The general solution of the given system of odes is
m=1 ; m=4 (real roots)
In arithmetic, a system of odes equations is a finite set of differential equations. Any such device may be either linear or non-linear. Also, such a machine can be both a machine of normal differential equations or a system of partial differential equations.
the compatibility conditions of an overdetermined system of odes equations may be succinctly stated in terms of differential forms (i.e., a shape to be specific, it needs to be closed). See integrability situations for differential systems for more.
It is an elaborately based poem praising or glorifying an event or character, describing nature intellectually as well as emotionally. A traditional ode is dependent on three essential parts: the strophe, the antistrophe, and the epode. Distinct forms together with the homostrophic ode and the abnormal ode also enter.
dx/dt = 2x+2y = x^1 = 2x+2y 1
dy/dt = x+3y = y^1 = x+ 3y 2
differentiating 1 with respect to 't'
x^11 = 2x^1+ 2y^1
y^1 = x+3y
x^11 = 2x^1= 2(x+3y)
x^11 = 2x^1+ 2x+ 6y
x^11 = 2x^1+ 2x+ 6(x^1-2x/2)
x^11 = 2x^1+ 2x+ 3x^1- 6x
x^11 = 5x^1 - 4x
x^11 -5x^1 - 4x
x^11 - 5x^1 -4x =0
Auxillary equation is m^5- 5m+4=0
m^2 - m - 4m + 4 = 0
m(m-1) -4 (m-1) =0
(m-1) (m-4) = 0
m=1 ; m=4 (real roots)
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The graph of y=√x is reflected in the x-axis and then translated
down 3 units. What is an equation that produces this transformation?
A. -√x-3
B. y= -3-(√x)
C. y= 3- (√x)
D. y= -(√x-3)
Two brothers are saving money to buy tickets to a concert. Their combined savings is $55. One brother had $15 more than the other. How much has each saved?
Answer:
20 and 35 dollars.
Step-by-step explanation:
x + x + 15 = 55
2x + 15 = 55
2x = 55 - 15
2x = 40
x = 40/2
x = 20
One of the brothers has saved 20 dollars, while the other has 35 dollars.
Someone help me please
45-45-90 triangles
Answer:
Side AB = [tex]9\sqrt{2}[/tex]
Side AB = [tex]9\sqrt{2}[/tex]
Side CB = 36
Step-by-step explanation:
This is a special right triangle and it's also an isosceles triangle
therefore the measure of AC = AB and they are both = [tex]9\sqrt{2}[/tex]
for this special triangle the measure of hypotenuse (CB in here) is represented with [tex]x\sqrt{2}[/tex] and the legs are represented with x, each
since legs' lengths are given as = [tex]9\sqrt{2}[/tex] then x = [tex]9\sqrt{2}[/tex]
replace the x in front of [tex]x\sqrt{2}[/tex] with [tex]9\sqrt{2}[/tex]
[tex]9\sqrt{2}[/tex] * [tex]\sqrt{2}[/tex] = 36
Find the Diameter of the Circle with the following equation. Round to the nearest tenth.
(x - 2)2 + (y + 6)2 = 20
Answer:
11.8 units
Step-by-step explanation:
The circle equation is given as:
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2Where
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2r
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we have
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sides
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sidesr = 5.9
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sidesr = 5.9Multiply by 2
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sidesr = 5.9Multiply by 22r = 11.8
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sidesr = 5.9Multiply by 22r = 11.8Hence, the diameter of the circle is 11.8 units
Answer: 8,9.
Step-by-step explanation:
[tex](x-2)^2+(y+6)^2=20\\Circle \ equation\\\boxed {(x-a)^2+(y-b)^2=r^2}\\r^2=20\\r*r=\sqrt{20}*\sqrt{20}\\ r=\sqrt{20}\\ r=\sqrt{4*5}\\ r=2\sqrt{5} \\ D=2r\\D=2*2\sqrt{5}\\ D=4\sqrt{5}\\ D\approx8,9.[/tex]
what is Rational Number
Answer:
In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. For example, −3/7 is a rational number, as is every integer.
A pizza has a diameter of 18 inches. If the pizza is
cut into 10 equal slices and 6 slices were eaten,
what is the area of the remaining pizza?
Answer:
25
Step-by-step explanation:
Can the sides of a triangle have lengths 6, 20, and 20?
Answer:
Yes.
Step-by-step explanation:
This would be an isosceles triangle - with 2 equal sides both 20 long with a base of length 6.
A triangle can be formed from 3 line segments as long as the sum of the length of any 2 sides exceeds the length of the third side.
Using the same functions given above, find (h−f)(x).
The results of subtraction of functions are listed below:
x - 8m(x) = x² + 10 · x + 5m(3) = 44How to use the subtract function operatorThere three fundamental binary operators (addition, multiplication, composition) and two secondary binary operators (subtraction, division) for functions. The subtraction is operation derived from addition, defined by the following expression:
(h - f) (x) = h(x) - f(x) (1)
Now we proceed to develop each expression:
i) (h - f) (x):
h(x) = 2 · x - 3, f(x) = x + 5 Given(h - f)(x) = (2 · x - 3) - (x + 5) Definition of subtraction between functions(2 · x - x) + [(- 3) + (- 5)] Associative and commutative properties / (- 1) · a = - ax - 8 Distributive property / Definitions of addition and subtraction / Resultii) m(x) = (g - j) (x):
g(x) = x² + 6 · x + 5, j(x) = - 4 · x Givenm(x) = (x² + 6 · x + 5) - (- 4 · x) Definition of subtraction between functionsm(x) = x² + (6 · x + 4 · x) + 5 Associative, commutative and distributive property / (- a) · (- b) = a · bm(x) = x² + 10 · x + 5 Distributive property / Definition of adition / Resultiii) m(3):
m(3) = 3² + 10 · 3 + 5
m(3) = 9 + 30 + 5
m(3) = 44
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In geometry, Heron's formula (sometimes called Hero's formula), named after Hero of Alexandria, gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, contrary to other formulas for the area of a triangle, such as half the base times the height. Use Heron's formula to find the area, in square yards, of ΔABC.
a = 12, b = 11, c = 7
Answer:
12 sqrt (10)
Step-by-step explanation:
S = (12 + 11 + 7) / 2 = 15
A = sqrt (s(s-a)(s-b)(s-c))
= sqrt (15(15-12)(15-11)(15-7))
= sqrt (15*3*4*8)
= sqrt (1440)
= 12 sqrt (10)
hello please answer need help
2x + 2y = 42
2w + q = 35
2w + v = 29
x + q + y - v = ?
x = 7
y = 14
w = 3
q = 29
v = 23
7 + 29 + 14 - 23 =
The answer is 27
Answer: [tex]\Large\boxed{27}[/tex]
Step-by-step explanation:
Given information converted into a mathematical statement
[tex]a = icecream\\b=cookie\\c=brownie\\d=cake\\e=creamed cake[/tex]
[tex]1)~a+b+a+b=42[/tex]
[tex]2)~c+d+c=35[/tex]
[tex]3)~c+c+e=29[/tex]
[tex]4)~a+d+b-e=\mbox{?}[/tex]
Simplify each equation
[tex]1)~2a+2b=42[/tex]
[tex]2)~2c+d=35[/tex]
[tex]3)~2c+e=29[/tex]
[tex]4)~(a+b)+(d-e)=\mbox{?}[/tex]
Factorize 2 out of the 1) equation
[tex]2a+2b=42[/tex]
[tex]2(a+b)=42[/tex]
Divide 2 on both sides
[tex]2(a+b)\div2=42\div2[/tex]
[tex]a+b=21[/tex]
Current system
[tex]1)~a+b=21[/tex]
[tex]2)~2c+d=35[/tex]
[tex]3)~2c+e=29[/tex]
[tex]4)~(a+b)+(d-e)=\mbox{?}[/tex]
Subtract 3) equation from the 2) equation
[tex](2c +d)-(2c+e)=(35)-(29)[/tex]
Expand the parenthesis
[tex]2c+d-2c-e=35-29[/tex]
Combine like terms
[tex]2c-2c+d-e=6[/tex]
[tex]d-e=6[/tex]
Current system
[tex]1)~a+b=21[/tex]
[tex]2)~d-e=6[/tex]
[tex]3)~(a+b)+(d-e)=\mbox{?}[/tex]
Substitute values into the 3) equation to determine the final value
[tex](a+b)+(d-e)[/tex]
[tex]=(21)+(6)[/tex]
[tex]\Large\boxed{=27}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Choose the correct simplification of 8x2(5x 2x2 − 3). 16x4 − 40x3 24x2 16x4 40x3 − 24x2 40x4 16x3 − 5x2 40x4 − 10x3 5x2
The correct simplification of 8x2(5x 2x2 − 3) is [tex]16x^{4} +40x^{3} -24x^{2}[/tex]
What do you mean by simplification?Simplifying procedures is one way to achieve uniformity in work efforts, expenses, and time. It reduces diversity and variety that is pointless, harmful, or unnecessary.Making anything simpler is the act or process of simplification. Everyone is in favor of streamlining court procedures.Certain "solving" issues are connected to "simplification" issues. Parentheses and even nested grouping symbols can be found in some equations, just like in some expressions. Whether we're working with equations (so we're also solving) or expressions (and only simplifying), the simplification procedure is the same in both cases.The correct simplification of 8x2(5x 2x2 − 3).
[tex]8x^{2} (5x+2x^{2+1} -3)=8*2x^{2+2} -8*3x^{2}[/tex]
[tex]=40x^{3} +16x^{4} -24x^{2}[/tex]
Rearranging the above expression in descending order of power, we get:[tex]16x^{4} +40x^{3} -24x^{2}[/tex]
The correct simplification of 8x2(5x 2x2 − 3) is [tex]16x^{4} +40x^{3} -24x^{2}[/tex]
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If NR is parallel to OQ AND OQ = 130m, what is the length of NR?
Answer: 260 m
Step-by-step explanation:
Let's say the length of NR is x m, using the similarity rule, we get the equation
175/130 = (175+175)/x
x = 260
So NR is 260 m
What is the equation of a line in slope-intercept form, of the line that passes through (0, 12) and has a slope of -5?
Answer:
y=-5x-12/5
Step-by-step explanation:
First you need to find y intercept
y=mx+b
plug in the points (0,12)
12=mx+0
now plug in -5
12=-5x+0
subtract 0 from both side
12=-5x
divide -5 from both side.
x=12/-5
Force equals mass times acceleration.
F = ma
Solve the equation for the
acceleration, a.
-A
Answer:
m = F / a is the answer
Step-by-step explanation:
F = ma
m = F / a
Determine the factors of 5x2 29x − 6. (5x − 1)(x 6) (5x − 6)(x 1) (5x − 3)(x 2) (5x − 2)(x 3)
The correct option is option(A) (5x-1)(x+6).
The factors of the given equation are (5x-1)(x+6).
What are the factors of a quadratic equation?An algebraic expression or number that divides another expression or number equally, leaving no remainder is known as factor.
The quadratic equation [tex]ax^{2} +bx+c=0[/tex] can be expressed as the product of its linear factors as (x - k)(x - h), where h, k are the roots of the equation. This is known as factoring quadratics.
What is splitting middle term of an equation?Dividing the middle term into two factors is used in quadratic factorization in this method. In splitting of the middle term, where x is the product of two factors and last term is the sum of the two factors.
Use the splitting middle term formula
[tex]5x^{2} +29x-6[/tex]
=[tex]5x^{2} +30x-x-6[/tex]
=5x(x+6)-1(x+6)
=(5x-1)(x+6)
The factors of the given equation are (5x-1)(x+6).
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Solve the right triangle. Round decimals to the nearest tenth
Answer:
j = 19.6
k = 25.9
J = 49°
Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to remind you of the relationships between sides and angles in a right triangle.
AnalysisThe given side is opposite the given angle. We want to find the other acute angle and the missing sides: the hypotenuse, and the adjacent side. The relations involving the opposite side are ...
Sin = Opposite/Hypotenuse ⇒ Hypotenuse = Opposite/Sin
Tan = Opposite/Adjacent ⇒ Adjacent = Opposite/Tan
Of course, the acute angles in a right triangle are complementary, so we can use that fact to find the missing angle.
ApplicationHypotenuse = Opposite/Sin
IJ = 17/sin(41°) ≈ 25.9
Adjacent = Opposite/Tan
IK = 17/tan(41°) ≈ 19.6
Angle J = 90° -41° = 49°
In summary, ...
j = 19.6
k = 25.9
J = 49°
Which statements are true for the functions g(x) = x2 and h(x) = –x2 ? Check all that apply.
For any value of x, g(x) will always be greater than h(x).
For any value of x, h(x) will always be greater than g(x).
g(x) > h(x) for x = -1.
g(x) < h(x) for x = 3.
For positive values of x, g(x) > h(x).
For negative values of x, g(x) > h(x).
The answer choice which is correct regarding the two functions is; For any value of x, g(x) will always be greater than h(x).
Which statement is true for the functions?It follows from the task content that the functions given are; g(x) = x² and h(x) = –x².
On this note, since all values of x return a positive value for g(x) due to the square, it follows that the corresponding value of h(x) is always lesser.
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Find the A.P whose second term is 12 and 7th term exceeds the 4th by 15
The 2nd term exists 12 and 7th term exceeds the 4th by 15 exists AP : 7,12,17,....
How to estimate the arithmetic progression?
Given : The second term exists 12th and the 7th term exceeds the 4th term by 15
The formula of the nth term :
[tex]$a_{n}=a+(n-1) d[/tex]
Where d exists a common difference
n be the number of terms
a be the first term
Substitute the value of n = 2
[tex]$a_{2}=a+(2-1) d=a+d[/tex]
Let, the second term exists 12
So, a + d = 12 ..........(1)
Substitute the value of n = 7
[tex]$a_{7}=a+(7-1) d=a+6 d[/tex]
Substitute n = 4
[tex]$a_{4}=a+(4-1) d=a+3 d[/tex]
We are given that the 7th term exceeds the 4th term by 15
So, a+6d-a-3d = 15
3d = 15
d = 5
Substitute the value of d in (1)
So, a+5 = 12
a = 12-5
a = 7
AP : a,a+d,a+2d,.... = 5, 7+5, 7+2(5),....=7,12,17,....
Therefore, AP : 7,12,17,....
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please solve by BODMAS rule
Answer:
Step-by-step explanation:
1/3 + 1/3 x 1/3 / 1/3 - 1/3
= 1/3 + 1/3 x 1/1 -1/3
= 1/3 + 1/3 - 1/3
= 2/3 - 1/3
= 1/3
Answer:
5/9.
Step-by-step explanation:
1/3 + 1/3 * 1/3 / 1/3 - 1/3 * 1/3
= 1/3 + 1/3 * 1 - 1/3 * 1/3
= 1/3 + 1/3 - 1/3 * 1/3
= 2/3 - 1/9
= 5/9.
Okay so this is super tricky, there is a riddle on my math quiz. Yk for extra credit and its 25% of my grade, according to Mr. Wells.
If you have 1 cow that is worth $2,500 and 2 cats worth $100. But one dog is worth $7000, what would the outcome be if there was only 1 of each animal? Hint: It could be division or multiplication.
A. 2 cats and one dog
B. 1 cow and 1 dog
C. $600 for each animal
D. If you think its none of these listed, you may write your own!
Note: this makes no sense whatsoever, so please help. Mr. Wells is a good teacher, but this question is hard
If there was just one of each animal, the outcome would be that of 1 cow and 1 dog.
Option(B) is correct.
The average cost, or how much it generally costs to produce a unit, can be discovered using the cost function.
If you own two cats worth $100 each and a cow worth $2,500. One dog, though, is worth $7000.
Cost of 1 cow = $2500
Cost of 2 cats = $100
Thus, cost of 1 cat = $100/2 = $50
Cost of 1 dog = $7000
If there was only 1 of each animal, total cost = $(2500+50+7000) = $9550.
This outcome resembles the situation of having 1 cow and 1 dog.
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I need help pls and thank you
Answer:
12 in, 7 in
Step-by-step explanation:
The area of a rectangle is the product of length and width. Here, you are given the area, and an additional relation between length and width.
SetupThe two relations between length and width described by this problem are ...
A = LW . . . . . . . dimensions are of a rectangle
L = W +5 . . . . . . length is 5 inches more than width
A = 84 . . . . . . . . area in square inches
SolutionSubstituting for L and A in the area formula, we have ...
84 = (W +5)(W)
We can solve this as a quadratic in any of several ways. One of those ways is by factoring.
Essentially, we're looking for factors of 84 that differ by 5. We can consider different factorizations of 84 to see what we get:
84 = 84×1 = 42×2 = 28×3 = 21×4 = 14×6 = 12×7
The differences between the factors in these pairs are 83, 40, 25, 17, 8, 5.
This means the last pair, with a difference of 5, is the one we're looking for.
W+5 = 12, W = 7
The rectangle is 12 inches long and 7 inches wide.
__
Additional comment
As a quadratic in standard form, we would have ...
W² +5W -84 = 0 ⇒ (W +12)(W -7) = 0 ⇒ W = {7, -12}
If you were to solve this by completing the square, you would have ...
(W +2.5)² = 90.25 ⇒ W = -2.5 ±9.5 = {7, -12}
Which function is represented in the
graph below?
Answer:
Option 2
Step-by-step explanation:
There is an amplitude of 1/2, a period of pi, and a non-zero y-intercept.
A highway sign shows a speed limit of 65 miles per hour. Which of the following car speed measurements represent the same level of accuracy compared to the speed limit sign?
a. 66 ,ph
b. 56mph
c. 60mph
d.64mph
The car speed measurements that represent the same level of accuracy compared to the speed limit sign is 64mph (option D).
What is accuracy?Accuracy is the exact conformity to truth or the degree of conformity of a measure to a true or standard value.
Accuracy is different from precision as precision deals with the closeness of an observed value with a true value.
According to this question, a highway sign shows a speed limit of 65 miles per hour. This suggests that a car speed measurement that will represent the same level of accuracy compared to the speed limit sign is 64mph.
64mph is the closest speed measurement to 65mph that does not exceed this speed limit. However, 66 mph is also close but exceeds the true value for the speed limit.
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Is the following number rational or irrational?
√64
√64 is rational.
Hope this helps :)
❄ Hi there,
let us consider this –
Is [tex]\sqrt{64}[/tex] a rational or irrational number?
Well, to answer that we need to work out [tex]\sqrt{64}[/tex].
And we know that
[tex]\sqrt{64} =8[/tex]
and 8 is a rational number.
That's it!
❄
The regression sum of squares (RSS) represents: a. The amount of variation in Y around its mean that the regression function can account for. b. The amount of variation in the dependent variable that is not explained by the regression function. c. The amount of variation in the independent variable that is not explained by the regression function. d. The amount of variation in the residuals that is explained by the regression function.
The regression sum of squares (RSS) represents: a. The amount of variation in Y around its mean that the regression function can account for.
What is regression sum of squares?
The regression sum of squares serves as the sum of the differences that exist between the predicted value and the mean of the variable.
The Sum of Squared Error however states the difference between the observed and the predictive value.
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Determine whether the given correlation coefficient is statistically significant at the specified level of significance and sample size. r=0. 835, α=0. 01, n=4
Yes, the correlation coefficient is statistically significance
The precise metric used in a correlation analysis to quantify the strength of the linear relationship between two variables is the correlation coefficient. In a correlation report, the r stands for the coefficient.
Given,
Sample size, n = 4
Where ρ is the population correlation.
Then the number of degrees of freedom is, df = n-2 = 4-2 = 2
The corresponding critical correlation value re for a significance level of a 0.01, for a two-tailed test is た= 0.254
Here,
The null hypothesis, [tex]H_{0}[/tex] = ρ - 0 is rejected
Suppose lr> re 0.254
Because on the sample correlation provided, we know that lrl = 0.835>=0.254.
Here, it is clear that the null hypothesis is rejected.
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Molly is thinking of a number. twice her number take away seven is the same as her number plus five. what is her number?
Answer:
Number = 12
Step-by-step explanation:
2n-7=n+5 (+7 to both sides)
2n=n+12 (-n to both sides)
n=12
The cost to produce a product is modeled by the function f(x) = 5x2 − 70x 258, where x is the number of products produced. complete the square to determine the minimum cost of producing this product. 5(x − 7)2 13; the minimum cost to produce the product is $13. 5(x − 7)2 13; the minimum cost to produce the product is $7. 5(x − 7)2 258; the minimum cost to produce the product is $7. 5(x − 7)2 258; the minimum cost to produce the product is $258.
The minimum cost to produce the product is $7.
What are functions?
A function from a set X to a set Y allocates exactly one element of Y to each element of X.To determine the minimum cost:
We have to determine the minimum cost of producing this product.
Since [tex]f(x) = 5x^{2} -70x+258[/tex].
Now, consider the equation [tex]5x^{2} -70x+258= 0[/tex].
Dividing the above equation by 5, we get
[tex]x^{2} -70x/5+258/5=0\\x^{2} -14x+258/5=0[/tex]
Now, considering the coefficient of 'x', dividing it by '2' and then adding and subtracting the square of the number which we got after dividing.
Since the coefficient of 'x' is 14, and half of 14 is '7'.
So, adding and subtracting from the above equation.
[tex]x^{2} -14x+(7)^{2} -(7)^{2}+258/5=0\\x^{2} -14x+49 -49+258/5=0\\(x-7)^{2} -49+258/5=0\\(x-7)^{2} +258-245/5=0\\(x-7)^{2} +13/5=0\\5(x-7)^{2} +13=0[/tex]
Now, we have to determine the minimum cost to produce the product.
Since [tex]f(x) = 5x^{2} -70x+258[/tex].
[tex]f'(x) = 10x-70[/tex]
Now, let f'(x)=0
[tex]10x-70=0\\10x=70[/tex]
Therefore, x=7
Now, consider which is greater than 0.
Therefore, x= 7 is the minimum cost.
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Answer: The minimum cost to produce the product is $13.
I apologize for the late answer, hope this helps in the future!
Step-by-step explanation:
To complete the square, we need to rewrite the given function in the form:
f(x) = a(x - h)^2 + k
where (h, k) is the coordinates of the vertex of the parabola defined by the function, and a is a positive constant that determines the shape of the parabola.
We start by factoring out the coefficient of x^2:
f(x) = 5(x^2 - 14x + 51.6)
To complete the square, we need to add and subtract a constant inside the parentheses that will allow us to write the expression inside the parentheses as a perfect square. The constant we need to add and subtract is half of the coefficient of x, squared:
f(x) = 5(x^2 - 14x + 51.6 + (7)^2 - (7)^2)
= 5((x - 7)^2 + 13)
Now we have the function in the desired form, with a = 5, h = 7, and k = 13. Since a is positive, we know that the vertex of the parabola is a minimum. Therefore, the minimum cost of producing the product is $13. So the correct answer is:
5(x − 7)2 + 13
A 3 tonne mix of gravel contains blue
metal and gravel in the ratio 2:3.
How much gravel is in the mix?
Answer:
1.8 tonne
Step-by-step explanation:
sum the parts of the ratio, 2 + 3 = 5 parts
divide the total mix by 5 to find the value of one part of the mix
3 tonne ÷ 5 = 0.6 tonne , then
3 parts = 3 × 0.6 = 1.8 tonne ← amount of gravel in the mix
13.
What is the value of b?
90°
bº
aº
110°
Answer:
b=67.5°
Step-by-step explanation:
hope it helps!!!
