The solution and extraneous solution of the equation as given are; x=7 and x=-2 respectively.
What is the solution of the equation?It follows that the equation given is;
(3/(x²+5x+6)) + ((x-1)/(x+2)) = 7/(x+3)
Hence, by multiplying both sides by (x²+5x+6); we have;
3 + x² +2x -3 = 7x + 14.
x²-5x -14 = 0
On this note, the solutions of the quadratic equation are; x =7 and x=-2.
It therefore follows that x= 7 is a solution while x=-2 is an extraneous solution because it renders (x-1)/(x+2) undefined.
Read more on extraneous solution;
https://brainly.com/question/26218294
#SPJ1
Answer:
x=7
x=-2
Step-by-step explanation:
Please help me with this
Answer:
altitude: 16 cmbase: 12 cmStep-by-step explanation:
The given relation can be used with the formula for the area of a triangle to give an equation for the altitude or base.
SetupLet b represent the length of the base. Then the altitude (height) is (b+4). The area formula tells us the area is ...
A = 1/2bh
Using given values, the equation becomes ...
96 = 1/2b(b +4)
SolutionSimplifying the equation and multiplying by 2, we have ...
192 = b² +4b
Adding (4/2)² = 4 will complete the square.
196 = b² +4b +4 = (b +2)²
Taking the square root gives ...
14 = b +2 . . . . . . we are not interested in the negative root
12 = b . . . . . . . . subtract 2
16 = b+4 . . . . . find the altitude
The base is 12 cm; the altitude is 16 cm.
Thanks!
1) You know that for any , neither sin nor cos can be greater than 1. How can you explain this using the unit circle definitions of sine and cosine? How can you explain it using the right triangle definitions of sine and cosine?
As a follow-up question, consider why it is important to have both the right triangle definitions of sine and cosine and the unit circle definitions of sine and cosine.
2) Can you give examples of situations that might be modeled with trigonometric functions? That is, can you give examples of phenomena that take on a series of values over and over again?
The trigonometric function gives the ratio of different sides of a right-angle triangle. The value of sine and cosine will be always less than a unit.
How to explain the trigonometry?In a unit circle, the radius of the circle represents the hypotenuse of the triangle. Since the hypotenuse is the largest side of the triangle, the ratio of the perpendicular to the hypotenuse and the base to the hypotenuse both will be less than the hypotenuse, therefore, 1. Hence, the value of sine and cosine will be always less than a unit.
In construction, we use trigonometry. For figuring areas of triangular shapes, similar to many concepts and phenomena in mathematics.
Learn more about trigonometry on:
https://brainly.com/question/24349828
#SPJ1
Giving away brainly for help ASAP
Answer:
[tex]g(f(x))=25x^2-15x-7[/tex]
domain: (-∞,∞)
Step-by-step explanation:
g of f means plug the function f(x) in to x in the function g(x)
[tex]g(f(x))=5(5x^2-3x-2)+3\\g(f(x))=25x^2-15x-10+3\\g(f(x))=25x^2-15x-7[/tex]
since this is a parabola with no interval, the domain (the graph on the x-axis from left to right) is all real numbers or (-∞,∞)
Question 5(Multiple Choice Worth 1 points)
(02.01 LC)
Which of the following tables represents a function?
its the first one
a system can only be a function if there is only one value of y for each value of x. there cannot be two or more values of y for one single value of x in a function.
4+4-3-4-2-5-1-8-9-0=a+c=a
Simplification of the expression gives 2a + c = -24
How to simplify the equation
4+4-3-4-2-5-1-8-9-0=a +c + a
First, let's add
[tex]8 -3 -4-2-5-1-8-9-0 = a+ c + a[/tex]
Then, let's substract
[tex]-24 = a + c + a[/tex]
[tex]-24 = 2a + c[/tex]
We then have,
[tex]2a + c = -24[/tex]
Thus, simplification of the expression gives 2a + c = -24
Learn more about algebraic expressions here:
https://brainly.com/question/723406
#SPJ1
The lengths of two sides of a triangle are shown below:
Side 1: 3x² - 2x - 1
Side 2: 9x + 2x² - 3
The perimeter of the triangle is 5x³+4x2 - x - 3.
Part A: What is the total length of the two sides, 1 and 2, of the triangle? (4 points)
Part B: What is the length of the third side of the triangle? (4 points)
Part C: Do the answers for Part A and Part B show that the polynomials are closed under
addition and subtraction? Justify your answer. (2 points)
(10 points)
Part A
[tex]3x^2 -2x-1+9x+2x^2 -3=\boxed{5x^2 + 7x-4}[/tex]
Part B
[tex](5x^3 +4x^2 - x-3)-(5x^2 + 7x-4)=\boxed{5x^3 - x^2 - 8x+1}[/tex]
Part C
No, because although they provide examples for specific polynomials being closed under addition and subtraction, there is a loss of generality.
What is the 32nd term of an arithmetic sequence with a first term of 7 and a common difference of 4?
Select one:
a. 119
b. 123
c. 127
d. 131
Answer:
a₃₂ = 131
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 7 and d = 4 , then
a₃₂ = 7 + (31 × 4) = 7 + 124 = 131
The number of visitors to the homepage of an online magazine can be modeled by the equation y = 1100.74x − 1976.47, where x = 5 represents the year 2005 and y represent the total number of visitors.
FIRST ONE GETS BRAINLIEST OR 5 STARS
The number of visitors to the homepage of an online magazine in the year 2005 is 3527
What is an equation?An equation is an expression that shows the relationship between two or more number and variables.
Let y represent the total number of visitors x years since 2000. Hence:
y = 1100.74x - 1976.47
In the year 2005 (x = 5):
y = 1100.74(5) - 1976.47 = 3527.23
The number of visitors to the homepage of an online magazine in the year 2005 is 3527
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
This market is a duopoly and the demand schedule as well as the total revenue is provided below. The number of customers you see and the total revenue is for the total market, not for an individual firm.
Answer:
??
Step-by-step explanation:
The counting numbers beginning with 101 and ending with 200 are listed. How many of the numbers have a 6 as a digit
Counting numbers from 101 to 200, those with 6 as a digit are 19
The numbers
Let's start by listing all the number between 101 and 200
101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200
Now, let's count the numbers with 6 as a digit
= 19 numbers has 6 as a digit
Thus, counting numbers from 101 to 200, those with 6 as a digit are 19
Learn more about counting numbers here:
https://brainly.com/question/1736789
#SPJ1
Given: quadrilateral MNOL with MN ≅ LO and ML ≅ NO
Prove: MNOL is a parallelogram.
Quadrilateral L M N O is shown. Sides M N and L O are congruent. Sides L M and O N are congruent.
Complete the paragraph proof.
We are given that MN ≅ LO and ML ≅ NO. We can draw in MO because between any two points is a line. By the reflexive property, MO ≅ MO. By SSS, △MLO ≅ △
. By CPCTC, ∠LMO ≅ ∠ and ∠NMO ≅ ∠LOM. Both pairs of angles are also , based on the definition. Based on the converse of the alternate interior angles theorem, MN ∥ LO and LM ∥ NO. Based on the definition of a parallelogram, MNOL is a parallelogram.
The answers to the quadrilateral are ONM, NOM, and alternate interior angles.
How to explain the quadrilateral?Based on the SSS postulate, the two triangles △MLO and △ONM are congruent since three sides of △MLO are respectively equal to the three sides of △ONM.
Based on CPCTC, all of the corresponding angles of △MLO and △ONM are congruent as well since the two triangles are congruent, that is,
∠LMO≅∠NOM and ∠NMO≅∠LOM.
Since the pair ∠LMO and ∠NOM as well as ∠NMO and ∠LOM are angles on the inner side of two lines but on opposite sides of the transversal MO, these pairs of angles are also alternate interior angles.
Learn more about quadrilateral on:
https://brainly.com/question/23935806
#SPJ1
Answer: ONM
NOM
alternate interior angles
Step-by-step explanation: Complete the paragraph proof.
We are given that MN ≅ LO and ML ≅ NO. We can draw in MO because between any two points is a line. By the reflexive property, MO ≅ MO. By SSS, △MLO ≅ △
✔ ONM
. By CPCTC, ∠LMO ≅ ∠
✔ NOM
and ∠NMO ≅ ∠LOM. Both pairs of angles are also
✔ alternate interior angles
, based on the definition. Based on the converse of the alternate interior angles theorem, MN ∥ LO and LM ∥ NO. Based on the definition of a parallelogram, MNOL is a parallelogram.
The product of the square of a number x and 2 subtracted from 3 is y.
The algebraic expression for the given statement is: 2x² - 3 = y.
How to Write an Algebraic Expression?To wrote an algebraic expression is translate a statement using numbers, variables, and mathematical sign into a mathematical statement.
Square of x is: x²
Product of x² and 2 is: 2x²
Thus, we would have:
2x² - 3 = y
The algebraic expression is: 2x² - 3 = y.
Learn more about algebraic expression on:
https://brainly.com/question/2164351
#SPJ1
Simplify the expression.
Answer:
D
please mark brainiest
pls answer fast , pls
Answer:
x is 14
1st is 14
2nd is 20
Step-by-step explanation:
4/7 (x ) = (34 - x )(2/5)
4x/7 + 2x/5 = 34 x 2/5 = 68/5
34x/35 = 68/5
x = 14
https://brainly.in/question/1110296
Determine the volume of a cube with a side length of 5 1/3 in.
Answer:
151 19/27 in^3
Step-by-step explanation:
volume of cube is (side length)^3
(5 1/3)^3 = (16/3)^3 = 4096/27 = 151 19/27
Write the log equation as an exponential equation. You do not need to solve for x.
Answer:
x² - 5x + 17 = [tex](2x)^{3x}[/tex]
Step-by-step explanation:
using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]
given
[tex]log_{2x}[/tex] (x² - 5x + 17) = 3x , then
x² - 5x + 17 = [tex](2x)^{3x}[/tex]
Triangle ABC was dilated using the rule Do,4. Triangle
A'B'C' is the result of the dilation.
3
A
B
C
A'
В'
C
What is OB'?
O 1.5 units
3 units
O4.5 units
O6 units
The value of OB based on the information given about the triangle is 3 units.
How to illustrate the information?It should be noted that dilation is the process of enlarging or shrinking of an object.
In this case, the triangle is dilated. Therefore, the length of OB will be:
= 3/4 × 4 = 3 units.
Therefore, the correct option is B.
Learn more about triangle on:
brainly.com/question/16771919
#SPJ1
What percentage of its total accounts receivable does grainger feel are uncollectible at december 31, 2016?
Using percentage of its total accounts the $50,000 is the amount to be uncollectible. The amount of $50,000 will be reported as an allowance for uncollectible accounts for the Year 2 on December 31 in the balance sheet.
According to the question,
Under the approach of the balance sheet, the ending balance of the allowance for the uncollectible accounts is the percentage (%) of the ending balance of the accounts receivable.
The amount of uncollectible accounts should reflect the aggregate needed ending balance of the allowance which amounts to $50,000.
Hence, using percentage of its total accounts the $50,000 is the amount to be uncollectible.
Learn more percentage here
https://brainly.com/question/24113041
#SPJ4
y=x The point F is the foot of the perpendicular from the point (1, 9) to the line y=x. Find the coordinates of F.
Answer: (5,5)
Step-by-step explanation:
The perpendicular to y=x has slope -1, and thus the equation of the perpendicular from (1,9) is [tex]y=-x+10[/tex].
Finding the point where they intersect, since both equations are set equal to y, we know that -x+10=x, and thus x=5.
If x=5, then y=5 as well.
So, F has coordinates (5,5).
A long oval is shown. Two lines are drawn where the sides are straight to form right angles.
How can you decompose the composite figure to determine its area?
as two semicircles and a rectangle
as two circles and a rectangle
as a circle and a square
as two semicircles and a trapezoid
The figure which is like a long oval can be decomposed to two semicircles and a rectangle so as to find the area.
Given a long oval and two lines are drawn where the sides are straight to form right angles.
We are required to find the way how we can decompose the composite figure to determine its area.
Area means the amount of space occupied by a two dimensional shape or object. The area of a figure can be decomposed to smaller figures so as to find the area.
The composed figure can be decomposed to two semicircles and a rectangle so as to find the area.
Hence the composite figure can be decomposed to two semicircles and a rectangle so as to find the area.
Learn more about area at https://brainly.com/question/25965491
#SPJ1
Answer:
a
Step-by-step explanation:
how meny grams are in 6 ounces?
Answer:
170.097 grams are in 6 ounces
Answer:
170.097 g to nearest thousandth
Step-by-step explanation:
1 ounce = 28.34952 g
6 = 170.09712 g
2. Mary receives $2.00 weekly as an allowance. If
she saves $0.70 of it, what percent does she
save?
Answer:
35%
Step-by-step explanation:
She is saving $0.70/$2.00 weekly.
To convert this into a percentage we covert it to decimal then multiply by 100 :
$0.70/$2.00 = 0.35
0.35 × 100 = 35%
Our final answer is 35%.
Hope this helped and have a good day
Which term describes the red curve in the figure below?
• A. Parabola
O B. Circle
• C. Hyperbola
O D. Ellipse
Answer:
the red curve is a hyperbola
if the area of a rectangle is represented by 25x^3y^6 and its width is represented by 10xy, express the length of the rectangle in terms of x and y
The length of the rectangle in terms of x and y, given that its area is represented by 25x³y⁶ and its width is represented by 10xy is 2.5x²y⁵.
The area of a figure is the total space enclosed in two dimensions within its boundary.
The area of a rectangle is given as, area = length*width.
In the question, we are given that the area of a rectangle is represented by 25x³y⁶ and its width is represented by 10xy, and are asked to express the length of this rectangle in terms of x and y.
We know that the area of a rectangle is given as, area = length*width.
Substituting the known values in the equation, we get:
25x³y⁶ = length*10xy.
Rearranging this equation, we get:
length = 25x³y⁶/10xy = (5x²y⁵)/2 = 2.5x²y⁵.
Thus, the length of the rectangle in terms of x and y, given that its area is represented by 25x³y⁶ and its width is represented by 10xy is 2.5x²y⁵.
Learn more about the area of a rectangle at
https://brainly.com/question/11435713
#SPJ4
I dentist the slope and a point on the line
Answer:
2/3 (0,-3) is one possible answer.
Step-by-step explanation:
y -1 = 2/3(x-6) We want to get this into the slope intercept form of a line. We want it to be in the form y = mx + b. Let's clear the fraction first by multiplying the whole equation through by 3.
3(y - 1) = 3[2/3(x - 6)]
3y -3 = 2(x -6)
3y - 3 = 2x -12
3y = 2x - 9 Now divide all the way through by 3 to get
y = 2/3x - 3
y = mx + b. The m part is the slope. In this equation the slope is 2/3
There are in infinite amount of points on a line. I do not know if they give you a picture or if you are just to create your own. I am going to create a point that have x = 0. I get to pick the point. I could pick any number. 0 is just usually really easy. So, if I substitute 0 for x I will get:
y = 2/3(0) - 3
y = 1 so my point is (0,-3)
Now that I think about it, I do not think that I would start out clearing the fraction even though it works. I think that I would do it like this"
y - 1 = 2/3(x - 6) Distribute the 2/3 through (x - 4) to get
y-1 = 2/3x -4 I can make -6 a fraction by putting it over 1. Now we have 2/3(-6/1) multiply across to get -12/3. A positive times a negative is a negative. -12 divided by 3 is -4.
y - 1 = 2/3x -4 now add 1 to both sides.
y = 2/3x -3
A magazine provided results from a poll of 1000 adults who were asked to identify their favorite pie. Among the 1000 ​respondents, 14​% chose chocolate​ pie, and the margin of error was given as +3 percentage points. What values do ​, ​, ​n, E, and p​ represent? If the confidence level is ​%, what is the value of ​?
The completion of the tabs are:
The value of [tex]\bar p[/tex] is the sample proportion.The value of [tex]\bar q[/tex] is found by evaluating [tex]1-\=p[/tex]The value of n is the sample size.The value of E is the margin of error.The value of p is the population proportion. α = 0.05.What is the margin of error.?You may calculate how many percentage points your findings will deviate from the actual population figure by using something called a margin of error.
In conclusion
The worth of p^ is the fraction of the sample.The worth of p^ is discovered by assessingThe sample size is given by the number n.The margin of error is expressed as E's value.The population percentage is represented by the value of p. α = 0.05.In conclusion,
Read more about the margin of error.
https://brainly.com/question/10501147
#SPJ1
Slope-intercept form?
Answer:
y=3x+4
Step-by-step explanation:
The original formula for slope-intercept is y=mx+b.
b is your y-intercept (where the line crosses the y-axis).
m is your slope which is 3/1 or just 3.
How many different 2-digit numbers are there with the following property: it is evan and its digits are distinct?
By counting all the even 2-digit numbers between 10 and 100, there are 41 even and distinct digits.
What is an even number?An even number can be defined as a type of number which is divisible by two (2) without any remainder.
How to determine this 2-digit number?Since this 2-digit numbers are even and its digits are distinct, we can infer and logically deduce the following points:
They are between 10 and 100.They are not repeated.They must contain two digits only.By counting all the even 2-digit numbers between 10 and 100, there are 41 even and distinct digits.
Read more on even number here: https://brainly.com/question/1800323
#SPJ1
Anyone know?? I’d appreciate it.
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: (1.6 \times 10 {}^{5} ) \sdot(2 .3 \times {10}^{1} )[/tex]
[tex]\qquad \sf \dashrightarrow \: (1.6 \times 2.3) \sdot(10 {}^{5} \times 10 {}^{1} )[/tex]
[tex]\qquad \sf \dashrightarrow \: 3.68 \times 10 {}^{6} [/tex]
pls help tysm!!!!!!!!!
Answer:
Second choice
Step-by-step explanation:
Analyse each sentences: The sum of x and y is 5 can be mathematically expressed as [tex]\displaystyle{x+y = 5}[/tex] since both are sum together and equal to 5.
Next, the value of y is one more than value of x can be mathematically expressed as [tex]\displaystyle{y=x+1}[/tex] because value of y is one more than value of x so y will be the value of x add with 1.
Therefore, form the simultaneous equation:
[tex]\displaystyle{\left \{ {{x+y=5} \atop {y=x+1}} \right}[/tex]
Hence, the answer is second choice.