Answer:
You can use the definition of perfect square trinomials to find which of the given trinomials are perfect squares.
The trinomials which are perfect squares are:
Option B:
Option D:
What are perfect squares trinomials?
They are those expressions which are found by squaring binomial expressions.
How to find which of the given trinomials are perfect square trinomials?
Since the given trinomials are with degree 2, thus, if they are perfect square, the binomial which was used to make them must be linear.
Let the binomial term was am + b(a linear expression is always writable in this form where a and b are constants and m is a variable), then we will obtain:
Checking all options:
Option A:
Comparing it with the standard form we obtained, we have:
Option B:
Comparing it with the standard form we obtained, we have:
Thus, this trinomial is perfect squares trinomial.
Option C:
Comparing it with the standard form we obtained, we have:
Option D:
Comparing it with the standard form we obtained, we have:
Thus, this trinomial is perfect squares trinomial.
Thus,
The trinomials which are perfect squares are:
Option B:
Option D:
Step-by-step explanation:
HELP!! I really need help on this bc I’m confused
the pair of points that are at a distance of 4 units are (2, 7) and (2, 3), which is option D.
Which points are separated by a distance of 4 units?For two points defined by the coordinates (a, b) and (c, d), we define the distance between these two points as:
distance = √(( a - c)^2 + (b - d)^2)
So you can just use that simple formula for the four pairs of points given and see which pair gives a distance of exactly 4 units, if we use the last pair wich is (2, 7) and (2, 3) and we replace the values in the correspondent places of the distance equation, we will get:
distance = √( (2 - 2)^2 + (7 - 3)^2) = 4
So we conclude that the pair of points that are at a distance of 4 units are (2, 7) and (2, 3), which is option D.
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A highway agent sampled cars going from one state to a neighboring state. In his report, he indicated that of the 93 cars sampled,
36 cars were driven by women, 56 cars were sport-utility vehicles, 47 cars had two or more passengers, 28 cars were driven by
women in sport-utility vehicles, 27 cars were driven by women and had two or more passengers, 22 cars were sport-utility vehicles
and had two or more passengers, and 16 cars were driven by women in sport-utility vehicles and had two or more passengers.
After his supervisor reads the report, she explains to the agent that he made a mistake. Explain how his supervisor knew that the
agent's report contained an error.
Select the correct choice below and fill in the answer box to complete your choice.
(Type a whole number.)
OA. The agent's last four statements indicate that at least
cars were driven by women. This contradicts the agent's first
statement, which says that only 36 such cars were seen.
OB. The agent's first three statements indicate that at least
or more passengers. This contradicts the agent's seventh
OC. The agent's last four statements indicate that at least cars were sport-utility vehicles. This contradicts the agent's
second statement, which says that only 56 such cars were seen.
cars were driven by women in sport-utility vehicles and had two
statement, which says that only 16 such cars were seen.
Records show that 19 million firearms were sold in the U.S. during 2020. Assume the average
firearm sold for $500 and the Pittman-Robertson Act collected an 11-percent excise tax. How
much money was raised for conservation from the sale of firearms during 2020? Be sure to show your work.
Answer:
$1,045,000,000 = $1.045 billion.
Step-by-step explanation:
Pittman–Robertson Act
The Pittman–Robertson Act (Federal Aid in Wildlife Restoration Act of 1937) requires an 11% excise tax to be paid on the sale of firearms, ammunition, and archery equipment to be used by state governments to fund wildlife restoration.
Given information:
Number of firearms sold during 2020 = 19,000,000Average selling price of a firearm = $500Rate of tax = 11%The money raised for conservation can be calculated by finding 11% of the number of firearms sold multiplied by the average selling price.
[tex]\begin{aligned}\textsf{Money raised}&=11\% \textsf{ of }19,000,000 \times \$500\\\\& = \dfrac{11}{100} \times 19,000,000 \times 500\\\\& = \dfrac{11\times 19,000,000 \times 500}{100} \\\\& = \dfrac{104,500,000,000}{100} \\\\& = 1,045,000,000\end{aligned}[/tex]
Therefore, the total amount of money raised was $1,045,000,000 ($1.045 billion).
Answer:
$1,045,000,000.Step-by-step explanation:
To calculate the amount of money raised for conservation from the sale of firearms during 2020, we'll follow these steps:
Step 1: Calculate the total revenue generated from firearm sales.
Total revenue = Number of firearms sold * Price per firearm
Total revenue = 19,000,000 * $500
Total revenue = $9,500,000,000
Step 2: Calculate the amount of excise tax collected.
Excise tax = Total revenue * Excise tax rate
Excise tax = $9,500,000,000 * 0.11
Excise tax = $1,045,000,000
Therefore, the amount of money raised for conservation from the sale of firearms during 2020, based on the given information, is $1,045,000,000.
what are 3 equivalent ratios for 1 2/3:4/4
Answer: Three Equivalent ratios for 1 2/3:4/4 = 4:1, 4:1, 4:1
Step-by-step explanation:
Define Equivalent ratio:
Equivalent ratios are the ratios that are the same when we compare them. Two or more ratios can be compared with each other to check whether they are equivalent or not. For example, 1:2 and 2:4 are equivalent ratios.
All equivalent fractions get reduced to the same fraction in their simplest form.
Explanation:
All those fractions obtained by multiplying both the numerator and denominator of 12/3 by the same integer are equivalent to 12/3.
12/3 × 2/2 = 24/6 = 4
12/3 × 3/3 = 36/9 = 4
12/3 × 4/4 = 48/12 = 4
4, 4, 4, ... are equivalent to 12/3.
All those fractions obtained by multiplying both the numerator and denominator of 4/4 by the same integer are equivalent to 4/4.
4/4 × 2/2 = 8/8 = 1
4/4 × 3/3 = 12/12 = 1
4/4 × 4/4 = 16/16 = 1
1, 1,1, ... are equivalent to 4/4.
Therefore,
Equivalent ratios for 1 2/3:4/4 = 24/6:8/8, 33/9:12/12, 48/12:16/16
Three Equivalent ratios for 1 2/3:4/4 = 4:1, 4:1, 4:1
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can someone please explain how to find the quotient of 405/27 fraction using long division? :)
The quotient of 405/27 fraction using division is 15.
How to calculate the fraction?It should be noted that the information is simply to divide the numbers.
In this case, the numerator is 405 and the denominator is 27
Therefore, the quotient based on the information illustrated will be:
= 405 / 27
= 15
Therefore, the quotient is 15.
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Given that x and y are integers, explain why the product of x+√y and its conjugate will always be an integer.
(x+√y)(x-√y) = x² - y is always an integer.
Given that x and y are integers.
Then x + √y is an irrational number.
The conjugate of (x + √y) is (x - √y).
We need to find the product (x + √y)(x -√y).
Use the identity, (a +b)(a-b) = a²-b²
So (x + √y)(x -√y) = x² - (√y)²
= x² - y
Given that x is an integer. The square of an integer is always an integer.
Since x² and y are integers, their difference is also an integer.
So we can conclude that x²-y is an integer.
Hence, (x+√y)(x-√y) = x² - y is always an integer.
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$640.76+_____ = $1,375.28
Answer:
734.52
Step-by-step explanation:
Subtract
Is the equation y=x+1 / x²+1 in simplest form? Explain how you can tell.
According to the question, the equation [tex]\frac{x+1}{x^{2} +1}[/tex] is the algebraic equation as well as polynomial equation. Using square root principles, the equation can be re-write.
The factors of the denominator term is not possible and it cannot be simplified. And the simplification is possible with the concept of complex number.
What is polynomial expression?
Polynomial expression are those equation whose highest degree is two. It is also called as quadratic equation. And it is simplified by performing the factors on the given expressions.
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the three perpendicular bisectors of a triangle meet at a point called the _____
Answer:
circumcentre
Step-by-step explanation:
the point of intersection of of the perpendicular bisectors of the triangle's sides is called the circumcentre.
The circumcentre is equally far away from the triangle's 3 vertices.
Which number should go in the shaded overlap factors if 30 -and factors if 20
Answer:
1,2,5,10
Step-by-step explanation:
hope this helps
My friend Yoy decided to buy some vreels and totts. Altogether, he
planned to buy 10 items.
Write an equation in standard form showing the relationship between
vreels (x) and totts (y).
Answer:
x + y = 10
Step-by-step explanation:
small insurance company offers two plans, catastrophic and bronze. The catastrophic plan costs $170 per person per month, and the bronze plan costs $480 per person per month. Each month, the insurance company earns $477,300 from the 1,285 people that have purchased their insurance plans. Which of the following systems of equations represents the relationship between the number of catastrophic plans, c, and the number of bronze plans, b, per month?
The system of equations are:
c + b = 1285
170c + 480b = 477,300
What are the equations?Two equations would be derived from the information provided in the question. The equations are known as simultaneous equations. The equations would have to be solved together in order to determine the required values.
The methods that can be used to solve simultaneous equations are:
Elimination method Substitution method Graph methodThe form of the equations is:
Number of catastrophic plan sold + number of bronze plans sold = total plans sold
Cost of the catastrophic plan x number of the plan sold) + (number of bronze plan sold x cost of the plan) = total cost of the plans
c + b = 1285
170c + 480b = 477,300
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All of the following expressions are equal to N except_
A -(-N)
B -N
C INI
D I-NI
Answer:
B -N
Step-by-step explanation:
A This is -1 x - N. a negative times a negative is always positive. So -1 x -N = 1N= N
C The absolute value of N is N so this is also correct.
D The absolute value of a negative number is always positive so |-N| = N
b. Reasoning Would the function y=6/x have the same domain and range as y=8/x or y=12/x? Explain.
YES , both the function will have same domain and range.
What is domain and range?Domain and Scope The domain of a function is the set of values that we are allowed to enter into our function. This collection includes the x values for a function like f. (x).
The range of values that a function can accept as input is known. When we enter an x value, the function returns this list of values.
CALCULATIONAll Real x, x not = 0 is the domain (the range of potential values for x).
Since 6/0, 8/0, and 12/0 are not defined, x = 0 is not considered.
All Real f(x), f(x) not = 0 is the range.
Because 6 / and 6 / - will never equal 0, f(x) = 0 is not included. The same is true for 8/x and 12/x.
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A 5 pack of jump ropes cost $12.65. What is unit price?
Answer:
$2.53
Step-by-step explanation:
Unit price = total price / quantity
Unit price = $12.65 / 5
Unit price = $2.53
Simplify each expression. x¹/₆ . x¹/₃
Which ordered pairs are on the graph of 7x - y = 2 ?
Select ALL that apply. Can you please show the work?
i think it is (0,-2). y=mx+b
Find the sum of the first 46 terms of the following series, to the nearest integer
12, 15, 18
Answer: 3657
Step-by-step explanation:
18-15=3
15-12=3
3 ==> rate of change per term
3*46=138
138-3=135
135+12=147 ==> 46th term
Now find the average of the first and 46th term of the sequence:
(147+12)/2=
159/2=79.5
Now multiply the average by 46 to find the sum of the sequence.
79.5*46=
159*23=3657 ==> sum of 46 terms
The first three rooms took the painter a total of 9 hours to paint. If the learning curve rate is 85%, how long will it take the painter to paint all 20 rooms in stately wayne manor?.
If the Learning curve rate is 85%, then the painter will need 35.5 hours to pant all 20 rooms.
Learning curve rate tells us that there will be improvement or the time for the task will decrease as the person learn the repetitive task.
The time for completing n units is given by the formula:
Tₙ = T₁ . nᵇ
Where:
T₁ = time to complete 1st task
n = number of units
b = ln (learning curve rate) / ln(2)
The given parameters:
T₃ = 9 hours
learning curve rate = 85%
Hence,
b = ln (0.85) / ln(2) = 0.693
Plug the values into the formula for n = 3
T₃ = T₁ . 3ᵇ
T₁ = T₃ / 3ᵇ = 9 / 3ᵇ
Substitute the parameters for n = 20.
T₂₉ = T₁ . 20ᵇ
= (9 / 3ᵇ) . 20ᵇ
= 9 . (20/3)ᵇ
Substitute b = 0.693
T₂₉ = 35.5 hours
Hence, it takes 35.5 hours for the painter to pant all 20 rooms.
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Express 763 thousandths in
scientific notation
[tex]763 \times 10 {}^{3} = 7.63 \times 10 {}^{5} [/tex]
Solve each equation. Round to the nearest ten-thousandth. Check your answers.
12y⁻²=20
12[tex]y^{-2}[/tex] = 20 => y = 0.774, by basic algebra.
What is basic algebra?Numbers, variables, constants, expressions, equations, linear equations, and quadratic equations are all part of the basics of algebra. Additionally, the algebraic expressions contain the basic arithmetic operations of addition, subtraction, multiplication, and division.Given: 12[tex]y^{-2}[/tex] = 20
=> [tex]\frac{12}{y^2}[/tex] = 20
=> [tex]\frac{12}{20} = y^2[/tex]
=> [tex]y^2 = \frac{3}{5} = 0.6[/tex]
=> y = 0.774.
Hence, 12[tex]y^{-2}[/tex] = 20 => y = 0.774, by basic algebra.
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How would I find the internal and external volume of something like this?
The figure consists of dodecahedrons having different edge length, e.
The external volume, [tex] V_{e}[/tex], is given by the formula;
[tex]V_e = \frac{15 + 7 \cdot \sqrt{5} }{4} \cdot {e_e}^{3} [/tex]The internal volume, [tex] V_{i}[/tex], is given by the formula;
[tex] V_i = \frac{15 + 7 \cdot \sqrt{5} }{4} \cdot {e_i}^{3} [/tex]What is the volume of a dodecahedron?The given figures consists of solids that are pentagonal faced.
The number of faces of the solid = 12
The shape of the solids are known as a dodecahedron
The formula for the external volume, [tex] V_{r}[/tex], is given as follows;
[tex]V_e = \frac{15 + 7 \cdot \sqrt{5} }{4} \cdot {e_e}^{3} [/tex]
Where;
[tex] e_{e}[/tex] = The length of the edges on the outside of the dodecahedron.
Given that the length of the edges on the inside are measured to be [tex] e_{i}[/tex], the internal volume is given by the formula;
[tex] V_i = \frac{15 + 7 \cdot \sqrt{5} }{4} \cdot {e_i}^{3} [/tex]
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Ayuda esto es de mates
[tex]\displaystyle\\Answer:\ 6\frac{1}{6}[/tex]
Step-by-step explanation:
[tex]\displaystyle\\4\frac{2}{3} -(-1\frac{1}{2})=\\\\ 4\frac{2}{3} +1\frac{1}{2}=\\\\\frac{4*3+2}{3} +\frac{1*2+1}{2}=\\\\\frac{12+2}{3}+\frac{2+1}{2}=\\\\\frac{14}{3}+\frac{3}{2}=\\\\\frac{(14)(2)+(3)(3)}{(3)(2)} =\\\\\frac{28+9}{6} =\\\\\frac{37}{6} =\\\\\frac{36+1}{6}=\\\\\frac{36}{6} +\frac{1}{6}=\\\\\frac{(6)(6)}{6}+\frac{1}{6}=\\\\6+\frac{1}{6}=\\\\6\frac{1}{6}[/tex]
Number 15. Find MN please! I do give brainliest!
Answer:
MN = 5
Step-by-step explanation:
From inspection of the given diagram:
[tex]\textsf{MN = $2.5x$}[/tex][tex]\textsf{NR = $x$}[/tex][tex]\textsf{MNR = $5x - 3$}[/tex]Therefore:
[tex]\implies \sf MN+NR=MNR[/tex]
[tex]\implies 2.5x+x=5x-3[/tex]
[tex]\implies 3.5x=5x-3[/tex]
Add 3 to both sides:
[tex]\implies 3.5x+3=5x-3+3[/tex]
[tex]\implies 3.5x+3=5x[/tex]
Subtract 3.5x from both sides:
[tex]\implies 3.5x+3-3.5x=5x-3.5x[/tex]
[tex]\implies 3=1.5x[/tex]
[tex]\implies 1.5x=3[/tex]
Divide both sides by 1.5:
[tex]\implies 1.5x \div 1.5=3 \div 1.5[/tex]
[tex]\implies x=2[/tex]
Substitute the found value of x into the expression for MN:
[tex]\implies \textsf{MN}=2.5(2)[/tex]
[tex]\implies \textsf{MN}=5[/tex]
What is the value of the expression
-13(21 4/9)
The value of the expression is 284 5/ 9
What is a fraction?A fraction can be defined as the part of a whole.
Some types of fractions are;
Mixed fractionsSimple fractionsImproper fractionsProper fractionsGiven the fraction;
-13(21 4/9)
First, we convert the mixed fraction in the bracket to a proper fraction
- 13( 197/ 9)
Now, let's expand the bracket
-2561/ 9
Find the quotient
284 5/ 9
Thus, the value of the expression is 284 5/ 9
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How many roots , real or complex, does the polynmial 7+5x^4 - 3x^2 have in all?
the number of roots of the polynomial 7 + 5 x⁴ - 3 x² is 4.
We are given a polynomial:
7 + 5 x⁴ - 3 x²
We need to tell the number of roots that the polynomial has.
a polynomial is an expression consisting of indeterminates and coefficients.
It is the one that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Example: x² − 4x + 7.
We know that:
Number of roots = highest power of the variable of the polynomial
Here, the number of roots will be:
roots = 4
Therefore, we get that, the number of roots of the polynomial 7 + 5 x⁴ - 3 x² is 4.
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Two points on the graph of the linear function f are (0,3) and (3,9) . Write a function g whose graph is a reflection in the x-axis of the graph of f. g(x)=?
The function g whose graph is a reflection in the x-axis of the graph of f is g(x) = -2x - 3
How to write a function g whose graph is a reflection in the x-axis of the graph of f?The points on the function f are given as
(0,3) and (3,9)
Calculate the slope of f using
m = (y2 - y1)/(x2 - x1)
So, we have
m = (9 - 3)/(3 - 0)
Evaluate
m = 2
A linear equation is represented as
y = mx + c
Where m = slope
i.e. m = 2
c = y-intercept
i.e. c = y, when x = 0
In (0,3), we have
c = 3
So, the equation is
y = 2x + 3
The reflection of the equation on the x-axis is
g(x) = -f(x)
So, we have
g(x) = -2x - 3
Hence, the function g whose graph is a reflection in the x-axis of the graph of f is g(x) = -2x - 3
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What is the solution of each equation? Check your answers.
(b) 2 e -x=20
The solution of each equation 2 e -x=20 is -7.281.
What is an equation ?
2 e -x=20
Here e=2.7182
e-x =10
x = -7.281
A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.
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A rental car agency charges $170 per week plus $0.25 per mile to rent a car. How many miles can you travel in one week for $330?
Let u=[-5 3], v=[4 -3] , and w=[2 2] . Find the following vectors . 2u+3v
Given u = [-5 3], v = [4 -3] , and w = [2 2], by applying addition and scalar multiplication of vectors, 2u + 3v = [2, -3]
In the 2D coordinate system, vectors can be split into x-component and y-component.
A vector s = [3,–1], which means:
x-component = 3
y-component = –1
Some vector operations:
Addition / subtraction of vectors: Just add or subtract the corresponding components. For example: q = [1,5] and s = [6,-3]In the given problem:
u = [-5 3], v = [4 -3] , and w = [2 2]
Then,
2u = 2.[-5 3]
= [2.(-5), 2. 3] = [-10, 6]
3v = 3. [4 -3]
= [3. 4, 3. (-3)] = [12, -9]
Hence,
2u + 3v = [-10, 6] + [12, -9]
= [-10+12, 6-9]
= [2, -3]
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