Answer:
Step-by-step explanation:
Starsky and Hutch shared their profits in the ratio 3:1. If Starsky got £606, how much did hutch get?
Answer:
£202
Step-by-step explanation:
It is import that you read ratios from left to right - the subjects/names and the ratio itself. In this case the "subjects" are Starksy and Hutch. So Starsky = 3, Hutch = 1.
Use cross multiplication:
S(Starksy):H(Hutch)
3 : 1
606. : ?
(606 * 1) divided by 3 = your answer = 202
Reply if you are unfamiliar with the cross multiplication method
Answer:
202
Step-by-step explanation:
Ratios
Starsky : Hutch
3 : 1
Starsky has 606 so divide 606 by 3
606/3 = 202
Multiply each term by 202
Starsky : Hutch
3*202 : 1*202
Starsky : Hutch
606 : 202
Fill the boxes with appropriate denominator /numerator
Answer:
the first box is 3 and the second box is 25
Step-by-step explanation:
Answer: Box 1: 3 Box 2: 25
Step-by-step explanation:
Box 1:
Since the top is divided by 3, you have to do the same to the bottom
9 / 3 = 3
Box 2:
The bottom is multiplied by 1 ⅔, so you do the same to the bottom
1 ⅔ x 15 = 25
PLEASE HELP ASAP WILL GIVE BRAINLIEST
Which linear graph represents a proportional relationship?
If a quantity increases or decreases as per the increase or decrease in other quantity, the two quantities are said to be in a proportional relationship.
And here, the graph representing the proportional relationship is the one with positive slope (2nd graph)
NO LINKS!! Part 1
Find an exponential function in y = ab^x form that satisfies the given information :
a. Has y-int (0, 2) and has a multiplier of 0.8
b. passes through the points (0, 3.5) and (2, 31.5)
Answer:
A) y = 2*0.8ˣB) y = 3.5*3ˣ-----------------------------------------
Part AUse the coordinates to determine the function.
Point (0, 2):
2 = a*b⁰ ⇒ 2 = aThe function becomes:
y = 2bˣIt has a multiplier of 0.8, so b = 0.8, so the function is:
y = 2*0.8ˣPart BUse the first point:
3.5 = a*b⁰ ⇒ 3.5 = aUse the second point:
31.5 = 3.5*b²9 = b²b = √9b = 3The function is:
y = 3.5*3ˣAnswer:
[tex]\textsf{a)} \quad y=2(0.8)^x[/tex]
[tex]\text{b)} \quad y=3.5(3)^x[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]
Question (a)Given:
y-intercept = (0, 2) ⇒ a = 2multiplier = 0.8 ⇒ b = 0.8Substitute the values of a and b into the exponential function formula:
[tex]\implies y=2(0.8)^x[/tex]
Question (b)The y-intercept is when x = 0. Therefore, given the function passes through point (0, 3.5), the y-intercept is 0.35 ⇒ a = 3.5.
Substitute the found value of a and given point (2, 31.5) into the exponential function formula and solve for b:
[tex]\implies 31.5=3.5b^2[/tex]
[tex]\implies b^2=9[/tex]
[tex]\implies b=3[/tex]
Substitute the values of a and b into the exponential function formula:
[tex]\implies y=3.5(3)^x[/tex]
Which value of x is in the domain of f(x)=√x - 8?
OA. x = 0
OB. x=7
OC. x = -8
OD. x = 10
SUBMIT
Answer: OC. x = -8 is not in the domain of the function f(x) = √x - 8 because the square root of a negative number is not a real number. Therefore, the only value of x that is in the domain of the function is x ≥ 0.
Step-by-step explanation:
find the length of the curve. r(t) = 6t i + 8t3/2 j + 6t2 k, 0 ≤ t ≤ 1
The length of the curve is given by the integral of the magnitude of the velocity vector, which is the derivative of the position vector. Taking the derivative of the position vector, we get the velocity vector as follows:
v(t) = 6i + 24t1/2j + 12tk
The magnitude of this vector is
√(6²+ 24²t + 12²t²)
= √(36 + 576t + 144t²).
To find the length of the curve, we need to integrate this magnitude from t=0 to t=1. This is given by the integral:
L = ∫0² √(36 + 576t + 144t²)dt
This evaluates to L = 18.75. Therefore, the length of the curve is 18.75.
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find the perimeter of the triangle with the vertices $(0,\ 1),\ (3,\ 6)$ , and $(4,\ 1)$ . if necessary, round your answer to the nearest hundredth.
The perimeter of the triangle having vertices (0,1),(3,6), and (4,1) will be 10.83 units.
Any two-dimensional figure's perimeter is determined by the space surrounding it. By summing the lengths of the sides, we can determine the perimeter of any closed shape.
Any polygon's perimeter is equal to the sum of its side lengths. Considering a triangle
The sum of the three sides equals the perimeter.
Units are always a part of the ultimate response. The final solution should be given in centimeters if the triangle's sides are in that unit.
Because the y values between U and V differ, the distance is equal to the x value difference.
Because the x values of V and W differ, the distance equals the difference between their y values.
The hypotenuse of a right triangle, or U to W, equals sqr (sum of squares on the other two sides)
Perimeter = sum of the 3 sides
[tex]= \sqrt{34} + \sqrt{26}+ \sqrt{16}= 5.83 + 5.1 + 4 = 10.83\:units[/tex]
As the value of 34 is 5.83 squared, 26 is 5.1 squared, 16 is about 4 squared.
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The total distances add up to the triangle's perimeter is 10.00
The triangle's perimeter may be calculated by summing the distances between its three vertices. Use the distance formula to calculate the separation between the points:
d = √((x2 - x1)2 + (y2 - y1)2)
The distances between the points are as a result for the triangle with vertices (0,1), (3,6), and (4,1)
Utilizing the distance formula, determine the separation between (0,1) and (3,6):
d = √((x2 - x1) 2 + (y2 - y1) 2) = √((3-0) 2 + (6-1) 2) = √(32 + 52) = √45
Utilizing the distance formula, determine the separation between (3,6) and (4,1):
d = √((x2 - x1) 2 + (y2 - y1) 2) = √((4-3) 2 + (1-6) 2) = √(12 + 52) = √25
Utilizing the distance formula, determine the separation between (4,1) and (0,1):
d = √((x2 - x1) 2 + (y2 - y1)2) = √((0-4) 2 + (1-1) 2) = √(42 + 02) = √16
The triangle's perimeter is calculated by adding the three distances together:
Perimeter = √45 + √25 + √16 = 10.00.
Hence, the perimeter of the triangle is 10.00, rounded to the closest hundredth.
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Joel hit b baseballs at practice and another 15 baseballs at the batting cage. Choose the expression that shows how many baseballs Joel hit in all.
The expression that shows how many baseballs Joel hit in all is y = b + 15.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is that Joel hit (b) baseballs at practice and another 15 baseballs at the batting cage.
We can write the expression that shows how many baseballs Joel hit in all is given by -
y = b + 15
Therefore, the expression that shows how many baseballs Joel hit in all is y = b + 15.
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The image point using the translation (x, y) → (x + 4, y – 1) for the point (3, 3) is:
None of these choices are correct.
(7, 2).
(1, 2).
(7, 4).
Answer:
(7,2)
Step-by-step explanation:
(3,3) 》(x+4, y-1)
3=x
3+4=7
3=y
3-1=2
=(7,2)
Answer:
(7, 2 )
Step-by-step explanation:
the translation rule (x, y ) → (x + 4, y - 1 ) means
add 4 to the original x- coordinate and subtract 1 from the original y- coordinate.
(3, 3 ) → (3 + 4, 3 - 1 ) → (7, 2 )
WILL MARK BRAINLIEST! please help with easy geometry problem
Answer:
10
Step-by-step explanation:
180-140=20
20÷2=10
×=10
y=10
Please help asap giving 50 points for it!!!
The inequality that can be used to find the number of windows is d + r ≤ 235 and 250r + 220d ≥ 55000
What is an equation?An equation is an expression that shows how two or more numbers and variables are related to each other. Types of equations can either be linear, quadratic or cubic
Inequalities are used to show the nonequal comparison of two or more numbers and variables
Let r represent the regular price and let d represent the discounted price.
Gerald company has an inventory of 235 windows, hence:
d + r ≤ 235 (1)
Also, the regular price is $250 and the discounted price is $220. The sales goal is $55000, hence:
250r + 220d ≥ 55000 (2)
The inequality is d + r ≤ 235 and 250r + 220d ≥ 55000
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Find the sums of the interior angles and the sum of the measures of the exterior angles of the polygon. Please answer 1, 2, and 3, 30 points!!!!!!!!!!!!!!!!!!!!!!!!
The sum of the internal angles of the polygons are
a) The sum is A = 540°
b) The sum is A = 360°
c) The sum is A = 1800°
What is the sum of the interior angles of a polygon?The sum of the interior angles of a polygon is given by the formula
Sum of Interior angles of a polygon with n sides is
nθ = 180° ( n - 2 )
where n is the number of sides
θ = angle in degrees
Given data ,
Let the sum of the internal angles of a polygon be represented as A
Now , the value of A is
The sum of exterior angle of n polygon is = 360°
Now ,
a)
The number of sides of the polygon = 5 sides
So , Sum of Interior angles of a polygon with n sides is
nθ = 180° ( n - 2 )
Substituting the value of n = 5 in the equation , we get
nθ = 180° ( 5 - 2 )
nθ = 180° x 3
nθ = 540°
b)
The number of sides of the polygon = 4 sides
So , Sum of Interior angles of a polygon with n sides is
nθ = 180° ( n - 2 )
Substituting the value of n = 4 in the equation , we get
nθ = 180° ( 4 - 2 )
nθ = 180° x 2
nθ = 360°
c)
The number of sides of the polygon = 12 sides
So , Sum of Interior angles of a polygon with n sides is
nθ = 180° ( n - 2 )
Substituting the value of n = 12 in the equation , we get
nθ = 180° ( 12 - 2 )
nθ = 180° x 10
nθ = 1800°
Hence , the sum of the internal angles of the polygon is solved
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What are the statements and reasons for this problems.
Anything helps! Thank you :)
From the congruency of triangles we can prove,
A: D is the midpoint of AC,
B: Measure of ∠D = ∠E,
C: BD bisect the angle ABC.
What are congruent triangles?Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance.
Given BD bisect ∠ABC
AB ≅ CB
from the figure, AB = CB
since BD bisects ∠ABC
∠1 = ∠2
and BD = BD (common side)
from SAS property,
ΔABD ≅ ΔCBD
Triangles can be shown to be congruent after which the final dimension can be anticipated without actually measuring the triangle's sides and angles.
from CPCT, AD = CD
since AD = CD so D should be the midpoint of AC.
B: Given B is the midpoint of AC,
AB = CB
and BD ║ AE,
so ∠1 and ∠2 are equal due to corresponding angles between parallel lines,
∠1 = ∠2
BD = AE
ΔABE ≅ ΔCBD
from CPCT, ∠D = ∠E
C: Given ∠A and ∠C are right angles,
∠A = ∠C = 90°
AD = CD
BD = BD (common side and hypotenuse of a right triangle)
from RHS property ΔABD ≅ ΔCBD
from CPCT, ∠ABD = ∠CBD
since both angles are equal so BD is the angle bisector.
Hence all the statements are proved by the congruency of triangles.
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Suppose that the number of hours that it takes for a student to finish an inquiry has density
f(x) =
{ 2/5(x + 1) if 1 < x < 2
{ 0 otherwise.
a) Find the probability that the student finishes the inquiry in less than 1.5 hours.
b) Find the mean and standard deviation of the number of hours it takes to finish the inquiry.
The probability that the student finishes the inquiry in less than 1.5 hours is 0.45.
Mean= 4/3 and standard deviation= √(11/90)
a) To find the probability that the student finishes the inquiry in less than 1.5 hours, we need to find the area under the probability density function (PDF) of f(x) between the lower limit of 1 and the upper limit of 1.5.
This is given by the definite integral of f(x) from 1 to 1.5:
∫f(x)dx from 1 to 1.5
= ∫(2/5(x + 1))dx from 1 to 1.5
= (2/5)∫(x + 1)dx from 1 to 1.5
= (2/5)[x^2/2 + x] from 1 to 1.5
= (2/5)[(1.5)^2/2 + 1.5 - (1)^2/2 - 1]
= (2/5)[2.25/2 + 1.5 - 1/2 - 1]
=(2/5)[2.25/2]
=0.45
b) To find the mean, we need to use the formula:
Mean = ∫x*f(x)dx from a to b
In this case:
Mean = ∫x*(2/5(x + 1))dx from 1 to 2
= (2/5)∫x(x + 1)dx from 1 to 2
= (2/5)[x^3/3 + x^2/2] from 1 to 2
=(2/5)[(2)^3/3 + (2)^2/2 - (1)^3/3 - (1)^2/2]
= (2/5)[8/3 + 4/2 - 1/3 - 1/2]
=(2/5)[7/3 + 3/2]
=(2/5)[(20)/6]
=4/3
=1.333
To find the standard deviation, we need to use the formula:
Standard deviation^2 =(∫(x-μ)^2*f(x)dx) from a to b
Where μ is the mean
In this case,
Standard Deviation ^2= ∫(x-μ)^2(2/5)(x+1) dx from 1 to 2
=(2/5)∫(x-μ)^2(x+1) dx from 1 to 2
Simplifying, we get,
(x-μ)^3*(3x+μ+4)/30 from 1 to 2
=[(2-μ)^3*(6+μ+4)-(1-μ)^3*(3+μ+4)]/30
=[(2-μ)^3*(10+μ)-(1-μ)^3*(7+μ)]/30
Substituting the value of μ,
=[(2-4/3)^3*(10+4/3)-(1-4/3)^3*(7+4/3)]/30
=11/90
Therefore, Standard Deviation= √(11/90)
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Statins are used to keep cholesterol in check and are a top-selling drug in the
U.S. The equation:
S - 1.5x = 4.9
gives the amount of sales (S) of statin in billions of dollars a years after 1998.
According to this equation, how much will/did people in the U.S. spend on
statins in the year 2010?
Answer: People in the U.S. will spend ??
Billion dollars on statins in 2010.
Answer: 87
Step-by-step explanation:
6. Explain what must occur to the parent
function f(x) = x² to transform the
function to g(x) = (x-4)² +2.
Answer:
4 units right, 2 units up
Step-by-step explanation:
For [tex]g(x)=(x-4)^2+2[/tex], the graph of [tex]f(x)=x^2[/tex] would need to move 4 units to the right and 2 units up. Hence, the vertex would be [tex](4,2)[/tex] if we compare the function g(x) with the form [tex]y=a(x-h)^2+k[/tex].
While playing basketball, Ava’s heartbeat `is 80` times in `30` seconds. While running, her heartbeat `was 60` times in `20` seconds. Which activity made Ava’s heart beat faster? Basketball, running, or they were the same.
Running made Ava’s heart beat faster.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
While playing basketball, Ava’s heartbeat is 80 times in 30 seconds.
And, While running, her heartbeat was 60 times in 20 seconds.
Clearly, Ava's heartbeat is faster when he was running.
So, Running made Ava’s heart beat faster.
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Solve the following inequality algebraically.
x + 2 >\ 13
X+2 is greater than 13
Answer:
[tex]x > 11[/tex]
Step-by-step explanation:
Greetings!!
Given equation
[tex]x + 2 > 13[/tex]
subtract 2 from both sides
[tex]x + 2 - 2 > 13 - 2[/tex]
simplify
[tex]x > 11[/tex]
[tex]solution \: \: x > 11 \\ interval \: notation \: (11, \infty )[/tex]
Hope it helps!!
convert to tons 2,600 pounds
2600 pounds are equal to 1.3 tons.
What is unit conversion?A unit conversion expresses the same property as a different unit of measurement. For instance, time can be expressed in minutes instead of hours, while distance can be converted from miles to kilometers, or feet, or any other measure of length.
Given,
2,600 pounds to tons
1 US ton = 2000 pound
1 pound = 1/2000 US tons
2,600 pound = 2600/2000 US tons
2600 pound = 1.3 US tons.
Hence, 1.3 US tons are there in 26000 pounds.
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Rashad had ducks and cows on his farm. These 14 animals had a total of 40 legs. How many cows and ducks were there?
The solution to the system of equations is
The number of ducks D = 8 ducks
The number of cows C = 6 cows
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of ducks be D
Let the number of cows be C
Now , the total number of animals = 14
So , D + C = 14 be equation (1)
And , the total number of legs = 40
Number of legs for ducks = 2 legs
Number of legs for cows = 4 legs
And , the total number of legs = 2D + 4C = 40
So , 2D + 4C = 40 be equation (2)
On simplifying the equations , we get
Multiply equation (1) by 2 , we get
2D + 2C = 28 be equation (3)
Subtracting equation (3) from equation (2) , we get
2C = 40 - 28
2C = 12
Divide by 12 on both sides of the equation , we get
C = 6 cows
Substituting the value of C in equation (1) , we get
D = 14 - 6
D = 8 ducks
Therefore , the value of C and D is 6 and 8 respectively
Hence , the number of cows is 6 and number of ducks is 8
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What number must be multiplied to the vector <-4,2,-3> so it is normalized
A. [tex]\frac{1}{\sqrt{29} }[/tex]
B. -[tex]-\sqrt{29}[/tex]
C. [tex]-\frac{1}{\sqrt{29} }[/tex]
D. [tex]\sqrt{29}[/tex]
please help me with this thank you
Answer:
3rd one is 100.6⁰F I think... not sure
Answer: B
Step-by-step explanation: 100.7 is current. In the past, it was lower so we have to subtract. We know how much we subtract (2.5). In B, if we subtract 2.5 we are taking 2.5 away from his current temp to get yesterday's temp.
Please help me step by step pls
there is no question!
If a rectangular garden is 45 ft. by 20 ft., how many feet of fence are needed to enclose it?
Answer:
130 feet
Step-by-step explanation:
45 feet is one of the lengths of the rectangular garden and 20 feet is the other.
The perimeter of a rectangle is 2(l+w) and we know that these must be the lengths and widths.
Communitive property of addition states that it doesn't matter the order that we add so we know it's just 20+45 (65) then times 2 which is 130
130 feet is your answer.
What is the measure of angle d1
What is the tangent ratio of angle C2
100 POINTS!!!
Answer:
[tex]\sf \tan\left(c_2\right)=\dfrac{OD}{OC}=\dfrac{2\sqrt{66}}{19}[/tex]
Step-by-step explanation:
**Please note that if the segment AO = 3.8 cm then the 50° angle on the given rhombus is incorrect. It should be 49.46° (2 d.p.)**
In a rhombus, all four sides are equal in length. Therefore:
CD = AB = 5cmDiagonals bisect each other at 90°. Therefore:
OC = AO = 3.8 cmm∠COD = 90°Therefore, triangle COD is a right triangle.
To find the tangent ratio of angle c₂, first find the length of OD using Pythagoras Theorem:
[tex]\implies OC^2+OD^2=CD^2[/tex]
[tex]\implies 3.8^2+OD^2=5^2[/tex]
[tex]\implies 14.44+OD^2=25[/tex]
[tex]\implies OD^2=10.56[/tex]
[tex]\implies OD^2=\dfrac{1056}{100}[/tex]
[tex]\implies OD^2=\dfrac{1056 \div 4}{100 \div 4}[/tex]
[tex]\implies OD^2=\dfrac{264}{25}[/tex]
[tex]\implies OD^2=\dfrac{4 \cdot 66}{25}[/tex]
[tex]\implies OD=\sqrt{\dfrac{4 \cdot 66}{25}}[/tex]
[tex]\implies OD=\dfrac{\sqrt{4 \cdot 66}}{\sqrt{25}}[/tex]
[tex]\implies OD=\dfrac{2\sqrt{66}}{5}[/tex]
[tex]\boxed{\begin{minipage}{6 cm}\underline{Tan trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\end{minipage}}[/tex]
Given:
θ = c₂O = ODA = OCSubstitute the values into the tan ratio:
[tex]\implies \sf \tan\left(c_2\right)=\dfrac{OD}{OC}[/tex]
[tex]\implies \sf \tan\left(c_2\right)=\dfrac{\frac{2\sqrt{66}}{5}}{3.8}[/tex]
Rewrite 3.8 as 19/5:
[tex]\implies \sf \tan\left(c_2\right)=\dfrac{\frac{2\sqrt{66}}{5}}{\frac{19}{5}}[/tex]
[tex]\implies \sf \tan\left(c_2\right)=\dfrac{2\sqrt{66}}{19}[/tex]
Can someone verify this?
The diagram that shows the C intercept D would be = diagram B. That is option B.
What is a universal set?A universal set is defined as the set that contains all the values that makes up a data.
The universal set contains the following:
A = ( yellow corn)
B = ( yellow corn with variety kernel)
C = ( white corn)
D= ( white corn with variety butter and sugar).
The C intercept means the contents that are in C that can be found in D. The diagram that represents this form is diagram B.
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Can someone please solve this.
The correct option is the root of auxiliary equation are 0 and6
What is differential equation?A differential equation is an equation which contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable (i.e., independent variable) dy/dx = f(x) Here “x” is an independent variable and “y” is a dependent variable. For example, dy/dx = 5x.General Differential Equations. Consider the equation y′=3x2, which is an example of a differential equation because it includes a derivative. There is a relationship between the variables x and y:y is an unknown function of x. Furthermore, the left-hand side of the equation is the derivative of y.Ordinary differential equations applications in real life are used to calculate the movement or flow of electricity, motion of an object to and fro like a pendulum, to explain thermodynamics concepts. Also, in medical terms, they are used to check the growth of diseases in graphical representationTo learn more about differential equation refers to:
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Consider the following equation, known as the Arrhenius Equation Two-point form.
Solve for:
a)
b)
c)
d)
It's worth noting that to solve for T2 you need to have the values of other variables such as K1, K2, Ea, R and T1
What is the Arrhenius Equation?
The Arrhenius equation is a mathematical equation that describes the relationship between the rate constant (K) of a chemical reaction and the temperature (T) of the reaction. The equation was first proposed by Svante Arrhenius in 1889 and it states that the rate constant of a chemical reaction is directly proportional to the exponential of the negative activation energy (Ea) of the reaction, divided by the gas constant (R) and the absolute temperature (T). The equation can be written as:
K = A * e^(-Ea / (R*T))
The Arrhenius Equation Two-point form is a mathematical equation that describes the relationship between the rate constant (K) of a chemical reaction, the activation energy (Ea) of the reaction, the universal gas constant (R), and the temperature (T) of the reaction.
Given the equation K2/K1 = Ea / R (1/T1 - 1/T2)
a. To solve for K2, we can multiply both sides of the equation by
K1: K2 = K1 * Ea / R (1/T1 - 1/T2)
b. To solve for K1, we can divide both sides of the equation by
Ea / R (1/T1 - 1/T2): K1 = K2 / Ea / R (1/T1 - 1/T2)
c. To solve for Ea, we can multiply both sides of the equation by
R (1/T1 - 1/T2): Ea = K2/K1 * R (1/T1 - 1/T2)
d. To solve for T2, we can use the equation 1/T2= 1/T1 - Ea/R * K1/K2
It's worth noting that to solve for T2 you need to have the values of other variables such as K1, K2, Ea, R and T1.
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Which is the rate of change for the interval between –6 and –3 on the x-axis?
The rate of change for the interval between –6 and –3 on the x-axis is; 2
How to find the rate of change of the graph?To find the rate of change for the interval between –6 and –3 on the x-axis, the first step is to locate the ordered pairs at those two points. Locating the two ordered pairs from the graph is seen to be (3, -2) and (6, 4).
Applying the slope formula with those two points, we can find the rate of change as;
slope; m = (y₂ - y₁)/(x₂ - x₁)
m = (4 + 2)/(6 - 3)
m = 6/3
m = 2
This value of m represents the rate of change
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please need help asap 28, and 29
The length of the mid-segment of the trapezoid for these problems is given as follows:
28. n + 12 = 17.
29. 2n + 11 = 27.
How to obtain the length of the mid-segment of a trapezoid?The length of the mid-segment of a trapezoid is half the sum of the lengths of the bases.
Hence the value of n for item 28 is given as follows:
n + 12 = 1/2(2n - 2 + 4n + 6)
n + 12 = 0.5(6n + 4)
n + 12 = 3n + 2
2n = 10
n = 5.
Hence the length of the mid-segment is of:
n + 12 = 5 + 12 = 17.
The value of n for item 29 is given as follows:
2n + 11 = 1/2(5n - 2 + n + 8)
2n + 11 = 0.5(6n + 6)
2n + 11 = 3n + 3
n = 8.
Hence the length of the mid-segment is of:
2n + 11 = 16 + 11 = 27.
(replacing n = 8 into 2n + 11).
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