Percent change formula:
C = x - x
2 1 / x
1
To calculate percent change we need to take the difference between the starting value and final value, divide by the absolute value of the starting value, and multiply the result by 100.
1. 72 is a 33.333% decrease of 108. Round is 33%.
2. 90 is a 20% increase of 75. Round is 20%.
3. 49 is a 75% increase of 28. Round is 80%.
11) -4, -1, -3
A) f(x) = x + 8x + 19x + 15
B) f(x) x + 8x? + 19x + 4
C) f(x)=r: 8x? 1 27x + 12
D) f(x) – xº +872 + 19x + 12
Write a polynomial function of least degree with integral coefficients that has the given zeros.
Answer:
The required polynomial is:
[tex]f\left(x\right)=x^3+8x^2+19x+12[/tex]
Step-by-step explanation:
Given the zeros
-4, -1, -3
Zeros can be written as:
x = -4, x = -1, x = -3
Finding the factors
x = -4
x +4 = 0
x = -1
x + 1 = 0
x = -3
x + 3 = 0
Thus, the factor are:
(x+4) (x+1) (x+3)
The original function can be computed by multiplying the factors
[tex]\left(x+4\right)\left(x+1\right)\left(x+3\right)=0[/tex]
as
[tex]\left(x+4\right)\left(x+1\right)=x^2+5x+4[/tex]
so the expression becomes
[tex]\left(x^2+5x+4\right)\left(x+3\right)=0[/tex]
Distribute parentheses
[tex]x^2x+x^2\cdot \:3+5xx+5x\cdot \:3+4x+4\cdot \:3=0[/tex]
[tex]x^2x+3x^2+5xx+5\cdot \:\:3x+4x+4\cdot \:\:3=0[/tex]
[tex]x^3+3x^2+5x^2+15x+4x+12=0[/tex]
Add similar elements: [tex]3x^2+5x^2=8x^2[/tex]
[tex]x^3+8x^2+15x+4x+12 = 0[/tex]
Add similar elements: [tex]15x+4x=19x[/tex]
[tex]x^3+8x^2+19x+12=0[/tex]
Thus, the required polynomial is:
[tex]f\left(x\right)=x^3+8x^2+19x+12[/tex]
Note: your answer choices are a little ambiguous, but I have explained the entire procedure. Hopefully, it will clear your concept.
Which of the following equations is equivalent to 4.12x + 5.2 = 8.23?
(1) 412x+ 52 = 823
(2) 412x + 520 = 823
(3) 9.32x =8.23
(4) 0.412x + 0.52 = 8.23
12n²-15nz³
j7yh6tg5rg6tg7h65t
Answer:
j7yh6tg5rg6tg7h65t
Step-by-step explanation:
need thanks and make me brainiest if it helps you
PLEASE HELP FAST ILL GIVE BRAINLIST MAKE SURE YOU READ IT BEFORE YOU ANSWER ITS QUESTION 18
Answer:
D. y=3x+15
Step-by-step explanation:
find the slope
[tex]\frac{1-(-5)}{-3-(-1)} =3[/tex]
y=mx+b
plug in known values
3=3(-4) + b
b=15
y=3x+15
What is the quadratic equation whose roots are 3/4 and 1/2 respectively
We need to know about the relation between roots of a quadratic equation for solving the question. The quadratic equation with roots 3/4 and 1/2 is [tex]8x^{2} -10x+3=0[/tex]
Quadratic equation is an equation with the highest order of variable being 2. Roots of a quadratic equation are the values that satisfy the equation.Since quadratic equation has the highest order as 2, the equation has two roots. Roots of a quadratic equation can be real and unique, real and equal or imaginary. The roots of a quadratic equation can be used to get the quadratic equation itself.
Let there be a quadratic equation:
[tex]ax^{2} +bx+c=0\\x^{2} +\frac{b}{a} x+\frac{c}{a} =0[/tex]
Let the roots of the quadratic equation be α and β, then
α+β=-b/a
αβ=c/a
In this question we know the two roots are 3/4 and 1/2. So we can derive the quadratic equation from them
[tex]\frac{3}{4} +\frac{1}{2} =\frac{-b}{a} \\\frac{-b}{a} =\frac{5}{4}[/tex]
[tex]\frac{3}{4}[/tex]×[tex]\frac{1}{2} =\frac{c}{a}[/tex]
[tex]\frac{c}{a} =\frac{3}{8}[/tex]
The quadratic equation is:
[tex]x^{2} -\frac{5}{4} x+\frac{3}{8} =0\\8x^{2} -10x+3=0[/tex]
Therefore we found the quadratic equation with roots 3/4 and 1/2 to be [tex]8x^{2} -10x+3=0[/tex]
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I’m very confused can someone please help me????
Answer:
Step-by-step explanation:
so the scale factor is 7:2
so we need to find 2 * x = 7
3.5 * 2 = 7
Multiply each length by 3.5 to find their new side lengths so:
12 * 3.5 = 42
9 * 3.5 = 31.5
5 * 3.5 = 17.5
the width, length, and height of a rectangular prism are each increased by $10\%$. what is the percent increase in the volume of the prism? express your answer to the nearest whole number.
The volume of the rectangular prism will increase by 33% if the width, length, and height are each increased by 10%.
Every three-dimensional object occupies some space. This space is measured in terms of its volume. Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.
The formula for the volume of a rectangular prism is:
V = l x w x h
where
“l” is the base length
“w” is the base width
“h” is the height of the prism
If the width, length, and height are each increased by 10%, the equation will now become:
[tex]V_{2}= 1.10 l * 1.10 w*1.10h[/tex]
[tex]V_{2}= 1.331* l*w*h[/tex] V = l*w*h
[tex]V_{2}= 1.331* V[/tex]
Hence, if the width, length, and height are each increased by 10%, the volume of the rectangular prism will increase by 33%.
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9e−7=7e−11
Solve for e
e = -2
that should be the correct answer
Answer:
e = 2
Step-by-step explanation:
Find the average rate of change for f(x) = x²-3x - 10 from x = -5 to x = 10.
Answer: Average rate of change = 2
Step-by-step explanation:
Can anybody help me with this math problems?
Answer:
All you have to do is replace the X with the number on the table
Step-by-step explanation:
so the first number is -3 so 3×-3+2
that equals -7 so put -7 as the first number under y. can continue like that
Answer:
1. -7, -4, -1, 2, 5, 8, 11
2. 5, 3, 1, -1, -3, -5, -7
3. -7, -6, -5, -4, -3, -2, -1
4. 13, 10, 7, 4, 1, -2, 5
Step-by-step explanation:
Write a linear function f with the values f(−1)=5 and f(3)=4.
Answer:
f(x)=-0.25x+4.75
Step-by-step explanation:
-0.25x+4.75
-0.25(-1)+4.75=5
-0.25(3)+4.75=4
Hope this helps!
CAN SOMEONE PLEASE HELP ME WITH THESE PLSSS!!
Answer:
e= 2
W= 15
m= 9
Step-by-step explanation:
for e: yout multiply 5 x 7 to get 35 so 2 x 7 = 14
for W: 20/10 = 2 so divide 30/2 to get 15
for m: 11 x 2 = 22 so do 18 divided 2 to get 9
Answer:
E = 2
W = 15
M = 9
Step-by-step explanation:
You just have to make the denominator / numerator the same.
[tex]\frac{E}{5}[/tex] = [tex]\frac{14}{35}[/tex]
Multiply the first fraction by 7 so that their denominators are both 35.
[tex]\frac{7E}{35}[/tex] = [tex]\frac{14}{35}[/tex]
7E = 14
E = 14 ÷ 7
E = 2
[tex]\frac{20}{30}[/tex] = [tex]\frac{10}{W}[/tex]
Multiply the second fraction by 2 so that their numerators are both 20.
[tex]\frac{20}{30}[/tex] = [tex]\frac{20}{2W}[/tex]
2W = 30
W = 30 ÷ 2
W = 15
[tex]\frac{M}{11}[/tex] = [tex]\frac{18}{22}[/tex]
Multiply the first fraction by 2 so that their denominators are both 22.
[tex]\frac{2M}{22}[/tex] = [tex]\frac{18}{22}[/tex]
2M = 18
M = 18 ÷ 2
M = 9
Solve the system using the elimination method. Answer in simplest fraction form. x+2y-z=3 -2x-y+z=-1 6x-3y-z=-7
For a real value of z, the general solution of above system of equations is x = -1/3 + (1/3)z, y = 5/3 + (1/3)z and z = z
In this question, we have been given a system of equations.
x+2y-z=3 ...........(1)
-2x-y+z=-1 ............(2)
6x-3y-z=-7 ...........(3)
We need to solve above system of equations using the elimination method.
We solve above system of equations by Gaussian elimination method.
First we write above system f equations in as an augmented matrix.
[tex]\begin{bmatrix}1 & 2 & -1 &|& 3 \\-2 & -1 & 1 &|& -1 \\6 & -3 & -1 &|& -7\end{bmatrix}[/tex]
We convert the augmented matrix into the row echelon form as:
[tex]\begin{bmatrix}1 & 2 & -1 & 3 \\0 & 3 & -1 & 5 \\0 & 0 & 0 & 0\end{bmatrix}[/tex]
So, we get an system of equations as:
x + 2y -z = 3 ............(4)
3y - z = 5 ...........(5)
From equation (5),
y = 5/3 + (1/3)z
Substitute above value of y in equation (4),
x = 3 - 2[5/3 + (1/3)z] + z
x = -(1/3) + (1/3)z
So, the general solution is,
[tex]\left(\begin{matrix}\frac{-1}{3}+\frac{1}{3}*z \\\\\frac{5}{3}+\frac{1}{3}*z \\\\z\end{matrix}\right)[/tex]
Therefore, for a real value of z, the general solution of above system of equations is x = -1/3 + (1/3)z, y = 5/3 + (1/3)z and z = z
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can triangles have sides with the given lengths?
3ft, 4ft ,9ft
Answer:
c
Step-by-step explanation:
3+4=7<9
determine whether each function has line symmetry.
Answer: 1 and 3 dont 2 and 4 do have a line of symmetry
Step-by-step explanation:
Graphs 1, 3 function are not line symmetry and 2 and 4 have line symmetry.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The line of symmetry is an imaginary line that runs through the centre of a line or shape creating two perfectly halves.
To check a function to be symmetrical about the origin we need to replace y with minus y and x with minus x and the function must be equal to original function.
In the given graphs, 1 and 3 are not symmetrical and 2 and 4 are symmetrical.
Hence graphs 1, 3 function are not line symmetry and 2 and 4 have line symmetry.
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I need help asap!!! (Geometry)
The length of the stake needs to be from the middle of her tent will be 6.9 feet. Then the correct option is C.
What is a right-angle triangle?
It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function. The Pythagoras is the sum of the square of two sides is equal to the square of the longest side.
A camper attaches a rope from the top of her tent, 4 feet above the ground, to give it more support. If the rope is 8 feet long.
Then the length of the stake needs to be from the middle of her tent will be
We have
P = 4 ft
H = 8 ft
Then the base is given by the Pythagoras theorem.
B² = H² - P²
B² = 8² - 4²
B² = 64 - 16
B² = 48
B = 6.9 ft
ether 12 or 4 feet.
sorry if i didnt help
The first side of a triangle measures 5 in. less than the second side, the third side is 3 in. more than the first side, and the
perimeter is 17 in. How long is the third side?
If s represents the length of the second side, which of the following represents the length of the third side?
s-5
S-2
s+3
Answer:
see explanation
Step-by-step explanation:
let s be the second side then the first side is s - 5 and the third side is
s - 5 + 3 = s - 2
-------------------------
the perimeter (P) is the sum of the 3 sides of the triangle.
given P = 17 , then
s - 5 + s + s - 2 = 17
3s - 7 = 17 ( add 7 to both sides )
3s = 24 ( divide both sides by 3 )
s = 8
third side = s - 2 = 8 - 2 = 6 in
What is the answer to this problem ?
Answer: The correct answer is 14.
Step-by-step explanation: We have X and Y together, multiply that and get 10. Then we add Z which is 4 and it gets you 14.
Make a conjecture about the diagram below. Do you think you can conclude that △JKL ≅ △XYZ? Explain your reasoning.
Triangles J K L and X Y Z are shown. Angles J K L and X Y Z are right angles. The lengths of J K and X Y are congruent and the lengths of J L and Z X are congruent.
Answer:
Since these are right triangles, the unmarked sides can be determined to be congruent because of the Pythagorean theorem. Once the third set of congruent sides is determined, the SSS or SAS theorem can be used to prove triangle congruency.
Step-by-step explanation:
sorry I know this is late but i just took the assignment and this was the answer
Answer:
they are right triangles so they are congruent
Step-by-step explanation:
got it right on edge
-36 divided by -3 = ___ ( i feel like its somewhere near 12 or 6 but im not sure )
Answer:
12
Step-by-step explanation:
which ratio is equivalent to 12:20?
a) 3:5
b) 20:12
c) 3:10
d) 2:3
Answer:
D
Step-by-step explanation:
Answer:
it is a 3:5
Step-by-step explanation:
use the accompanying statcrunch session to obtain a simple random sample of 5 high schools in the city of chicago. loading... click on the icon to view the statcrunch session.
Using sampling concepts, one sample of 5 high schools in the city of Chicago is given by:
Brooks, Hyde Park, Young Womens, Marshall, Noble - UIC.
What is the missing information?The problem is incomplete, but researching it on a search engine, it gives us a list of 15 high schools in Chicago, and asks us to take a sample of 5.
What is population and sample?Population: Collection or set of individuals or objects or events whose properties will be studied.Sample: The sample is a subset of the population, and a well chosen sample, that is, a representative sample will contain most of the information about the population parameter. A representative sample means that all groups of the population are inserted into the sample.Hence, from the concepts of sample and populations, the sample of 5 means that we have to select 5 schools from the 15 listed, hence one possible option is given by:
Brooks, Hyde Park, Young Womens, Marshall, Noble - UIC.
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Given f(x)=1, solve for x.
Answer:
I hope u get an answer
Step-by-step explanation:
thx
As an estimation we are told 5 miles is 8 km.
Convert 35 miles to km.
if you answer you get the brainlist idk the name
Which linear function has the same y-intercept as the one that is represented by the graph?
A painter needs to paint the bottom of a circular pool. The pool has a diameter of 60 find the area of the bottom of the pool
Answer:
188.5
Step-by-step explanation:
in order to find the circumference you need to know the radius which is half of the diameter. the picture shows the formula used.
4) The speed of light is 3 x 10^8 meters per second. The distance to the
sun is 1.5 x 10^11 meters. How long does it take light to reach the Earth
from the Sun. 0.5 seconds
5 seconds
50 seconds
500 seconds
Answer:
500 seconds
Step-by-step explanation:
This is a distance = rate × time problem
d = 1.5 × 10^11 m
rate = 3 × 10^8 m/s
So, d = rate × t
t = d ÷ rate = 1.5 × 10^11 m ÷ 3 × 10^8 m/s = 500 s
Hey! Can you plz help me? I promise to give brainliest
Answer: answer D
Step-by-step explanation:
i am pretty sure it is D. not 100%, but like 90%. they are both on the outside of the lines, so that is why i know they are exterior. and, they are on opposite sides, so that makes them alternate.
.. pls help me....!!!!! Determine whether the point (-2,4) satisfy y<3x+5,y=3x+5 or y >3x+5..
Given:
The point is (-2,4).
To find:
Whether the point (-2,4) satisfy [tex]y<3x+5,y=3x+5[/tex] or [tex]y >3x+5[/tex].
Solution:
We have a point (-2,4).
Substituting x=-2 in 3x+5 and check whether it is greater, equal or less than y value, i.e., 4.
[tex]3x+5=3(-2)+5[/tex]
[tex]=-6+5[/tex]
[tex]=-1[/tex]
-1 is less than 4.
[tex]3x+5<4[/tex]
[tex]3x+5<y[/tex]
In can be written as
[tex]y>3x+5[/tex]
Therefore, the given point (-2,4) satisfy [tex]y >3x+5[/tex].
What is the sign of the product (–7)(–2)(–5)(1)?
Answer:
Negative
Step-by-step explanation:
When an even number of negatives are multiplied together, the product will be positive (because two negatives cancel out). When an odd number of negatives are multiplied together, the product will be negative.
In the given expression, there is also a singular (1) at the end, which we can ignore since anything multiplied by 1 is itself. The other numbers are all negative and there are 3 of them, and since 3 is an odd number, the product will be negative.
I hope this helps!
Answer:
The third choice
Step-by-step explanation:
Negative, because the product (–7)(–2) is positive, and the product (–5)(1) is negative and the product of a positive and a negative number is negative,
pls mark as brainliest hope you have a nice day!