IWhat is the equation of a line that passes through the points (3, 6) and (8, 4)?
Answers
Answer:
\( (x_1 =2, y_1 = 6), (x_2 = 2, y_2 = 4)\)
\( m =\frac{y_2 -y_1}{x_2 -x_1}\)
And replacing we got:
\( m=\frac{4-6}{8-3}= -\frac{2}{5}\)
And for this case we can use the first point to find the intercept like this:
\( 6 = -\frac{2}{5}(3) +b\)
And solving we got:
\( b = 6 +\frac{6}{5}= \frac{36}{5}\)
And then the line equation would be given by:
\( y = -\frac{2}{5}x +\frac{36}{5}\)
Step-by-step explanation:
For this case we have the following two points given:
\( (x_1 =2, y_1 = 6), (x_2 = 2, y_2 = 4)\)
And for this case we want an equation for a line with the two points given by:
\( y = mx+b\)
Wher m is the slope and b the y intercept. We can find the slope with this formula:
\( m =\frac{y_2 -y_1}{x_2 -x_1}\)
And replacing we got:
\( m=\frac{4-6}{8-3}= -\frac{2}{5}\)
And for this case we can use the first point to find the intercept like this:
\( 6 = -\frac{2}{5}(3) +b\)
And solving we got:
\( b = 6 +\frac{6}{5}= \frac{36}{5}\)
And then the line equation would be given by:
\( y = -\frac{2}{5}x +\frac{36}{5}\)
Related Questions
Can someone help with this question please? it's in the imagine
Answers
Answer:
I am pretty sure it's 6
Step-by-step explanation:
If am pretty sure it is 6
Solve 2^x-2=8^4 but not solving for x
Answers
Without explicitly solving for x, we can conclude that the solution to the equation 2^x - 2 = 8^4 is x = 12.
To solve the equation 2^x - 2 = 8^4 without explicitly solving for x, we can simplify the equation using exponent rules and observe the relationship between the numbers.
First, let's simplify the equation:
2^x - 2 = 8^4
We know that 8 can be expressed as 2^3, so we can rewrite the equation as:
2^x - 2 = (2^3)^4
Applying the exponent rule (a^m)^n = a^(mn), we can simplify further:
2^x - 2 = 2^(34)
Simplifying the right side of the equation:
2^x - 2 = 2^12
Now, we can observe that both sides of the equation have the same base, which is 2. In order for the equation to hold true, the exponents must be equal:
x = 12
Therefore, we may deduce that the answer to the equation 2x - 2 = 84 is x = 12 without having to explicitly solve for x.
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departmental store: a box of 6 bottles of
a drink for 24 and a crate of 30 bottles
of the same drink for 105. Which is a
better deal?
Shailjas144
Answers
Answer:
the box of 6 for 24 is better
Step-by-step explanation:
which must be true in order for the relationship zyx~wvu to be correct
Answers
In order for the relationship zyx ~ wvu to be correct, the following conditions must be true:
Corresponding angles are congruent: The angles formed by matching vertices should have the same measures in both triangles. This ensures that the corresponding angles are equivalent.
Corresponding sides are proportional: The lengths of the sides that connect the corresponding vertices of the triangles should have a consistent ratio. This implies that the corresponding sides are proportional to each other.
These conditions are based on the definition of similarity between two triangles. If both the corresponding angles are congruent and the corresponding sides are proportional, then the triangles zyx and wvu are considered similar (denoted by ~).
Therefore, in order for zyx ~ wvu to be correct, the congruence of corresponding angles and the proportionality of corresponding sides must hold true.
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find the equation of the line through point (4,-7) and parallel to y = -2/3x + 3/2.
Answers
Answer:
y = -2/3 x - 13/3
Step-by-step explanation:
y = -2/3 x + 3/2
y = mx + b
m = -2/3
The slope of the given line is -2/3. Parallel lines have equal slopes, so our line also has slope -2/3.
m = -2/3
y = mx + b
y = -2/3 x + b
Substitute the given point for x and y and solve for b.
-7 = -2/3 (4) + b
-21/3 = -8/3 + b
b = -13/3
Answer: y = -2/3 x - 13/3
5x - y = -7
4x + 2y = – 14
Answers
Answer:
\(\boxed{\sf \ \ x=-2, \ y=-3 \ \ }\)
Step-by-step explanation:
Hello,
I assume that you want to solve this system of two equations
(1) 5x - y = -7
(2) 4x + 2y = -14
We will multiply (1) by 2 and add to (2) so that we can eliminate the terms in y
2*(1)+(2) gives
10x - 2y + 4x + 2y = -7*2 -14 = -14 - 14 = -28
<=>
14x = - 28 we can divide by 14 both parts
x = -28/14 = -2
and then we replace x in (1)
5*(-2)-y=-7
-10-y=-7 add 7
-10-y+7=0
-3-y=0 add y
-3 = y
which is equivalent to y = -3
do not hesitate if you have any question
Answer:
x = -2, y = -3
Step-by-step explanation:
5x - y = -7
4x + 2y = – 14
Multiply the first equation by 2
2(5x - y) = 2*-7
10x -2y = -14
Add this to the second equation to eliminate y
10x -2y = -14
4x + 2y = – 14
---------------------------
14x = -28
Divide by 14
14x/14 = -28/14
x = -2
Now find y
4x+2y = -14
4*-2 +2y = -14
-8+2y = -14
Add 8 to each side
2y = -6
Divide by 2
2y/2 = -6/2
y = -3
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answers
By answering the presented question, we may conclude that This circle's radius is the same as the radius of the circle whose equation is \(x^{2} + y^{2} = 9\). (False)
what is expression ?In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator
A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to contrast expressions and phrases.
An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.
The above equation may be rewritten as follows:
(x-1)² + y² = 10
When this equation is compared to the usual form of the circle equation:
(x-a)² + (y-b)² = r²
We can observe that the circle's centre is (1,0) and its radius is sqrt (10).
As a result, the following assertions are true:
The circle's radius is three units. (False) The circle's centre is on the x-axis. (False) The circle's centre is on the y-axis. (This is correct.) The usual form of the equation is (x-1)² + y² = 3. (False)
This circle's radius is the same as the radius of the circle whose equation is \(x^{2} + y^{2} = 9.\) (False)
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Need help ASAP !!
Type your response in the box
Simplify these algebraic expressions
Answers
Answer:
1. 8x+10
2. -5x-5
3. 2x-20
Step-by-step explanation:
1. Combine like terms, 12x-4x = 8x, 3+7 = 10
2. Combine like terms. -7x+2x=-5x, 8-13 = -5
3. combine like terms, -3x+5x = 2x, -18-2 = -20
dentify the radius and the center of a circle whose equation is (x – 5)² + y² = 81.
The radius of the circle is units.
The center of the circle is at (, ).
Answers
Answer:
Step-by-step explanation:
General formula
(x-h)^2 + (y-k)^2 = r^2
where (h,k) center of circle whose radius r
applying the formula to our Q
(x – 5)² + y² = 81
(x – 5)² + (y-0)² = 9^2
---> center of circle (5,0)
---> radius is 9
Can someone help me find \(\frac{8}{7} = m + \frac{2}{8}\)
Answers
Answer:
m=25/28
Step-by-step explanation:
Let c be a positive number. A differential equation of the form dy/dt=ky^1+c where k is a positive constant, is called a doomsday equation because the exponent in the expression ky^1+c is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term My^1.01. If 2 such rabbits breed initially and the warren has 16 rabbits after three months, then when is doomsday?
Answers
Answer:
The doomsday is 146 days
Step-by-step explanation:
Given
\(\frac{dy}{dt} = ky^{1 +c}\)
First, we calculate the solution that satisfies the initial solution
Multiply both sides by
\(\frac{dt}{y^{1+c}}\)
\(\frac{dt}{y^{1+c}} * \frac{dy}{dt} = ky^{1 +c} * \frac{dt}{y^{1+c}}\)
\(\frac{dy}{y^{1+c}} = k\ dt\)
Take integral of both sides
\(\int \frac{dy}{y^{1+c}} = \int k\ dt\)
\(\int y^{-1-c}\ dy = \int k\ dt\)
\(\int y^{-1-c}\ dy = k\int\ dt\)
Integrate
\(\frac{y^{-1-c+1}}{-1-c+1} = kt+C\)
\(-\frac{y^{-c}}{c} = kt+C\)
To find c; let t= 0
\(-\frac{y_0^{-c}}{c} = k*0+C\)
\(-\frac{y_0^{-c}}{c} = C\)
\(C =-\frac{y_0^{-c}}{c}\)
Substitute \(C =-\frac{y_0^{-c}}{c}\) in \(-\frac{y^{-c}}{c} = kt+C\)
\(-\frac{y^{-c}}{c} = kt-\frac{y_0^{-c}}{c}\)
Multiply through by -c
\(y^{-c} = -ckt+y_0^{-c}\)
Take exponents of \(-c^{-1\)
\(y^{-c*-c^{-1}} = [-ckt+y_0^{-c}]^{-c^{-1}\)
\(y = [-ckt+y_0^{-c}]^{-c^{-1}\)
\(y = [-ckt+y_0^{-c}]^{-\frac{1}{c}}\)
i.e.
\(y(t) = [-ckt+y_0^{-c}]^{-\frac{1}{c}}\)
Next:
\(t= 3\) i.e. 3 months
\(y_0 = 2\) --- initial number of breeds
So, we have:
\(y(3) = [-ck * 3+2^{-c}]^{-\frac{1}{c}}\)
-----------------------------------------------------------------------------
We have the growth term to be: \(ky^{1.01}\)
This implies that:
\(ky^{1.01} = ky^{1+c}\)
By comparison:
\(1.01 = 1 + c\)
\(c = 1.01 - 1 = 0.01\)
\(y(3) = 16\) --- 16 rabbits after 3 months:
-----------------------------------------------------------------------------
\(y(3) = [-ck * 3+2^{-c}]^{-\frac{1}{c}}\)
\(16 = [-0.01 * 3 * k + 2^{-0.01}]^{\frac{-1}{0.01}}\)
\(16 = [-0.03 * k + 2^{-0.01}]^{-100}\)
\(16 = [-0.03 k + 0.9931]^{-100}\)
Take -1/100th root of both sides
\(16^{-1/100} = -0.03k + 0.9931\)
\(0.9727 = -0.03k + 0.9931\)
\(0.03k= - 0.9727 + 0.9931\)
\(0.03k= 0.0204\)
\(k= \frac{0.0204}{0.03}\)
\(k= 0.68\)
Recall that:
\(-\frac{y^{-c}}{c} = kt+C\)
This implies that:
\(\frac{y_0^{-c}}{c} = kT\)
Make T the subject
\(T = \frac{y_0^{-c}}{kc}\)
Substitute: \(k= 0.68\), \(c = 0.01\) and \(y_0 = 2\)
\(T = \frac{2^{-0.01}}{0.68 * 0.01}\)
\(T = \frac{2^{-0.01}}{0.0068}\)
\(T = \frac{0.9931}{0.0068}\)
\(T = 146.04\)
The doomsday is 146 days
What numbers are missing from the pattern below? Enter your answer, using
a comma to separate each number.
57, 53, 49, 45, ?, ?, ?, ?, 25, 21, 17, 13
Answer here
Answers
The numbers that are missing from the pattern are 41, 37, 33, and 29
How to determine the numbers that are missing from the patternFrom the question, we have the following parameters that can be used in our computation:
57, 53, 49, 45, ?, ?, ?, ?, 25, 21, 17, 13
The above pattern is an arithmetic pattern that has the following features
First term = 57
Common difference = 4
using the above as a guide, we have the following:
Next term = 45 - 4 = 41
Next term = 41 - 4 = 37
Next term = 37 - 4 = 33
Next term = 33 - 4 = 29
Hence, the numbers that are missing from the pattern are 41, 37, 33, and 29
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Which angle number represents SXU?
Answers
Answer:
Angle 2
Step-by-step explanation:
Find S and find X.
Then find U.
The angle at X connected to S and U is the angle number.
52.76= 52+0.7+____
i hate this app a bit
Answers
Answer:
52.76= 52+0.7+52.76
Step-by-step explanation:
write an equation from write an equation from a table of values
Answers
To solve the exercise, you can first graph the points to see if they have a linear relationship, that is, if all the points are on the same line. So, you have
Since the relationship of the points is linear, then you can take two of the points through which the line passes, find the slope of the line, and then use the formula point-slope.
The formula for the slope is
\(\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where m is the slope of the line and} \\ (x_1,y_1),(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}\)If for example, you take the points
\(\begin{gathered} (x_1,y_1)=(2,9) \\ (x_2,y_2)=(6,-7) \end{gathered}\)You have
\(\begin{gathered} m=\frac{-7-9}{6-2} \\ m=\frac{-16}{4} \\ m=-4 \end{gathered}\)Now using the formula point-slope, that is,
\(y-y_1=m(x-x_1)\)You have
\(\begin{gathered} y-9_{}=-4(x-2_{}) \\ y-9_{}=-4x-4\cdot-2 \\ y-9_{}=-4x+6 \\ \text{ Add 9 }to\text{ both sides of the equation} \\ y-9+9=-4x+6+9 \\ y=-4x+17 \end{gathered}\)Therefore, the equation representing the values in the table is
\(y=-4x+17\)
A proportional relationship is shown in the table below:
�
xx
0
00
1.3
1.31, point, 3
2.6
2.62, point, 6
3.9
3.93, point, 9
5.2
5.25, point, 2
�
yy
0
00
1
11
2
22
3
33
4
44
What is the slope of the line that represents this relationship?
Graph the line that represents this relationship.
Answers
The slope of the line that represents the relationship is 0.76.
What is slope of a line?Slope in mathematics relates to how steep a line is. It measures how much the y-coordinate shifts upward or downward for every unit increment in the x-coordinate. The ratio of the vertical change (rise) to the horizontal change (run) between any two locations on a line is, in other words, the slope of the line.
The following equation can be used to determine a line's slope: slope = (y2 - y1) / (x2 - x1).
where any two points on the line (x1, y1) and (x2, y2).
Positive, negative, zero, or undefinable slopes are all possible. A line with a positive slope is moving upward from left to right, whereas one with a negative slope is moving downward.
The slope of the line is given by the formula:
slope = (change in y) / (change in x)
Substituting the point from the table we have (0, 0) , (1.3, 1) thus:
m = 1 - 0 / 1.3 - 0
m = 1 / 1.3 = 0.76
Now, using the slope intercept form we have:
y - y1 = m(x - x1)
For (0, 0) we have:
y = 0.76x
Hence, the slope of the line that represents the relationship is 0.76.
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The complete question is:
Hey big men i need help with this no bots or spam PLZZZ
Answers
Answer:
The correct answer is A
Step-by-step explanation:
Hope this helps
1. Which relationship describes 2:5
a. The ratio of desks to chairs if there are 5 chairs and 2 desk
b. The ratio of boys to girls if there are 2 girls and 5 boys
c. The ratio of girls to boys if there are 2 girls and 5 boys
d. The ratio of chairs to desk if there are 5 chairs and 2 desk
Answers
Answer:
c
Step-by-step explanation:
it is c because it said girls to boys, then explained girls to boys, while b was out of order. a and d said 5 first, contrary to the original question
Answer:
C because all the other options are from boys to girls or 5 to 2 and were looking for girls to boys or 2 to 5.
Step-by-step explanation:
How would you make the approximate probability values very close to the actual probability values? pa help, step by step explanation ):
Answers
Answer:
Using the exact probabilities from the binomial we can find the probability of obtaining 18 or more successes out of 20 trials.
hope it helps!
X is carrying out a series of experiments which involve using increasing amounts of a chemical. In the first experiment he uses 6g of the chemical and in the second experiment he uses 7.8g of the chemical.
(i) Given that the amounts of the chemical used form an arithmetic progression, find the total amount of chemical used in the first 30 experiments. [4]
(ii) Instead it is given that the amounts of the chemical used form a geometric progression. X has a total of 1800g of the chemical available. Show that N, the greatest number of experiments possible, satisfies the inequality
1.3N ≤ 91.
and use logarithms to calculate the value of N.
Answers
Answer:
a) 963g
b) 17
Step-by-step explanation:
i) Now we must first find the common difference of the AP
d = 7.8 -6 = 1.8
Now the sum of the AP gives the total amount of chemical used for 30 experiments
Sn = n/2 [2a + (n-1)d]
n= 30, a = 6, d= 1.8
Sn = 30/2[2(6) + (30-1) (1.8)]
Sn = 15[12 + 52.2]
Sn = 963g
ii)For the G.P the common ration is (r)= 7.8/6 = 1.3
Since r>1, sum of GP = a (r^n -1)/r-1
If sum = 1800g
1800= 6(1.3^n -1)/1.3 - 1
1800 = 6(1.3^n -1)/0.3
1800 * 0.3 = 6(1.3^n -1)
540 = 6(1.3^n -1)
540/6 = (1.3^n -1)
90 = 1.3^n -1
90 + 1 = 1.3^n
1.3^n = 91
log 1.3^n = log 91
nlog1.3 = log 91
n = log91/log 1.3
n = 1.959/0.114
n = 17
Answer:
a) 963g
b) 17
Step-by-step explanation:
i) Now we must first find the common difference of the AP
d = 7.8 -6 = 1.8
Now the sum of the AP gives the total amount of chemical used for 30 experiments
Sn = n/2 [2a + (n-1)d]
n= 30, a = 6, d= 1.8
Sn = 30/2[2(6) + (30-1) (1.8)]
Sn = 15[12 + 52.2]
Sn = 963g
ii)For the G.P the common ration is (r)= 7.8/6 = 1.3
Since r>1, sum of GP = a (r^n -1)/r-1
If sum = 1800g
1800= 6(1.3^n -1)/1.3 - 1
1800 = 6(1.3^n -1)/0.3
1800 * 0.3 = 6(1.3^n -1)
540 = 6(1.3^n -1)
540/6 = (1.3^n -1)
90 = 1.3^n -1
90 + 1 = 1.3^n
1.3^n = 91
log 1.3^n = log 91
nlog1.3 = log 91
n = log91/log 1.3
n = 1.959/0.114
n = 17
Simplify the expression using properties of operations 7 1/3t-(10 2/3t-6)
Answers
The result is 6-13/3×t after simplification by multiplying first and added the like term.
What do you mean by properties of operation?The procedure of calculation which we use in arithmetic. We perform our mathematical calculation by using particular operational properties such as addition, subtraction, multiplication and division.
How do we simplify mathematical terms?we can simplify any expression by using the properties of addition, subtraction, multiplication or division depending on the statement given.
in the above expression 7×(1/3)t- [10×(2/3)t-6]
we simplify it (7/3)t- (20/3)t+6
-(13/3)t+6
hence, 6-13/3t
hence, the result is 6-13/3×t
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A dressmaker bought 2/5 meter of yellow cloth, 1/3 meter of blue cloth and 1/6 meter of red cloth to make a dress for her daughter. What is the total length of cloth that
dressmaker bought ?
What is asked?
What are the given facts?
What operation shall be used to solve the problem?
Solution and answer
please need it badly
Answers
Question
Terry has an investment account which
compounds interest continuously at a rate of
1.4%. He puts $1600 in the account initially. After
3 years, how much money is in the account?
Round to the nearest dollar.
Answers
Answer:
1800 dollars
Step-by-step explanation:
We can set up an equation here to represent the exponential growth in Terry's bank account.
\(y = 1600(1.04)^x\)
We can plug in 3 for x since x is the # of years the account is receiving compound interest on.
\(y = 1600(1.04)^3\)
\(1.04^3 = 1.124864\\1.124864*1600= 1800\)
Find the length of side X in simple radical form with a rational denominator
Answers
The length of side X in simple radical form with a rational denominator is 25/√3.
What is a 30-60-90 triangle?In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.
This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):
Adjacent side = 5/√3
Hypotenuse, x = 5 × 5/√3
Hypotenuse, x = 25/√3.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
How is 1.03 written as a percent?
Answers
Answer:
103%
Step-by-step explanation:
It doesn't matter if the number is bigger than 100 in math my teacher told me.
Please say my answer was the most helpful. I want to have a brainliest.
can someone please help with my math??
Answers
Answer: 6.4 miles/hour
Step-by-step explanation:
Speed = distance/time
19.2/3 = 6.4
Hope this helps!
Write the equation of a line with the slope of 2, which contains the point
(4,-8).
Write your equation in slope intercept form and do NOT put any spaces in your answer.
Answers
Answer:
y=2x-16
Step-by-step explanation:
So since we have a point and the slope, we can use the point-slope equation to find our equation of a line
y - y₁ = m(x - x₁)
Here our (x₁, y₁) point is (4, -8) and our m is 2
Plugging in these values to our equation gives us:
y - (-8) = 2(x - (4)) → distributing the negative to the -8 gives y + 8 = 2(x - 4) → distributing the 2 to the (x - 4) gives y + 8 = 2x - 8 → and finally subtracting the 8 from both sides gives our equation of a line y = 2x - 16
If two angles are complementary then the sum of their measures is _______.
(Answer with a number ONLY)
Answers
If the two angles are complementary, then their sum is 90 degrees.
The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.
If the two angles are complementary, then their sum is 90 degrees.
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A student runs laps around a track. Each lap is 1/4 mile. The student runs 2 1/2 miles each day and has a goal to run a total of 45 miles. The student wrote this equation to find x, the number of days needed to complete the goal.
Answers
Answer:
x=18 days
Step-by-step explanation:
since the student runs 2 1/2 miles everyday divide that into 45 miles and you get 18 therefore x=18
Jose earns $24.30 per hour teaching swimming lessons.
2
How much will he earn in 7.5 hours?
Answers
Answer:
$182.25
Step-by-step explanation:
You just times the per hour to the amount of hours. Hope this helps