Find the equation of a line that passes through the point (3,-1) and has a
gradient of 1/3
Leave your answer in the form y=mx + c
Answer: y=-4x/9 + 1/3
Step-by-step explanation:
y=mx + c
**Substitute known variables into the equation**
-1=3m + 1/3
(-1=3m + 1/3)*3 ==> Multiply equation by 3 to get rid of fractions
-3=9m+1
9m=-4
m=-4/9
y=-4x/9 + 1/3
I would like to know what is; 8 1/4 x 6 4/5 = ?
Answer:
56.1
Step-by-step explanation:
Solve each equation. Check each solution. 1/x + x/2 = x+ 4/2x
The solution of the given equation /x + x/2 = x+ 4/2x for x is i√2.
According to the given question.
We have an equation 1/x + x/2 = x+ 4/2x.
Since, we have to solve th egiven equation 1/x + x/2 = x+ 4/2x, for x.
Therefore, the solution of the given equation 1/x + x/2 = x+ 4/2x for x is given by
1/x + x/2 = x+ 4/2x
⇒ 1/x - 4/2x = x - x/2
⇒ 1/x -2/x = x - x/2
⇒ (1-2)/x = (2x -x)/2
⇒ -1/x = x/2
⇒ -2 = x^2
⇒ x = √(-2)
⇒ x = i√2 (√-1 = i)
Hence, the solution of the given equation /x + x/2 = x+ 4/2x for x is i√2.
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Solve negative one sixth times the quantity 3 minus 15 times the quantity one third squared end quantity end quantity.
two thirds
18 over 54
negative two ninths
negative two and 42 over 54
The result of the given expression is negative fifth sixth
Solving linear equationThe interpretation of the statement as a linear function is expressed as;
-1/6(3) - 3(1/3)²
Expand the fraction in parenthesis
-1/6(3) = -1/2
3(1/3)² = 3(1/9) = 1/3
Substitute
-1/6(3) - 3(1/3)²
-1/2 - 1/3
-3-2/6
-5/6
Hence the result of the given expression is negative fifth sixth
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(-2)^4÷(-4)-2(-3)(8-4)
Answer:
the answer would be 20.
Step-by-step explanation:
-
Answer:
[tex](((-2)^{4} )/(-4))-(2*(-3)*(8-4))\\[/tex] = 20
Step-by-step explanation:
breaking into 2 parts:
calculate within parenthesis: [tex](((-2)^{4} )/(-4))[/tex] = 16/(-4) = -4
calculate within parenthesis: (2*(-3)*(8-4)) = (2*(-3)*(4)) = -24
add and subtract (left to right): -4-(-24)=20
Dadas las siguientes condiciones, determina la ecuación de la recta en su forma general Ax+By+C=0.
Pasa por (−5,0) y tiene pendiente m=32.
32(-5) + 0 + 160 = 0 is the line in the general form of the line the passing through (−5,0) with the slope 32.
What is slope?A number that describes a line's direction and steepness is known as the slope or gradient of a line in mathematics. There is no obvious reason why the letter m is used to represent slope, although it first appears in English in O'Brien (1844), who wrote the equation for a straight line as "y = mx + b," and it may also be found in Todhunter (1888), who wrote it as "y = mx + c."
Let us write the given data in slope-intercept form that is
y = m(x) + b
where m = slope of the line
b = y-intercept
So substituting the values we get
0 = 32(-5) + b
-b = -160
b = 160
so we have the slope intercept form
0 = 32(-5) + 160
Converting this to General form
ax + by + c = 0
32(-5) + 0 + 160 = 0
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Translated question
Given the following conditions, determine the equation of the line in its general form Ax+By+C=0.
It passes through (−5,0) and has slope m=32.
Determine whether each sequence is arithmetic or geometric. Then identify the common difference or common ratio. 3/32, 3/16, 3/8, 3/4, 3/2, 3,6, . . . .
The sequence 3/32, 3/16, 3/8, 3/4, 3/2, 3,6, ... is a geometric sequence with common ratio 2.
To determine whether the sequence is an arithmetic or geometric one, we need to check how the consecutive terms relate to each other.
If it is an arithmetic sequence, then:
a(n) = a(n-1) + d
where d is the common difference.
If it is a geometric sequence, then:
a(n) = a(n-1) . r
where r is the common ratio.
The given sequence is:
3/32, 3/16, 3/8, 3/4, 3/2, 3,6, . . . .
Notice that
a(2) : a(1) = 3/16 : 3/32 = 2
a(3) : a(2) = 3/8 : 3/16 = 2
and so on
Since the ratio of consecutive terms are constant, then the given sequence is a geometric sequence. Furthermore, its ratio, r = 2
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Please help!! 20 points!
Solve for A.
r + A/n = b^2
Answer: A=n(b^2-r)
Step-by-step explanation:
r + A/n = b^2
r-r+A/n = b^2-r
A/n = b^2-r
A*n/n=n(b^2-r)
A=n(b^2-r)
There are 2 gyms. One, Buff Billy's, has a joining cost
of $80 and charges $25 a month. The other,
Shredded Eddie's, has no joining cost but charges
$35 a month. At what month are both gyms the same
total cost?
In linear equation, the intersection at coordinate (9, 315).
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.Gym one:
f(x) =80 x + 25
Gym two:
g(x) = 35x (+ 0 [since there was no joining fee])
The first month is easy.
Gym one's cost is just the joining fee plus the one month of membership fee. Or...
105 = 80(1) + 25
Gym two's cost is just that first month's membership fee. Or...
35 = 35(1) + 0
then second month
[f(x) = 185 = 80(2)+25
g(x) = 70 = 35(2)],
then a tenth month [
f(x) = 825 = 80(10) + 25;
g(x) = 350 = 35(10)]
and that gym one's cost exceeded the cost of gym two,
back one month and found the answer.
By month nine, both gyms had equalized at $315.
the intersection at coordinate (9, 315).
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Simplify the expression.
8-17 / 12-(-3)
The simplified expression is -3/5.
To simplify the given expression in question, we will solve it step wise. Firstly we will simplify the numerator by performing operation according to the sign. Similar approach will be repeated for the denominator. Then we will write it in fraction form to find the simplified form of expression.
Numerator -
Numerator = 8 - 17
Here subtraction of large number is required form small number, so the result will be subtracted value with negative sign
Numerator = -9
Denominator -
Denominator = 12 - (-3)
Here two negative signs are present, so, we will perform addition and the result will be with positive sign
Denominator = 12 + 3
Denominator = 15
Writing the fraction form -
Expression = -9/15
Dividing the expression by 3
Expression = -3/5
Hence, the simplified expression is -3/5.
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A square is inscribed in a circle. What is the ratio of the area of the circle to the area of the square?
The side of the square inscribed in a square be a units then the required ratio is π : 2.
What is an inscribed square?
A square is inscribed in a circle or a polygon if its four vertices are on the circle's circumference or the polygon's sides.
Inscribed in the circle is a square that fits snugly inside a circle. The square's corners will touch but not intersect the circle's boundary, and the diagonal of the square will equal the diameter of the circle. Furthermore, as with any square's diagonal, it equals the hypotenuse of a 45°-45°-90° triangle.
Let the side of the square inscribed in a square be a units.
Hence, the required ratio is 2 : 1.
Let ABCD be a square inscribed in a circle of radius 'r'.
Now, the diameter of the circle is the diagonal of the square.
Therefore, BD = 2r.
In △BDC, using Pythagoras theorem
[tex]BC^2+CD^2=BD^2[/tex]
⇒ [tex]a^2+a^2=(2r)^2[/tex]
⇒ [tex]2a^2=4r^2[/tex]
⇒ [tex]a^2=2r^2[/tex]
Area of square=[tex]2r^2[/tex]
Area of circle =[tex]$$\pi r^2[/tex]
Required ration = [tex]$\pi r^2:2r^2[/tex] = π : 2
Therefore, the required ration is π : 2.
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what is the least common denominator of 7/10 and 1/2
Answer:
10
Step-by-step explanation:
:D
what is the standard form or (4 x 1,000) + (7x 10) +(6x1) + ( 8 x 0.001)?
very urgent please
The given expression written in standard form is 4.076008 × 10³
Writing an expression in standard formFrom the question, we are to simplify the given expression in standard form
The given expression is
(4 × 1000) + (7 × 10) + (6 × 1) + (8 × 0.001)
Simplifying
(4 × 1000) + (7 × 10) + (6 × 1) + (8 × 0.001)
(4000) + (70) + (6) + (0.008)
= 4000 + 70 + 6 + 0.008
= 4076.008
In standard form, we get
4.076008 × 10³
Hence, the given expression written in standard form is 4.076008 × 10³
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Solve each system by substitution. Check your answers.
y = 2x - 1 , 3x - y = -1
By substitution, the solution of the system of equations, y = 2x - 1 and 3x - y = -1, is (-2 , -5).
A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Using substitution method, given two linear equations in x and y,
y = 2x - 1 (equation 1)
3x - y = -1 (equation 2)
Since the first equation is already expressed in y in terms of x, substitute the value of y to the second equation.
3x - y = -1 (equation 2)
3x - (2x - 1) = -1
3x - 2x + 1 = -1
Combining all terms containing the variable x on one side and the constants on the other side of the equality, and solving for x.
3x - 2x + 1 = -1
3x - 2x = -1 - 1
x = -2
Substitute the value of x in the first equation.
y = 2x - 1 (equation 1)
y = 2(-2) - 1
y = -4 - 1
y = -5
Hence, the solution of the given system of equations is (-2 , -5).
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Use area to explain why the centroid of a triangle is its center of gravity. Then use this explanation to describe the location for the balancing point for a rectangle.
A triangle's centroid is the point through which all of the mass of a triangular plate appears to act.
Why is the centroid the center of gravity of a triangle?The centroid of a triangle is the point through which all of the mass of a triangular plate appears to act. Also known as the "center of gravity," "center of mass," or "barycenter." A fascinating fact is that the centroid is the point at which the triangle's medians intersect.
The triangle's centroid is defined as the point of convergence. Three triangle medians intersect at the figure's centroid "G." The center of gravity is another name for a centroid.
The triangle is divided into two equal-area triangles by each median. The centroid is the intersection of the three medians The centroid is the intersection of the three medians. The three medians divide the triangle into six triangles, each with the same area.
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A hose with a larger diameter working alone can fill a swimming pool in 9 hours. a hose with a smaller diameter working alone can fill a swimming pool in 18 hours. working together, how long would it take the two hoses to fill the swimming pool? the rate of the hose with the large diameter is
According to the question, the given data is as shown below:
A hose with a larger diameter working alone is [tex]9[/tex] hours
A hose with a smaller diameter working alone is [tex]18[/tex] hours
Now, the time taken by the larger hose to fill the pool is [tex]\frac{1}{9}[/tex]
Similarly, the time taken by the smaller hose to fill the pool is [tex]\frac{1}{18}[/tex]
When they are working together, the expression can be written as:
[tex]\frac{1}{9} +\frac{1}{18} =\frac{1}{a}[/tex]
[tex]\frac{1}{a} =\frac{27}{9X18} =\frac{1}{6}[/tex]
The total time taken by the two hoses to fill the swimming pool is [tex]6[/tex] hours.
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Answer:
The rate of the hose with the large diameter is : 1/9
What is the unknown in the problem? : C. The time it takes for the hoses working together to fill the pool
What part of the job does the hose with the large diameter do? : x/9
Simplify the ratio
4 days: 2 weeks
Answer:
2 days: 1 week
Step-by-step explanation:
4 days : 2 weeks
2 2
2:1
Answer:
Step-by-step explanation:
So we Have 4 days to 2 weeks
In order to simplify this, we need to turn weeks into days
2 x 7 = 14
so 4 days to 14 days
Now we divide and fnd a common multiple
4/2 = 2
and 14/2 = 7
so, 2 days to 7 days, or 2/7
We can leave it at that, or turn it into a decimal
4/14 =0.2857
Hope this helps!^^
State whether sentence is true or false. If false, replace the underlined word or phrase to make a true sentence.
The sum of two vectors is the ₋resultant .
Given statement 'The sum of two vectors is the resultant.' is True.
We know that in mathematics, a vector is a quantity that has both magnitude and direction but no position.
Examples : velocity, force and acceleration.
Also, the resultant vector is the vector sum of two or more vectors. We find the resultant vectors by adding two or more vectors together. Any two vectors can be added if and only if they are the same vector quantity.
For vector P = [tex]a\vec i+b\vec j[/tex] and vector Q = [tex]m\vec i+n\vec j[/tex]
The resultant vector R would be,
R = P + Q
R = [tex](a+m)\vec i+(b+n)\vec j[/tex]
Therefore, given statement 'The sum of two vectors is the resultant.' is True.
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COORDINATE GEOMETRY Find the measures of the sides of ΔJ K L and classify each triangle by the measures of its sides. (Lesson 4-1)
J(4,6), K(4,11), L(9,6)
ΔJKL has sides that measure 17.07 units.
What is the definition of a triangle?A triangle is a three-sided polygon with three edges.It is a basic geometric shape.Triangle ABC is a three-vertical triangle with the letters A, B, and C.In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.So,
The formula of perimeter: √(x₂−x₁)²+(y₂−y₁)²
Filling the values in the formula, we obtain:
= √(4−4)²+(11−6)²= 17.07 unitsThen, each side of the triangle will be: 17.07 units
Therefore, ΔJKL has sides that measure 17.07 units.
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Explain how you know the
measure of angle ABC
Sentence Frame
Angle ABC =
angle ABC is
because...
degrees,
degrees
E
A
B
40°
D
C
Answer:
The answer is in the attached screenshot!!! :)
Step-by-step explanation:
Please let me know if you have any questions!!! :)
HELP URGGENNT :3 TYYY !
Answer:
Answers on attached image
Step-by-step explanation:
PLEASE HELP THIS IS DUE SOON
Answer:
Common difference = x - 2.
Step-by-step explanation:
Differences:
-2x - 9 - (-3x - 7)
= -2x - 9 + 3x + 7
= x - 2
-x - 11 - (-2x - 9)
= - x - 11 +2x + 9
= x - 2
So, it is Arithmetic.
Answer:
Arithmetic sequence.
Common difference = -x - 11
Step-by-step explanation:
This is an arithmetic sequence.
-3x - 7, -2x - 9, -x - 11, ...
Find the common difference.
Common difference =second term - first term.
= -2x - 9 - (-3x - 7)
= -2x - 9 + 3x +7
= -2x + 3x - 9 + 7 {Combine like terms}
= x - 2
If we add the common difference to the second term, we will get the third term.
Third term = second term + common difference
= -2x - 9 + x - 2
= -2x + x - 9 - 2
= -x - 11.
Hence this is an arithmetic sequence.
Find the sum, difference, product, or quotient
1.29 + 35
2.90 - 34
Estimate the sum, difference, product, or quotient.
5.284 - 48
6. 147 X 5
7. 1004 +678
Find the value of the power.
9. 102
10. 73
quo tient.
3. 32 X 18
Evaluate the expression.
13. 9 + 7 X 4
16. Phone Card Your phone card h
14. 27 ÷ 3² + 5
11. 26
4. 124 ÷ 8
8. 163 4
12. 105
15. 3 x (327)
Answer:
................................
Solve each equation. Check your answer. 2-3(x+4)=8
the length of a room is 4metres longer than its width.If the area of the room is 32square metres,find the length.
Answer:
https://www.calculator.net/volume-calculator.html
Step-by-step explanation:
Answer:
x = 8
Step-by-step explanation:
[tex](x)(x+4) = 32\\x^2 + 4x - 32 = 0\\(x - 8)(x + 4)\\\\x - 8 = 0\\x = 8 \\\\x + 4 = 0\\x = -4\\\\x = 8 \\x = -4[/tex]
8 is the answer as in a measurement there is no negative number.
Find the equation of a line that passes through the point (2,3) and has a gradient
of 1/3
Leave your answer in the form y=mx+c
Answer: y=4x/3 + 1/3
Step-by-step explanation:
y=mx+c
**Substitute already known variables**
3=2m+1/3=
(3=2m+1/3)*3= ==> Multiply the equation by 3 to get rid of fractions
9=6m+1
6m=8
m=8/6
m=4/3
y=4x/3 + 1/3
Which if the following is the correct graph for the solution of the unequal -8 >= -5x + 2 > -38
Step-by-step explanation:
Given that
The function-8 ≥ -5x + 2 > -38
To find
We have to choose correct graph for the solution of the inequality.So, according to the question
we have,
The function-8 ≥ -5x + 2 > -38
For finding the solution of this function let's solve it on two part,
First part
-8 ≥ -5x + 2, and
Second part
-5x + 2 > -38
For solution of first part ,
-8 ≥ -5x + 2,
Add (-2) both side
We will get,
-8 +(-2) ≥ -5x + 2 +(-2)
-8 -2 ≥ -5x + 2 -2
-10 ≥ -5x
10 ≥ 5x
Divide 5 both side,
We will get,
[tex]\frac{5x}{5} \ge \frac{10}{5}[/tex]
x ≥ 2
Now, for solution of second part,
-5x + 2 > -38
Add (-2) both side
We will get,
-5x + 2 +(-2) > -38+(-2)
-5x + 2 -2 > -38 -2
-5x > -40
40 > 5x
Divide 5 both side,
5x/5 < 40/5
x < 8
So, the solution of given function,
2 ≤ x < 8
Answer:
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6. Which one of these pictures is not like the others? Explain what makes it different using
ratios.
How do i explain this
Jan needs to buy a backpack and several folders for school. If she shops at Smart Supply, the backpack will cost $45 and folders cost $0.45 each. If she shops at The Supply Guys, the backpack will cost $50.40 and folders cost $0.15 each. Write and solve an inequality to find the number of folders Jan would need to buy for The Supply Guys to be the cheaper option.
Answer: Lord Farquaad
Step-by-step explanation: E
Answer:
x>18
Step-by-step explanation:
45+0.45x>50.40+0.15x
-0.15 -0.15
45+0.3>50.40
-45 -45
5.4>0.3
X>18
A 45° - 45° - 90° right triangle is inscribed in a circle. If the radius of the circle is given, explain how to find the lengths of the right triangle's legs.
Answer:
X = √2 R , where X is the length of the legs as R is the length of the radius .
Step-by-step explanation:
The opposite sides of two same angled triangle is also same . So in this case we can say two legs are in same length as their opposite angles are same (45°)
Now , suppose the given radius is R (look at the diagram) then total diameter is 2R ( DIAMETER = 2 × RADIUS )
Now , we will consider the length of the legs are X ( as the are same ).
Now, we will apply Pythagoras theorem ( The squares on the legs of a right triangle is equal to the square on the hypotenuse . )
∵ X² + X² = (2R)²
or , 2X² = 4R²
or, X² = 2R²
We will root both side
X = √2R
So , X is the length of the legs as R is the length of the radius .
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