what is the multiplicative rate of change of the function described in the table ?
Answers
Hence, the multiplicative Rate of change is:
5
Step-by-step explanation:The multiplicative Rate of change refers to the fixed constant which when multiplied to the output will lead to increase/decrease in the next output value.
We have the table of values as:
x y
-1 1/10
0 1/2
1 5/2
2 25/2
3 125/2
Hence, we see that when 5 is multiplied to the output value we obtain the next output value.
i.e.
1/10×5=1/2
1/2×5=5/2
5/2×5=25/2
25/2×5=125/2
Hence, the multiplicative Rate of change is:
5
Related Questions
Given: Triangles ABC and DBC are isosceles, m∠BDC = 30°, and m∠ABD = 155°.
Find m∠ABC, m∠BAC, and m∠DBC.
Answers
Answer:
- m∠ABC = m∠ACB = 25° (as triangle ABC is isosceles).
- m∠BAC = 130°.
- m∠BDC = m∠DCB = 30° (as triangle DBC is isosceles).
Explanation:
We can solve this problem by using the properties of isosceles triangles and the fact that the sum of angles in a triangle is 180 degrees.
1. Since triangle DBC is isosceles, m∠DBC = m∠DCB.
Therefore, m∠DCB = 30°.
2. In triangle ABC, since it's isosceles, m∠ABC = m∠ACB.
3. We know that m∠ABD = 155°. Since triangle ABD is a triangle, the sum of its angles is 180 degrees. So, m∠ABD + m∠BAD + m∠ADB = 180°. Therefore, m∠BAD + m∠ADB = 180° - 155° = 25°.
4. Since triangle ABC is isosceles, m∠ABC = m∠ACB = 25°.
5. In triangle ABC, the sum of its angles is 180 degrees. So, m∠ABC + m∠BAC + m∠ACB = 180°. Substituting the known values, we get 25° + m∠BAC + 25° = 180°. Solving for m∠BAC,
we find m∠BAC = 180° - 25° - 25° = 130°.
How many gallons of rocket fuel containing 80% liquid oxygen must be mixed with 250 gallons containing 40% liquid oxygen to produce a mixture containing 70% oxygen?
Answers
Answer:
750
Step-by-step explanation:
for others
750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.
What is Percentage?
percentage, a relative value indicating hundredth parts of any quantity
We need to find how many gallons of 80%
8x, since we don't know how many gallons
mixed with 250 gall of 40%: 0.40(250)
and we want a mix at 70%. The mix will include the 0.8x and the 0.4(250) Like this:
8x+0.4(250)=0.7x+0.7*250
Multiply on both sides of the equation
0.8x+100= 0.7x+175 Subtract 100 on both sides
0.8x= 0.7x+75
Subtract 0.7 on both sides
0.1x= 75
Divide both sides by 0.1
x= 750
You need 750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.
Hence, 750 gallon of fuel at 80% to mix with the 250 gallon at 40% in order to get a mixture at 70% liquid oxygen.
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2X +105+ 8X -20+10 X +94+12 X -15=900 solve for x
Answers
32x + 164 = 900
. - 164 -164
32x = 736
÷32x. ÷32x
x = 23
The sum of two numbers is 67 . the smaller number is 9 less than the larger number. what are the numbers? larger number: smaller number:
Answers
Smaller Number is L -9
Larger # + Smaller # = 67
L + L - 9 = 67
2L - 9 = 67
2L = 67 + 9
2L = 76
L = 76/2
L = 38
Smaller Number = Larger Number - 9
38 - 9
Smaller # = 29
Check. .. 38+29=67 CORRECT!
Larger #: 38
Smaller #: 29
To solve the problem, two equations were set up based on the conditions given. After substitution and simple algebraic operations, the larger number was found to be 38 and the smaller number to be 29.
The question involves finding two numbers where the sum is 67, and the smaller number is 9 less than the larger number.
Let's define the larger number as x and the smaller number as y. According to the problem:
x + y = 67 (Equation 1)y = x - 9 (Equation 2)Substitute Equation 2 into Equation 1:
x + (x - 9) = 67
2x - 9 = 67
2x = 67 + 9
2x = 76
x = 38
Now, we can find y using Equation 2:
y = x - 9
y = 38 - 9
y = 29
Therefore, the larger number is 38 and the smaller number is 29.
Which expression represents " 5 less than twice x " ?
1. 2x-5
2. 5-2x
3. 2(5-x)
4. 2( x-5)
Answers
The mathemtical expression for the word expression 5 less than twice x " is 2x - 5 option (A) 2x -5 is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that:
The word expression is:
5 less than twice x
Twice the x = 2x
5 less than twice the x:
= 2x - 5
Thus, the mathematical expression for the word expression 5 less than twice x " is 2x - 5 option (A) 2x -5 is correct.
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Identify the base, exponent, and the expression’s value. 3 to the power of 4 base= exponent= value=
Answers
Final answer:
In the expression 3 to the power of 4, the base is '3', the exponent is '4', and the value of the expression is 81 after multiplying the base by itself for the number of times indicated by the exponent.
Explanation:
The expression given is 3 to the power of 4, which is written in mathematical terms as 34. The base of this expression is the number that is being multiplied by itself, which in this case is "3". The exponent is the number that indicates how many times the base is multiplied by itself, and here it is "4".
Finally, the value of the expression is the result of carrying out the multiplication that the exponent indicates, so for 3 raised to the 4th power, it's 3 x 3 x 3 x 3, which equals to 81.
A square piece of tile with sides 12 inches is cut along a diagonal, What is the length of the diagonal rounded to the nearest inch?
Answers
To find the length of the diagonal of a square tile, you can use the Pythagorean theorem. Given that the side length of the tile is 12 inches, the length of the diagonal is approximately 17 inches when rounded to the nearest inch.
Explanation:To find the length of the diagonal of a square tile, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the two sides of the right triangle are the sides of the square tile, and the hypotenuse is the diagonal. Given that the side length of the tile is 12 inches, we can calculate the length of the diagonal as follows:
Square the length of one side: 12 x 12 = 144
Multiply the result by 2: 144 x 2 = 288
Take the square root of the result: √288 ≈ 16.97 inches
Rounded to the nearest inch, the length of the diagonal of the square tile is 17 inches.
Final answer:
The length of the diagonal of the square, rounded to the nearest inch, is 17 inches.
Explanation:
The length of the diagonal of a square can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the two sides of the square are both 12 inches long. So, we have:
hypotenuse² = side1² + side2²
hypotenuse² = 12² + 12²
hypotenuse² = 144 + 144
hypotenuse² = 288
To find the length of the hypotenuse (or the diagonal), we take the square root of both sides:
hypotenuse = √(288)
hypotenuse = 16.97 inches (rounded to the nearest inch)
Joanna has a flat wooden triangular piece as part of a wind chime. the piece is suspended by a wire anchored at a point equidistant from the sides of the triangle. where is the anchor point located?
Answers
Final answer:
Joanna's wind chime is suspended from the centroid of the triangular piece, which is the intersection point of the triangle's three medians and serves as its center of gravity.
Explanation:
The anchor point where Joanna has suspended the flat wooden triangular piece of the wind chime is known as the centroid of the triangle. The centroid is the point where the three medians of the triangle intersect, and it is always located inside the triangle. A median of a triangle is a line segment connecting a vertex to the midpoint of the opposing side. The centroid is also the triangle's center of gravity, meaning it is the balance point where the triangle can be suspended and remain in equilibrium. For any given triangle, the centroid will be found at a point that is one-third of the distance from each vertex to the midpoint of the opposite side.
The number of chickens to the the number of ducks on a farm was 6:5. after 63 ducks were sold, there were three times as many chickens as ducks left. how many chickens were there on the farm
Answers
6x/(5x-63)=3/1
15x-189=6x
9x=189
x=21
6x=123 chickens were on the farm
☺☺☺☺
Answer:
126
Step-by-step explanation:
No Following
What is the perimeter of a polygon with vertices at (3, 2) , (3, 9) , (7, 12) , (11, 9) , and (11, 2) ? Enter your answer in the box. Do not round any side lengths.
Answers
Answer is 32. hope i helped.
Answer:
32 units
Step-by-step explanation:
Verified by test results
Hope this helps:)
Números write the numbers as words. 38 116 573 1.821 754.322 6.615.010
Answers
To write the given numbers as words, you can break them down into groups of three digits from right to left and then write each group separately. For example, 38 is written as thirty-eight.
Explanation:To write the numbers as words, we can break them down into groups of three digits from right to left. Here are the numbers written as words:
38: thirty-eight 116: one hundred sixteen 573: five hundred seventy-three 1.821: one thousand eight hundred twenty-one 754.322: seven hundred fifty-four thousand three hundred twenty-two 6.615.010: six million six hundred fifteen thousand ten Learn more about Writing numbers as words here:
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To write the given numbers as words, we break them down into their place values. 38 can be written as thirty-eight, 116 as one hundred sixteen, 573 as five hundred seventy-three, 1.821 as one thousand eight hundred twenty-one, 754.322 as seven hundred fifty-four thousand three hundred twenty-two, and 6.615.010 as six million six hundred fifteen thousand ten.
Explanation:In order to write the given numbers as words, we can break them down into their place values. Let's analyze each number:
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Adjacent, right angles are complementary. always, sometimes, or never
Answers
- Two angles are adjacent when they lie next to each other across a line. Imagine you have two line segments forming an angle, and that that angle is cut in half by another line segment, forming two smaller angles. Each of those smaller angles is adjacent to the other.
- A right angle is an angle formed at the meeting point of two perpendicular lines. For an example of what it means to be perpendicular, think of the angles a plus sign forms at each of its corners - those lines are what are called perpendicular.
- Complementary angles are two angles which add up to a right angle.
With this knowledge, take a look at the question again. Is it possible for two right angles that are next to each other to add up to another right angle? Can any number greater than zero, when added to itself, ever equal itself?
Let f(x)=2x-1 and g(x)=4-x^2. Find (f o g)(x).
Answers
[tex]fog(x)=f(g(x)) \\ \\ \\ =2.(4-x^2)-1 \\ \\ \\ = -2x^2+7 \\ \\ \\ GOOD \quad LUCK [/tex]
First write the ratio as a fraction. make sure both terms have the same unit of measure. note that 1 foot equals 12 inches 1 foot=12 inches. then divide the numerator and denominator by their greatest common factor (gcf) to write the ratio in simplest form. ok
Answers
Frank needs a total of $360 to cover his expenses of the week he earns $195 a week working at a restaurant and also walks dogs to supplement his income frank charges $15 per dog that he walks which equation can be used to find the number of dogs d that frank needs to walk to cover his expenses and how many dogs is that
Answers
you don't show the options but it should look something like this:
195 +15d = 360
answer:
subtract 195 from each side
15d = 165
d = 165/15 =11
he needs to walk 11 dogs
The equation which can be used to find the number of dogs d that frank needs to walk to cover his expenses is 15d+195=360 and number of dogs is 11.
What is an unknown variable?Unknown variables are used to find the unknown values of the problem using the algebraic expressions.
To find the values of unknown quantity, the statements of a problem is converted in the algebraic equation form using the variable in place of unknown numbers.
Frank needs a total of $360 to cover his expenses of the week. He earns $195 a week working at a restaurant and also walks dogs to supplement his income, frank charges $15 per dog that he walks.
The equation, which can be used to find the number of dogs d that frank needs to walk to cover his expenses,
[tex]15d+195=360[/tex]
Solve it further to find the number of dogs d,
[tex]15d+195=360\\15d=360-195\\d=\dfrac{165}{15}\\d=11[/tex]
Thus, the equation which can be used to find the number of dogs d that frank needs to walk to cover his expenses is 15d+195=360 and the number of dogs is 11.
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Find, to the nearest tenth, the area of the region that is inside the square and outside the circle. the diameter of the circle is 14 in. 10.5 in2 42.1 in2 153.9 in2 196 in2
Answers
Answer:
Option [tex]42.1\ in^{2}[/tex]
Step-by-step explanation:
we know that
The area of the region that is inside the square and outside the circle is equal to the area of the square minus the area of the circle
see the attached figure to better understand the problem
Step 1
Find the area of the square
Remember that
The area of the square is
[tex]A=b^{2}[/tex]
where
b is the length side of the square
we have
[tex]b=14\ in[/tex]
substitute
[tex]A=14^{2}=196\ in^{2}[/tex]
Step 2
Find the area of the circle
Remember that
The area of the circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=14/2=7\ in[/tex]
substitute
[tex]A=\pi(7^{2})=153.9\ in^{2}[/tex]
Step 3
Find the area of the region
[tex]196\ in^{2}-153.9\ in^{2}=42.1\ in^{2}[/tex]
(1-sin squared times tan is equal to ?
Answers
i) [tex]\sin^2x+\cos^2x=1[/tex]
ii) [tex]\tanx = \frac{\sinx}{\cosx} [/tex].
We want to simplify [tex](1-\sin^2x)\cdot \tanx[/tex].
Since, [tex]\sin^2x+\cos^2x=1[/tex], then [tex]1-\sin^2x=\cos^2x[/tex]. Thus, the expression
[tex](1-\sin^2x)\cdot \tanx[/tex]
becomes
[tex]\displaystyle{ \cos^2x \cdot \frac{\sin x}{cosx} = \cos x \sin x.[/tex]
Answer: [tex] \ sinx \ cosx[/tex], or [tex]\displaystyle{ \frac{\sin2x}{2} [/tex].
5. Given the following triangle side lengths, identify the triangle as acute, right or obtuse. Show your work. a. 3in, 4in, 5 in b. 5in, 6in, 7in c. 8in, 9in, 12in
Answers
5^2 ? 3^2 + 4^
25 ? 9 + 16
25 = 25
Because the two sides are equal, this is a right triangle.
b. 5in, 6in, 7in
7^2 ? 5^2 + 6^2
49 ? 25 + 36
49 < 61
Because 49 < 61, this is an acute triangle.
c. 8in, 9in, 12in
12^2 ? 8^2 + 9^2
144 ? 64 + 81
144 < 145
Because 144< 145 , this is an acute triangle.
From the information, A is a right triangle, B is an acute triangle and C is an acute angle.
What are triangles?A polygon with three sides, angles, and vertices is called a triangle.
Given that, triangle side lengths, we need to identify the triangle as acute, right or obtuse,
How to solve the triangle?
It will be a right triangle if a² + b² = c², It will be аcute if a² + b² > c² and it'll be obtuse if a² + b² < c².
1) a² + b² = 3² + 4² = 9 + 16 = 25 and c² = 5² = 25
25 = 25
This is a right triangle.
2) a² + b² = 5² + 6²
= 25 + 36 = 61
c² = 7² = 49
61 > 49 = аcute triangle.
3) a² + b² = 8² + 9²
= 64 + 81 = 145
c² = 12² = 144
145 > 144 = аcute triangle.
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Solve the following equation 5x+3(x-1)=8(x+2)-10
Answers
5x + 3x - 3 = 8x + 16 - 10
8x - 3 = 8x + 6
0 - 3 = 6
3 =/= 9
NO SOLUTION.
8x-3=8x+16-10
8x-3=8x+6
-8x -8x
-3=6
This is not a true solution
What skills and practices were important for the growth and spread of early civilizations?
Answers
use exponential form to evaluate log8(2)
Answers
Answer: [tex]\frac{1}{3}[/tex]
Explanation:
let y = [tex]log_{8} (2)[/tex]
whenever we transfer base from log from one side to other it will remain be base after shifting to the other side.
Change log to exponent form [tex]\log_xm=n\\m =x^{n}[/tex]
here we have n = y, m=2, x=8 by substituting the values
we will get
[tex]8^{y} = 2[/tex] (1)
we can write 8 in power of 2 that is [tex]2^{3}[/tex]
we will rewrite the above equation (1) as
[tex]2^{3y} = 2[/tex]
we can equate the power when base is same then we will get
3y = 1
then
[tex]y=\frac{1}{3}[/tex]
The result of the logarithmic expression [tex]log _82=x[/tex] is 1/3
Let the given logarithmic function be x to have:
[tex]log _82=x[/tex]
This can be transformed into indices to have:
[tex]8^x = 2[/tex]
Solve the resulting indices for "x" a shown:
[tex](2^3)^x = 2^1\\2^{3x}=2^1[/tex]
Cancel the base and equate the power to have:
[tex]3x = 1\\x = \frac{1}{3}[/tex]
Hence the result of the logarithmic expression [tex]log _82=x[/tex] is 1/3
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The party planning committee has to determine the number of tables needed for an upcoming event. If a square table can fit 8 people and a round table can fit 6 people, the equation 150 = 8x + 6y represents the number of each type of table needed for 150 people. The variable x represents the number of . The variable y represents the number of . If y = 9, find the value of x. The committee needs square tables.
Answers
Answer:
The variable "x" is the number of square tables and the variable "y" represents the number of round tables.
The committee needs 12 square tables.
Step-by-step explanation:
You know that the equation is 150 = 8*x + 6*y. You also know that 8 people can fit on a square table and 6 people can fit on a round table. Then 8 people multiplied by the amount of square tables plus 6 people by the amount of round tables should add 150 people. So in the previous equation the variable "x" is the number of square tables and the variable "y" represents the number of round tables.
If the number "y" of round tables is 9, you can replace this value in equation 150 = 8*x + 6*y, with 150 = 8*x + 6*9. Solving this last equation, you can calculate the value of the variable "x", that is, calculate the amount of square tables needed.
150= 8*x + 6*9
150= 8*x + 54
150-54= 8*X +54 - 54
96 = 8*x
[tex]\frac{96}{8} =\frac{8}{8} *x[/tex]
12=x
So, the committee needs 12 square tables.
The number of square tables that's needed will be 12 square tables.
The equation given is 150 = 8x + 6y and this represents the number of each type of table that's needed for 150 people.
Since 6 people are already give for the round tables, then to solve the square tables will be:
150 = 8x + 6y
150 = 8x + (6 × 9)
150 = 8x + 54
Collect like terms
8x = 150 - 54
8x = 96
Divide both side by 8
8x/8 = 96/8.
x = 12
Therefore, the number of square table that's needed will be 12 square tables.
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Two sides of a triangle are 9 cm and 12 cm long. What is the range of possible lengths for the third side? Enter your answer in the boxes below.
Answers
Answer:
Possible length range of third side is between 3<x<21.
Step-by-step explanation:
Sum of two sides of triangle cannot be equal or less than third side. Therefore, one side length of a triangle must be between subtract and sum of other two sides. Than, range of third side is:
[tex](12-9)<x<(12+9)\\3<x<21[/tex]
Please help me!
Write and solve the compound inequality
A student scored a 73 and 81 on their first
two tests. Write and solve a compound
inequality to find the possible values for a
3rd quiz score that would give them an
average between 80 and 85
my answer is 86<=x<=101, but I don't know if it is right
Answers
73 + 81 + 86 = 240
240 / 3 = 80
80%
That's true, now let's check 101.
73 + 81 + 101 = 255
255 / 3 = 85
85%
That's true.
Your inequality is correct.
simplify the expression (-2 -c) (-1)
Answers
multiply -1 to both -2 & -c
-1 x -2 = 2
-1 x -c = c
2 + c is your answer
hope this helps
Lauren would like to have an average of 88 in her math class. There are five assignments with the following grades: 85, 100, 88, 80, 95. What grade will lauren need to make on the last assignment to meet her goal
Answers
85+100+88+90+95+80=528
528/6=80
Find the inverse of g(x)
Answers
1) Replace f(x) with y.
2) Switch x and y.
3) Solve for y.
4) Replace y with f^(-1)(x).
Line is parallel to line b and m<7=135. Find m<4
Answers
what is the approximate value of q ? q+log26=2q+2
Answers
Solve. 10 = c/3 – 4 + c/6
Show steps