O( 0,0 ) A(9 , 0 ) D( 0,3 ) ( 9, 2) , ( 6 , 3 ) that are vertices of the feasible region.
What do math vertices mean?
The spots where two or more line segments or edges intersect are known as vertices in forms (like a corner). Vertex is the singular form of vertices. For instance, a cone only has one vertex whereas a cube has eight. Although vertices are occasionally referred to as corners, the term "vertex" is preferable when discussing 2D and 3D designs.The line 2x + 6y = 30
when x = 9 , 18 + 6y = 30
y = 2
So B = ( 9, 2)
So, C= ( b , 3 )
then , we can show O( 0,0 ) A(9 , 0 ) D( 0,3 )
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write the equation of the line that is parallel to y=1/3x-3 and passes through the point (6,2)
PLEASE HELP
[tex]\textsf{Hi Brainy User, I'm Here to Help you!}[/tex]
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\textsf{Parallel lines have the same slope, thus:}[/tex]
[tex].\qquad\bullet\sf{Slope\:of\:the\:line\:that's\:parallel\:to\:the\:given\:line: \dfrac{1}{3}}[/tex]
[tex]\textsf{Next, we'll apply the \textbf{Point-Slope Formula:}}[/tex]
[tex].\qquad\bullet\sf{y-y_1=m(x-x_1)}[/tex]
[tex]\textbf{\underline{Setting the values:}}[/tex]
[tex].\qquad\bullet\sf{y_1=2}\\.\qquad\bullet m=1/3\\.\qquad\bullet x_1=6}}[/tex]
[tex]\textbf{\underline{Plugging in the values:}}[/tex]
[tex].\qquad\bullet\sf{y-2=\dfrac{1}{3} (x-6)}\\\\.\qquad\bullet y-2=\dfrac{1}{3}x-2}\\\\.\qquad\bullet y=\dfrac{1}{3} x}[/tex]
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\large\overbrace{\underbrace{\textsf{\textbf{Reflection - RoSe}}}}^\star_\star[/tex]
Solve each equation. Check your answers. -3(x-4)=2(x+8)
The solution of the given equation -3(x-4)=2(x+8) is at x = -4/5.
According to the given question.
We have a linear equation in one variable.
-3(x-4)=2(x+8).
As we know that,the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
Thereofre, the solution of the given equation is given by
-3(x - 4) = 2(x + 8)
⇒ -3x + 12 = 2x + 16
⇒ -3x - 2x = 16 - 12
⇒ -5x = 4
⇒ x = -4/5
We get the solution of the given equation is at x = -4/5.
Now, we can check that x = -4/5 is a solution of the given equation or not.
Therefore,
L.H.S
= -3(-4/5 - 4)
= 12/5 + 12
= (12 + 60)/5
= 72/5
Similarly,
R.H.S
= 2(-4/5 + 8)
= -8/5 + 16
= -8 + 80/5
= 72/5
So, L.H.S = R.H.S
Hence, the solution of the given equation -3(x-4)=2(x+8) is at x = -4/5.
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Evaluate the expression for the given values of the variables.
11(a+2b)+2(a-2b);a=-3 and b=4
The value of expression is 33
For evaluating the expression, we will keep the given values of variables in the expression. Further solving will be done according to the mathematical operators.
Rewriting the equation -
Value = 11 (a + 2b) + 2 (a - 2b)
Now keeping the values of variables in expression -
Value = 11 (-3 + 2×4) + 2 (-3 - 2×4)
Firstly solving the brackets
Value = 11 ( -3 + 8) + 2 (-3 - 8)
Value = 11 (5) + 2 (-11)
Performing multiplication
Value = 55 - 22
Performing subtraction
Value = 33
Hence, the expression for the given values of the variables is 33.
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Write an equation for each line. m=0 and the y -intercept is (0,-2) .
The equation of a line with slope = 0 and y-intercept = (0,-2) is: y = -2
What is the equation of a line to the curve?A line's equation has the standard form ax + by + c = 0. Here, the variables are x and y, the coefficients are a and b, and the constant term is c.It is a first-order equation with the variables x and y.The coordinates of the point on the line shown in the coordinate plane are represented by the values of x and y.Now,
Given:
Slope of the given line = 0Coordinates of the y-intercept = (0,-2)To find: Equation of the line
Finding:
Now, we know that the slope-point form method to find the equation of a line, requires only two things: slope of the line and coordinates of the y-intercept.
The equation so given by the method: y = mx + c, where
m = slope of the line
c = y-intercept
On substituting the given values in the above equation, we get:
=> y = 0x - 2, which the required equation of the line.
Hence, The equation of a line with slope = 0 and y-intercept = (0,-2) is: y = -2.
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Pls pls help whoever gets it right gets a crown
Line MS is perpendicular to line OP. If M(-6,8), O(k+3,-20), P(13,k-2) and S(-2,5) find k
The value of the variable k must equal to - 2 such that the line segment MS is perpendicular to the line segment OP.
What is the value of a variable associated with line segments perpendicular to each other?
According to analytical geometry, two lines are perpendicular to each other if the product of their slopes are equal to - 1. Slopes can be determine by secant line formula:
m₁ = (5 - 8) / [- 2 - (- 6)]
m₁ = - 3 / 4
m₂ = [(k - 2) - (- 20)] / [13 - (k + 3)]
m₂ = (k + 18) / (10 - k)
(- 3 / 4) · [(k + 18) / (10 - k)] = - 1
(- 3 / 4) · (k + 18) = - (10 - k)
- 3 · (k + 18) = - 4 · (10 - k)
- 3 · k - 54 = - 40 + 4 · k
7 · k = - 54 + 40
7 · k = - 14
k = - 2
The value of the variable k must equal to - 2 such that the line segment MS is perpendicular to the line segment OP.
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The price of an item was reduced by 35 percent . The original price was $33. What is the price of the item now?
Answer:
11.55
Step-by-step explanation:
You buy3.9 pounds of trail mix. The mix costs $2.88 per pound. What is the total price for the trail mix?
Step-by-step explanation:
$2.88 per pound
so, then how much for e.g. 2 pounds ?
right : the price for 1 pound plus 1 pound = 2×$2.88 = $5.76
and so on.
therefore, 3.9 pound cost :
3.9 × $2.88 = $11.232 ≈ $11.23
Answer:
11.232
Step-by-step explanation:
3.9×2.88=11.232
Why does -3.6 -(-4) have the same result as -3.6 + 4?
Tom delivers papers on a rural route from his car. If he throws a paper from a height of 4 feet, and it lands 15 feet from the car, at what angle of depression did he throw the paper to the nearest degree?
The angle of depression, at which Tom threw the paper is 14.93°
In this question,
Tom throws a paper from a height of 4 feet, and it lands 15 feet from the car.
We need to find the angle of depression, at which he threw the paper.
Consider the following diagram.
Let the θ be the angle of depression, at which he threw the paper.
Consider the tangent of angle θ.
⇒ tan(θ) = 4/15
⇒ θ = [tex]tan^{-1}(\frac{4}{15} )[/tex]
⇒ θ = 14.93°
Therefore, the angle of depression, at which Tom threw the paper is 14.93°
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Express your answer as a polynomial in standard form.
ƒ(x) = 2x² + 5x + 15
g(x) = -x + 5
Find: (fog)(x)
Answer:
2x² - 25x + 90
Step-by-step explanation:
→ Replace every x in 2x² + 5x + 15 with -x + 5
2 × ( -x + 5 )² + 5 ( -x + 5 ) + 15
→ Simplify
2 ( x² - 10x + 25 ) - 5x + 25 + 15
→ Expand
2x² - 20x + 50 - 5x + 40
→ Simplify
2x² -25x + 90
I don’t understand 15 through 18
Answer:
Step-by-step explanation:
15. True
16. False
17. True
18. True
Answer:
15 )true because they are opposite angles.
16) false 2 and 4 are opposite angles so should be the same value.
17 true ) because angle 4+1=180.
18 true) because the two angles make a 180 degree.
A football was kicked vertically upward from a height of 4 feet
with an initial speed of 60 feet per second. The formula
h = 4 + 60t - 16t
2
describes the ball’s height above the ground, h, in feet, t seconds
after it was kicked. Use this formula to solve Exercises 19–20.
19. What was the ball’s height 2 seconds after it was kicked?
Answer: h=60 feet
Step-by-step explanation:
h=4+60t-16t²
h(2)=4+(60)(2)-(16)(2)²
h(2)=4+120-(16)(2)(2)
h(2)=124-64
h(2)=60 feet
Solve for x (5x+3)=(7x-7)
answer:
5
explanation:
(5*5) + 3=28
(7*5) - 7= 28
How do you show your work to 3x-4
It should be noted that the value of to 3x-4will be -12.
How to compute the value?It should be noted that this simply has to do with multiplication.
In this case we have to multiply the values that are given.
Also, it's important note that minus multiplied by plus is minus.
Therefore, (3 × -4) = -12.
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in how many years will the population of village be 209475 from 190000 at the growth rate of 5% per annum?
Answer:
The period would be 2 years
Step-by-step explanation:
Can some please help me on this? It’s due tmrw
help, please :) I APPRECIATE IT
Find point X on AB such that the ratio of AX to XB is 1:3
The point X on AB such that the ratio is 1.25 units.
XB=AX×3
AX+XB=AB
AX+(AX×3)=AB
AX×4=AB
AX×4=9
AX=2.25
X=-1+2.25
X=1.25 units
Ratio shows how often one number is contained in another. For instance, the proportion of oranges to lemons in a bowl of fruit is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3). The proportions of oranges to the overall amount of fruit are 8:14 for oranges and 6:8 (or 3:4) for lemons (or 4:7).
The quantities in a ratio can be of any form, including counts of people or things, measures of lengths, weights, or times, etc.
Hence , the Coordinate in units: (2,1.25). In most contexts, both numbers are restricted to be positive.
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Divide. State any restrictions on the variable. 3x-6/12 x-24 ÷ x²5 x+6 / 3 x² - 12
The division of given rational expression [tex]\frac{3x-6}{12x-24}\div \frac{x^2+5x+6}{3x^{2} -12}[/tex] is [tex]\frac{3(x-2)}{4(x+3)}[/tex] provided x ≠ -3
In this question,
we have been given a complex rational expression [tex]\frac{3x-6}{12x-24}\div \frac{x^2+5x+6}{3x^{2} -12}[/tex]
We need to find the division of given rational expression.
We rewrite given rational expression as,
[tex]\frac{\frac{3x-6}{12x-24}}{\frac{x^2+5x+6}{3x^{2} -12}}\\\\\\= \frac{3x-6}{12x-24}\times \frac{3x^2-12}{x^2+5x+6}[/tex]
First we simplify the quadratic expression x² + 5x + 6
x² + 5x + 6
= x² + 3x + 2x + 6
= x(x + 3) + 2(x + 3)
= (x + 3)(x + 2)
And the simplified form of quadratic expression 3x² - 12 would be,
3x² - 12
= 3(x² - 4)
= 3(x² - 2²)
= 3(x + 2)(x - 2)
So, the given rational expression would be,
[tex]\frac{3x-6}{12x-24}\div \frac{x^2+5x+6}{3x^{2} -12} \\\\\\ = \frac{3x-6}{12x-24}\times \frac{3x^2-12}{x^2+5x+6}\\\\\\=\frac{3(x-2)}{12(x-2)}\times \frac{3(x+2)(x-2)}{(x+3)(x+2)}[/tex]
[tex]\\\\=\frac{3}{12}\times \frac{3(x-2)}{(x+3)}\\\\\\=\frac{3(x-2)}{4(x+3)}~~~~~~~~~~~~~(provided~~x\neq -3)[/tex]
Therefore, the division of given rational expression [tex]\frac{3x-6}{12x-24}\div \frac{x^2+5x+6}{3x^{2} -12}[/tex] is [tex]\frac{3(x-2)}{4(x+3)}[/tex] provided x ≠ -3
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I am struggling with 6 2/5 revolutions in 2 2/3 seconds and turning it into a unit rate
[tex]\frac{12}{5}[/tex] = [tex]2\frac{2}{5}[/tex] revolutions per second is the unit rate.
What is unit rate ?An item's unit rate is its price for one of it. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate.
1) Convert mixed fractions into fractions.
[tex]6\frac{2}{5}[/tex] = [tex]\frac{((6*5) + 2)}{5}[/tex] = [tex]\frac{32}{5}[/tex]
[tex]2\frac{2}{3}[/tex] = [tex]\frac{((2*3) + 2)}{3}[/tex] = [tex]\frac{8}{3}[/tex]
2) [tex]\frac{32}{5}[/tex] ÷ [tex]\frac{8}{3}[/tex] ; where [tex]\frac{32}{5}[/tex] is the 1st fraction and [tex]\frac{8}{3}[/tex] is the 2nd fraction
a) Find the second fraction's reciprocal:
From [tex]\frac{8}{3}[/tex] to [tex]\frac{3}{8}[/tex]
b) Multiply the first fraction by the second fraction's reciprocal, which is 32/5, 5/3, or (5/3), to get 96/40.
c) Simplify the fraction.
Divide 96 / 40 by 4 to get 24/10.
Divide 24/10 by 2, and the result is 12/5. The 96/40 simple fraction
[tex]\frac{12}{5}[/tex] = [tex]2\frac{2}{5}[/tex] revolutions per second is the unit rate.
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Simplify by combining like terms. x(3-y) + y(x+6)
By combining the like terms, the simplified form of the expression x(3-y)+y(x+6) is 3x+6y
Given,
The algebraic expression = x(3-y)+y(x+6)
Apply distributive property and expand the term
x(3-y)+y(x+6)=3x-xy+xy+6y
Combine like terms
3x-xy+xy+6y= 3x+6y
Hence, by combining the like terms, the simplified form of the expression x(3-y)+y(x+6) is 3x+6y
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Find the value of c that completes the square. r^2+21r+c
Answer:
c = 110.25
(r + 10.5)²
Step-by-step explanation:
Hello!
Perfect Square Trinomial: [tex](a + b)^2 = a^2 + 2ab + b^2[/tex]
21r is basically 2 times r and b, the missing number.
Solve for b21r = 2*r*b10.5 = bThe missing number, b, would be 10.5
Now c is basically b², so we just have to simplify 10.5²:
10.5²110.25c should be 110.25 for it to be a Perfect Square Trinomial. The factored form would be (r + 10.5)².
Write an equation for each line. m=-5 and the y -intercept is (0,-7) .
The equation of the line for given values is y = -5x - 7.
Given a point and a slope, how do you build an equation for a line?When you know the slope of the line to be investigated and the provided point is also the y intercept, you may utilize the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.
The standard equation of straight line is y = mx + c.
Given m = -5 and y - intercept is -7
So, the equation of the line becomes y = -5x - 7
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Necesito ayuda con este problema si no lo entiendes traducelo y ayudame me puedes explicar en español ya que lo entiendo
Answer:
F
Step-by-step explanation:
La respuesta es f porque la tasa vigente en el lado x es por 2 y la tasa vigente en el lado y es por 12.
Simplify: 31−(5−3⋅4)2+26÷4
Answer:
51.5
Step-by-step explanation:
Simplify:
31−(5−3⋅4)*2+26÷4=
31-(5-12)*2+6.5=
31-(-7)*2+6.5=
31+14+6.5=
51.5
Write the specified type of proof.
two-column proof
Given: CB bisects ∠A B D and ∠A C D .
Prove: Δ A B C ≅ ΔD B C
ΔABC ≅ ΔDBC under angle-side-angle (ASA) condition.
What precisely is meant by a triangle's congruency?Two triangles are considered to be congruent if their three corresponding sides are equal and their three corresponding angles are equal in size.These triangles can be decided to move, rotated, flipped, and turned to appear identical.If they are repositioned, they will coincide.Two triangles are congruent if they satisfy all five congruence conditions.They are side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), and right angle-hypotenuse-side (RHS).So,
To prove: ΔABC ≅ ΔDBC
BC = BC = (common:given)∠BCA = BCD = (Given: CB bisects ∠C)∠CBA = CBD = (Given: CB bisects ∠B)Then, ΔABC ≅ ΔDBC under angle-side-angle (ASA) condition.
(Refer the table shown below)
Therefore, ΔABC ≅ ΔDBC under angle-side-angle (ASA) condition.
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A shop owner sold 27 books on Friday. This was 9 more than the number of books he sold on Thursday. Identify an equation and its solution that shows the number of books he sold on Thursday.
x − 9 = 27; 36 books
x + 27 = 36; 9 books
x + 9 = 27; 18 books
9x = 27; 3 books
The expression that shows the number of books he sold on Thursday is x + 9 = 27; 18 books
How to determine the equation and the solution?The given parameters are
Friday sales = 27
Friday sales = 9 more than the number of books he sold on Thursday.
Let the number of books he sold on Thursday be x
So, we have
Friday = 9 + x
This gives
27 = 9 + x
Rewrite as
x + 9 = 27
Solve
x = 18
Hence, the expression that shows the number of books he sold on Thursday is x + 9 = 27; 18 books
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a certain function is represented by f(x)-4^2-3x+2. what is the value of f(-2)?
Answer: -8
Step-by-step explanation:
replace x in the function with -2-4^2-3(-2)+2-16+8-8How do I solve this equation 3.2x+12=48
Answer:11.25
Step-by-step explanation: first subtract 12 from both sides then you would have 3.2x=36
and then divide both sides by 3.2 which is x=11.25
Answer: x=11.25
Step-by-step explanation: 48-12> 36> 3.2x=36> divide 36 by 3.2> x= 11.25
Hope this helped
