Answer:
Step-by-step explanation:
(a + b)² = 37
a^2 + 2ab + b^2 = 37
---
ab = 5
a = (5/b)
----
a^2 + 2ab + b^2 = 37
(5/b)^2 + 2(5/b)b + b^2 = 37
(25/b^2) + 10 + b^2 = 37
(25/b^2) + b^2 = 27
25 + b^4 = 27b^2
b^4 - 27b^2 + 25 = 0
I don't know how to factor this expression. The roots seem complex.
A cube has a surface area of 600 cm2 what is the area of one face of the cube
Answer:
The surface area of one face of the cube is 100 square centimeters.
Step-by-step explanation:
From the given diagram, we can conclude that a cube has 6 faces. To get the surface area of one face, we take the total surface area and divide it by 6, as following:
[tex]\frac{600}{6}\rightarrow100[/tex]This way, we can conclude that the surface area of one face of the cube is 100 square centimeters.
Which pair of terms is a pair of like terms?
O a²b and ab²
O a³ and 6³
O 3b³ and 5b³
8a and 8b
The pair of terms which is a pair of like terms is 3b³ and 5b³
What are Similar Terms?Similar phrases are used to define similar variables and powers. The coefficients do not necessarily have to concur. It is claimed that two or more terms are unlike when they do not have the same variables or powers. The order of the variables doesn't matter unless there is a power.
Which two terms are similar must be determined.
Exponents and variables for similar words must match.
The same variables are shared by both words in the first option, but they have different exponents. Therefore, a2b and ab2 are unrelated words.
The second choice has both a3 and 63, one of which has a variable. They are distinct from terms.
The fourth option has two unique variables, 8a and 8b. Thus, they are different.
In the third alternative, the words 3b³ and 5b³ share the same variable b and exponent 2.
Thus, 3b³ and 5b³ are Like terms.
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the fox population in a certain region has a continuous growth rate of 6 percent per year. it is estimated that the population in the year 2000 was 21700.
Answer:
In 2022 the population will be 78196
Step-by-step explanation:
Nf - number of foxes = ?
No - number of foxes in 2000 = 21700
p - growth rate = 6%
n - numebr of years = 22
[tex]N_{f}=N_{o} * (1+\frac{p}{100})^{n}[/tex]
[tex]N_{f}=21700 * (1+\frac{6}{100})^{22}[/tex]
[tex]N_{f} = 78196 foxes[/tex]
2/3 + 9/10 adding fractions
My teacher is making us show work :(
Answer: 47/30
Step-by-step explanation:
1) Find the common denominator
2/3 + 9/10
10/10 * 2/3 + 9/10 * 3/3
2) Add the numerator
20/30 + 27/30
47/30
write a percent that is between 3/4 and 7/9
Answer:
76%
Explanation:
We want to write a percentage that is between 3/4 and 7/9.
First, begin by converting each of the fractions to its decimal equivalent.
[tex]\begin{gathered} \frac{3}{4}=0.75 \\ \frac{7}{9}\approx0.78 \end{gathered}[/tex]Thus, we can say that:
[tex]\begin{gathered} 0.75<0.76<0.78 \\ 0.76=0.76\times100=76\% \end{gathered}[/tex]A percentage that is in between 3/4 and 7/9 is 76%.
Juan Fuentes is a computer programmer. His annual salary is
$32,190.00. Benefits he receives consist of $1,881.73 in vacation time,
holidays worth $1,287.60, health insurance premiums of
$2,300.00 paid by the employer, Social Security of $1,995.78,
Medicare of $466.76, and unemployment insurance of $541.06.
a. What are the total benefits?
b. What is the rate of benefits?
In linear equation,$7185.33 is the total benefits.
What are a definition and an example of a linear equation?
An equation with only one variable is referred to as a linear equation in one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. One such linear equation in one variable is 9x + 78 = 18.the total benefits of Juan Fuentes = $1,881.73 + $2,300.00 + $1,995.78 +
$466.76 + $541.06
= $7185.33
the rate of benefits of Juan Fuentes = $1,287.60
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Question 8
Given the equations y=-4x-4 and y=4(x+1), is (-1,0) a solution of the system of
equations?
True
False
Question 9
The solution to the system of linear equation
1 pts
1 pts
Yes is (-1,0) a solution of the system of equations.
A linear equation is defined.A linear equation is one that has a maximum degree of 1. No variable in a linear equation has an exponent greater than 1, thus. A linear equation's graph is always a straight line.
Since each term in a linear equation has an exponent of 1, graphing an algebraic equation always yields a straight line. It is called a "linear equation" because of this.
Given
y=-4x-4...(i)
y=4(x+1)
=> y =4x + 4....(ii)
Adding (i) and (ii) we get
y= 0
Now putting y = 0 in Equation (i)
we get x = -1
Therefore (-1,0) is the solution of the two given equations.
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"Complete the table" can i get some help with this pls and thank you
f(x)=√x+11. Find the inverse of f(x).
O A. f¹(x) = x³ – 11
O B. f¹(x) = (x - 11)³
O c. f¹(x) = x³ + 11
O D. f¹(x) = (x +11)³
Answer: Your answer would be C: f¹(x) = x³ + 11
A tissue factory produces 3,876 tissues a day. How many tissues does it produce after 7 days?
Answer:
27,132 tissues
Step-by-step explanation:
if it produces 3,876 tissues a day, and a week has 7 days, then the answer would be 3,876 x 7=27,132 tissues
Answer:
27132 tissues
Step-by-step explanation:
everyday 3876 tussues are made
so the equation would be 3876×7 to get how many tissues are made in 7 days
The sum of three numbers is fifty-eight. The
second number is four more than the first
number and the third number is eight more
than the second number. What are the
numbers?
The ages of five students in a class are 11, 11.5, 12, 14, 12.5 The mean age (in years) is
(a)10.2 (b) 11.2 (c) 12.2 (d) 13.2
Answer: c)12.2
Step-by-step explanation:
let me show you how to answer this question
1. add all the numbers 11+11.5+12+14+12.5=61
2. then divide 61 by how many numbers we had to add in this case is 5 (the equal number doesn't count.) 61÷5=12.2
Answer:
Mean= Sum of all values ÷ Number of values
so...
the answer is 14.6
hope you are all clear with mean now just use the formula everytime when calculating MEAN
f(x)=5x+10 solve when f(x)=20
When f(x) = 20
Then
5x + 10 = 20
Therefore
5x=20-10=10
x = 10 / 5 = 2
x= 2
(5 points) use coordinate vectors to test the linear independence of the sets of polynomials. do they form a basis for the space of polynomials of third degree? why or why not? explain your work.
The linear independence of vector sets forms the basis of the space of polynomials of third degree.
In vector space theory, a collection of matrices is said to be heavily dependent if there is a nontrivial concatenation of the vectors that equal the zero vector. If no such linear combination exists, the vectors are said to be linearly independent. These concepts are crucial to the concept of dimension.
The maximum number of nonzero vectors determines whether the dimensions of a vector space are finite or infinite. The capacity to recognize whether a subset of columns in a vector space is dependent, as well as the concept of linear dependence, are crucial for determining a vector space's dimensionality.
If the same vector appears twice in a vector sequence, it must be dependent. The linear dependency of a vector series is independent of the order of the terms. A restricted collection of vectors can have linear independence if the sequence obtained by sorting a finite number of lines is linearly independent. In other words, the following outcome is frequently useful.
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when we divide the number of seconds in december by the number of seconds in november, we get a remainder of $r$. if we then divide $r$ by $11$, what remainder do we get?
The remainder when r is divided by 11 is 6.
Remainder is the amount left after dividing a number by another. After dividing a number with another, it will result to an integer and a remainder, which is less than the divisor.
Divide the number of seconds in December by the number of seconds in November and get the remainder, r.
number of seconds in December ÷ number of seconds in November
31days(24h/day)(60min/h)(60s/min) ÷ 30days(24h/day)(60min/h)(60s/min)
= 2678400 s ÷ 2592000 s
= 1 r. 86400
r = 86400
Divide r by 11 and get the remainder.
86400 ÷ 11 = 7854 r. 6
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In the figure below, m < 1 = (x + 14) and m < 2 = 3x
Find the angle measures.
The angle measures are;
m < 1 = 33°
m < 2 = 57°
How to determine the anglesIt is important to note that complementary angles are defined as pairs of angles that sum up to 90 degrees.
From the information given, we have the angle measures as;
m < 1 = (x + 14) m < 2 = 3xThis can be represented as;
m < 1 + m < 2 = 90
Now, let's substitute the values into the equation, we have;
(x + 14) + 3x = 90
expand the bracket, we have;
x + 14 + 3x = 90
collect like terms
4x = 90 - 14
subtract the values
4x = 76
Make 'x' the subject of formula, we get;
x = 76/4
x = 19
Then,
m < 1 = (x + 14) = 19 + 14 = 33°
m < 2 = 3x = 3(19) = 57°
Hence, the values are 33° and 57° respectively.
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The complete question is;
In the figure below, m < 1 = (x + 14) and m < 2 = 3x, are both complementary to each other
Find the angle measures.
Estimate the difference by rounding each number
to the nearest hundredth: 0.076 -0.011
A 0.08
B 0.06
C 0.05
D 0.07
Answer:
answer is D= 0.07
Step-by-step explanation:
The equation:
0.076 - 0.011
By rounding to the nearest hundredth
0.076 = 0.08
0.011 = 0.01
=0.08-0.01
=0.07
the length of a small garden is 12.64 feet. the width of the garden is 14 feet. samuel wants to fence the garden in on all sides. he has 50 feet of fencing. calculate the perimeter of the garden to determine if samuel has enough fencing.
Answer:
He does not have enough for fencing the garden
Step-by-step explanation:
The garden is in the shape of a rectangle
The perimeter of a rectangle of length L and width W is given by
P = 2 (L + W)
Since we are given L = 12.64 ft and W = 14 ft, the perimeter of the garden is
2 ( 12.64 + 14) = 2 (26.64) = 53.28 feet
Since Samuel only has 50 feet of fencing, there is not enough to fence. He is short by 3.28 feet
Solve the system of equations
Answer x=-1 and y = 7
Explanation:
1. Is the UPC code 0-32281-69425-1 valid? Show how you know this.
Yes the UPC code 0-32281-69425-1 valid. Because a string of unique black bars, and the unique 12-digit number beneath it.
What is UPC code?UPC codes are unique to each version of a product. If you previously distributed a release with another distributor but are now transferring it to Symphonic, we encourage you to re-use the UPC code as long as the release is the exact same version. UPC Product Registries and the Global UPC Database There is currently no single globally recognized UPC database. Unfortunately, there are numerous online websites that falsely claim to be authorized databases and provide invalid data. A UPC, or universal product code, is a type of code that is printed on retail product packaging to help identify a specific item.To learn more about UPC code, refer to:
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Find the values of a and b that the solution to 2(3x+5)+ax=5(4x-b) is real numbers
The value of "a" and "b" is 14 and -2,respectively.
We are given an equation. The equation is a linear equation with one variable.A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions."x" is the variable in the equation."a" and "b" are constants.The equation is :2(3x+5)+ax=5(4x-b)Simplify the above equation.6x + 10 + ax = 20x - 5bCombine the like terms.(6 + a)x + 10 = 20x - 5bCompare the coefficients of x and the constants with each other.6 + a = 20a = 1410 = -5bb = -2The values of the constants "a" and "b" are 14 and -2.To learn more about equations, visit :
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Give the domain and range of each relation below. (help please)
Answer:
Domain is (-infinity, infinity), range is (-infinity, 0]
Step-by-step explanation:
The x values are infinite on both sides, but the y values are not. Let me know if you want me to explain more :)
Naomi is driving on a long road trip. She currently has 10 gallons of gas in her car. Each hour that she drives, her car uses up 0.75 gallons of gas. How much gas would be in the tank after driving for 4 hours? How much gas would be left after tt hours?
After 4 hours of driving, there will be 3 gallons of gas left in the tank. After t hours,10 - 0.75t of gas will still be present.
Describe algebra.Algebra is the study of mathematical symbols, and logic is the manipulation of those symbols.
Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction are all part of the PEMDAS formula. To solve the equation properly and accurately, this rule is applied.
Naomi is traveling by car a long distance. She has 10 gallons of gas in her automobile right now. Her car consumes 0.75 of gas per hour that she is on the road.
After four hours of driving, the amount of gas in the tank will be
⇒ 0.75 x 4
= 3 gallons
After t hours, the amount of gas remaining will be
⇒ 10 - 0.75t
After 4 hours of driving, there will be 3 gallons of gas left in the tank. After t hours, there will be 10 - 0.75t of gas left.
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Let the graph of g be a translation 2 units left and 1 unit down, followed by a reflection in the y -axis of the graph of f(x)=(2x+1)^2-4 . Write a rule for g .
The rule for the function g(x) is (2x + 5)² - 5.
We are given a function f(x). The function f(x) is defined as given below :
f(x) = (2x + 1)² - 4
A function connects an input with an output. It is analogous to a machine with an input and an output. And the outcome is somehow connected to the input.
We first need to do a translation with 2 units left.
The translation is given by f(x + 2).
f(x + 2) = (2x + 5)² - 4
We now need to do a translation with 1 unit downwards.
The translation is given by f(x + 2) - 1.
f(x + 2) - 1 = (2x + 5)² - 4 - 1
f(x + 2) - 1 = (2x + 5)² - 5
The definition of the function is given below :
g(x) = (2x + 5)² - 5
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Are the triangles similar? If so write the similarity statement and state which postulate allows them to be similar and why.
The Triangles are not similar as they do not predict any similar triangle properties that is SSS, SAS , AA properties.
What are the triangle similarity criteria?Two triangles are similar if they meet one of the following criteria.
AA: Two pairs of corresponding angles are equal.
Example: Let Two triangles with Two angles of the first triangle are congruent to two angles of the second triangle.
SSS: Three pairs of corresponding sides are proportional.
Example: Let Two triangles with The first triangle has sides of length a, b, and c. The second triangle has corresponding sides of length k times a, k times b, and k times c.
SAS: Two pairs of corresponding sides are proportional and the corresponding angles between them are equal.
Example: Let Two triangles with both have one congruent angle. In the first triangle, the congruent angle is between sides of length a and b. In the second triangle, the congruent angle is between corresponding sides of length k times a and k times b.
So, We have given that
Two Triangles namely ABC and DEF
So, For ΔABC,
∠A = 105°, ∠C=34°, ∠B= 180-(105+34)=180-139=41°
Now Similarly for ΔDEF,
∠E = 105°, ∠D=43°, ∠F= 180-(105+43)=180-148=32°.
So, For both triangles
∠A~∠E but no other similar property found between the both Triangle.
So, we can conclude that the ΔABC and ΔDEF are not similar as they don't show any similar triangle properties.
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Devon records 4 hours of reality shows on her dvr. she records comedy shows for 3/8 of that amount of time. devon watches all the reality and comedy shows in half hour sittings.
If Devon records 4 hours of reality shows on her dvr and she records comedy shows for 3/8 of that amount of time, then the number of hours taken to record the comedy show is 1.5 hours
Number of hours the Devon record the reality shows = 4 hours
she records comedy shows for 3/8 of that amount of time
The number of hours taken to record the comedy show = (3/8)×Number of hours the Devon record the reality shows
Substitute the values in the equation
= (3/8)×4
= 12/8
= 1.5 hours
Hence, if Devon records 4 hours of reality shows on her dvr and she records comedy shows for 3/8 of that amount of time, then the number of hours taken to record the comedy show is 1.5 hours
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Please help, thank you
Answer:
Step-by-step explanation:
Because 2x+19 and x + 23 are alternative exterior angles, they have an equal value. Thus:
2x+19 = x + 23
Solve for x:
x + 19 = 23
x = 4
amie and Nashwa share some money in the ratio 10:7. Jamie gets $36 more than Nashwa. How much do they get each?
The amount Jamie got be x = $36,
The amount Nashwa got be y = $25.2
We can get Jamie and Nashwa got $10.8 altogether.
Based on the given conditions,
Amount Jamie got = $36Ratio of Jamie to Nashwa = 10 : 7To find how much Jamie gets more than Nashwa.
First of all, we would have to solve for Jamie share from the money.
x : y = 10 : 7 (Equation-1)
But,
Jamie got amount = $36
We can substitute in x = $36 in equation-1,
Let us assume,
Jamie = x
Nashwa = y
So,
We can write,
x : y = 10 : 7
$36 : y = 10 : 7
[tex]\frac{36}{y} =\frac{10}{7}[/tex]
We can cross-multiplying,
36*7 = 10y
252 = 10y
y = 252/10
We can divide the products,
y = 25.2
Hence,
Nashwa = $25.2
Difference of the Jamie and Nashwa,
Difference = x - y
Difference = $36 - $25.2
Difference = $10.8
We can write,
Jamie gets $36 more than Nashwa.
$25.2 + $10.8 = $36
$36 = $36
Therefore,
The amount Jamie got be x = $36
The amount Nashwa got be y = $25.2
We can get they got $10.8 altogether.
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I need some help with my math please
The perimeter of rectangle is ( 19.2 d - 25 f ) cm
What is perimeter of rectangle?A rectangle's perimeter (P) is the sum of the lengths of its four sides. A rectangle has two equal lengths and two equal widths since its opposite sides are equal. The following is the formula for calculating a rectangle's perimeter: The formula for perimeter is length + length + width + width. P = l + l + w + w.
Given the length of the rectangle = (2.4 d - 7.6f) cm
width of the rectangle = (7.2 d - 4.9 f ) cm
The perimeter of rectangle = 2 ( length + width )
2 ( 2.4 d - 7.6f + 7.2 d - 4.9 f )
2 (9.6 d - 12.5 f )
( 19.2 d - 25 f ) cm
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Find the inverse of f(x) = 12x - 3
ANSWER
[tex]f^{-1}(x)\text{ = }\frac{y}{12}+\frac{1}{4}[/tex]EXPLANATION
We want to find the inverse of the function given:
f(x) = 12x - 3
First, replace f(x) with y:
y = 12x - 3
Now, make x the subject of the function:
y + 3 = 12x
[tex]\begin{gathered} \Rightarrow\text{ x = }\frac{y}{12}\text{ + }\frac{3}{12} \\ x\text{ = }\frac{y}{12}\text{ + }\frac{1}{4} \end{gathered}[/tex]Now, replace x with f-1(x) and y with x:
[tex]f^{-1}(x)\text{ = }\frac{y}{12}+\frac{1}{4}[/tex]That is the inverse function.
