attached to x
x/y -z= w
add both sides by z
x/y-z+z= w+z
x/y= w+z
multiply both sides by y
x/y×y=(w+z)y
therefore x= y(w+z)
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NEED NOW!! WILL GIVE BRAINLIEST + 100 POINTS.
Answer:
D) The slope is -0.3, which indicates a negative correlation.---------------------------------------
The equation is giveny = 39 - 0.3xRearrange the equation and show in slope-intercept form y = mx + by = - 0.3x + 39, where slope is m = - 0.3Slope is negative and therefore it represent a negative correlation.
The matching choice is D
Answer:
d) The slope is -0.3, which indicates a negative correlation.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Given equation:
[tex]y=3.9-0.3x[/tex]
The slope of a linear equation is the coefficient of the term in x.
Therefore, the slope of the given line of best fit is -0.3.
If the slope of the line of best line is negative, it indicates a negative correlation.
If the slope of the line of best line is positive, it indicates a positive correlation.
Therefore, as the slope is negative, it indicates a negative correlation.
an actual distance of 50km corresponds to 4cm on the map
Using the given information, the scale of the map is 1 : 1250000
Determining the scale of a mapFrom the question, we are to determine the scale of the map.
From the given information,
An actual distance of 50km corresponds to 4cm on the map
To determine the scale of the map,
First, we will convert 50 km to cm
50 km = 50000 m
50000m = 5000000 cm
∴ 50 km = 5000000 cm
Thus,
An actual distance of 5000000 cm corresponds to 4cm on the map
That is,
4 cm represents 5000000 cm
Dividing by 4
Then,
1 cm represents 1250000 cm
Hence,
The scale is 1 : 1250000
Here is the complete question:
What is the scale if: an actual distance of 50km corresponds to 4cm on the map.
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a website advertises job openings on its website, but job seekers have to pay to access the list of job openings. the website recently completed a survey to estimate the number of days it takes to find a new job using its service. it took the last 30 customers an average of 60 days to find a job. assume the population standard deviation is 10 days. calculate a 95% confidence interval of the population mean number of days it takes to find a job.
(56.42155, 63.57845) is the 95% confidence interval of the population mean number of days it takes to find a job.
What is confidence interval ?In frequency statistics, a confidence interval is the range of estimated values for an unknown parameter. Confidence intervals are computed at the specified confidence level. A 95% confidence level is the most common, but other levels such as 90% and 99% are sometimes used.
CalculationGiven a=0.05, Z(0.025)=1.96
SO 95% confidence interval is
xbar+/-Z*s/vn
--> 60+/- 1.96*10/sqrt(30)
-> (56.42155, 63.57845)
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