The factors of given equation are -3/4 and -2.
Rewriting the equation -
4x² + 11x + 6 = 0
The factors for the given expression will be calculated based on two factors -
1. The sum of factors should be equal to sum of numeral value of b (11 in this case)
2. The product of factors should be equal to product of numeral values of a and c (24 in this case)
As per the above rules, the appropriate factors should be 8 and 3.
Rewriting the given equation with possible factors -
4x² + 8x + 3x + 6 = 0
Taking common values
4x(x + 2) +3(x + 2) = 0
(x + 2) (4x + 3) = 0
x = -3/4, -2
Thus, the factors of given expression are -3/4 and -2.
To check the correctness of factors, we will keep each value of x in equation.
When x = -3/4
4x² + 11x + 6 = 0
4(-3/4) + 11(-3/4) + 6 = 0
9/4 -33/4 + 6 = 0
9/4 = 2.25 and 33/4 = 8.25
2.25 - 8.25 + 6 = 0
-6 + 6 = 0
0 = 0
When x = -2
4x² + 11x + 6 = 0
4(-2)² + 11(-2) + 6 = 0
16 - 22 + 6 = 0
22 - 22 = 0
0 = 0
Since both values of x give 0 on both sides of equation, the factors of equation are correct.
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Your friend invested $1000 in an account that pays 6% annual interest. How much interest will your friend have after her college graduation in 4 years?
b. What equation should you use to model this situation?
The equation that suits the model is given as I = Prt and the interest the friend will have after her college graduation in 4 years will be $240
The formula to be used to is given as :
I = Prt (1)
where, I = simple interest
P = principal amount or amount initially deposited.
r = annual interest rate
t = time
According to the question we have been given that
P = $1000
r = 0.06
t = 4 years
Putting the required values in equation (1) we get
I = 1000*0.06*4
I = 240
hence the equation that suits the model is given as
I = Prt
and the interest the friend will have after her college graduation in 4 years will be $240
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The loudness in decibels dB of a sound is defined as 10 log I/I₀ , where I is the intensity of the sound in watts per square meter (W / m²) . I₀ , the intensity of a barely audible sound, is equal to 10⁻¹²W/m². Town regulations require the loudness of construction work not to exceed 100 dB . Suppose a construction team is blasting rock for a roadway. One explosion has an intensity of 1.65x10²W/m² . Is this explosion in violation of town regulations?
a. Which physical value do you need to calculate to answer the question?
a) The explosion does violate the town regulation
b) The two physical quantities are the I(intensity of the sound) and
[tex]I_{o}[/tex] (detectable intensity)
The values that we have been given are
L = loudness of the sound = 10 log(I/[tex]I_{o}[/tex])
I = intensity of the sound in watts per square meter = [tex]1.65 * 10^{2} W/m^{2}[/tex]
[tex]I_{o}[/tex] = intensity of barely audible sound = [tex]10^{-12} W/m^{2}[/tex]
Putting the required value in the equation of the loudness we get
a) L = [tex]10 log(\frac{1.65*10^{2} }{10^{-12} } )\\[/tex]
L = 10 * 14.217 dB = 142.17 dB
And according to the town regulation the loudness of the construction work should not exceed 100dB.
Thus the explosion is in violation of the town regulation as it exceeds 100dB.
b) the two physical value we have to calculate are I which is intensity of the sound in watts per square meter and [tex]I_{o}[/tex] which is intensity of barely audible sound. The respective values are
I = intensity of the sound in watts per square meter = [tex]1.65 * 10^{2} W/m^{2}[/tex]
[tex]I_{o}[/tex] = intensity of barely audible sound = [tex]10^{-12} W/m^{2}[/tex]
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WARM UP: Graph the coordinates of the triangle in the coordinate plane. Multiply each coordinate by a scale factor of 3 (k=3). Then, graph the new triangle.
The two triangles are similar triangles and the graph of the triangles are attached
Graph the coordinates of the triangle in the coordinate plane.The coordinates of the triangle are given as
A (0, 3), B (3, 3) and C (3, -1)
So, we enter the above coordinates in a graphing calculator
See attachment for the graph of the triangle
Multiply each coordinate by a scale factor of 3 (k=3).
Here, we have
A' 3 * (0, 3), B' 3 * (3, 3) and C' 3 * (3, -1)
This gives
A' (0, 9), B' (9, 9) and C' (9, -3)
Next, we enter the above coordinates in a graphing calculator
See attachment for the graph of the triangle
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Simplify each expression.
ln 1
ln (1) = 0, by properties of logarithms.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Now,
ln (1) = [tex]log_e(1)[/tex]
By properties of logarithms, we get that: [tex]log_b(1) = 0[/tex], for any value of b.
Hence, ln (1) = 0, by properties of logarithms.
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10x−y = 10
−2x+ 5y = −2
Answer:
x=1 & y=0
Step-by-step explanation:
The results of a survey of customers at a pet supply store showed that 33 owned dogs, 42 owned parrots, and 20 owned both dogs and parrots. How many owned either a dog or a parrot?
of the customers surveyed, owned either a dog or a parrot
(Type an integer or a decimal.)
Based on the number of customers who owned parrots, dogs and parrots, and dogs, the number who owned either a dog or a parrot were 55 customers
How to find the number who owned either a dog or parrot?The number of people who owned a parrot was 42. 33 people also owned a dog. Some of these people owned both a dog and a parrot and they numbered 20.
To find the number of customers who owned either a dog or a parrot, the formula is:
= Number of customers who owned a dog + Number of customers who owned a parrot - Number of customers who owned both a dog and parrot
= 33 + 42 - 20
= 75 - 20
= 55 customers
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ILL GIVE 20 POINTS TO WHOEVER ANSWERS FIRST
I've been waiting for 2 hours
Which of the following numbers is irrational? (5 points)
negative 7 over 4 , 2 over 3 , square root of 3 , square root of 4
negative 7 over 4
2 over 3
square root of 3
square root of 4
The irrational number in this data-set is given by the square root of 3.
What are rational and irrational numbers?Rational numbers are numbers that can be represented by fractions, such as numbers that have no decimal parts, such as whole numbers, or numbers in which the decimal parts are terminating or repeating.Irrational numbers are numbers that cannot be represented by fractions, being non-terminating and non-repeating decimals, such as non-exact square roots and also for the pi number.In this problem, we have that:
7/4 and 2/3 are fractions, hence they are rational.The square root of 3 is a non-exact square root, hence it is irrational.The square root of 4 is a exact square root, hence it is rational.Hence:
The irrational number in this data-set is given by the square root of 3.
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helpppp pls !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The entries that complete the blanks are 20.39, 20.78, 21.17 and 20 + 0.39n
How to determine the total amounts?The given parameters are
Invitation = $20
Stamps = $0.39 per stamp
So, the total amount spent is calculated as
Total = Invitation + Stamps * Number stamps
This gives
Total = 20 + 0.39 * Number stamps
For stamps 1, 2, 3 and n, we have
Total = 20 + 0.39 * 1 = 20.39
Total = 20 + 0.39 * 2 = 20.78
Total = 20 + 0.39 * 3 = 21.17
Total = 20 + 0.39 n
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Multiply. (3+√2)(4+√2)
The multiplication of the expression ( 3 + √2)( 4 +√2 ) is 14 + 7√2.
Multiplication in elementary algebra is the process of figuring out the outcome of multiplying a number by a number b. The product of a and b is the outcome of multiplication, and each of the integers a and b is referred to as a factor of the product ab.
Consider the expression,
y = ( 3 + √2)( 4 +√2 )
Using the distributive property,
a( b + c ) = ab + ac
y = ( 3 + √2)( 4 +√2 )
y = 3( 4 + √2 ) + √2( 4 + √2 )
y = 3 × 4 + 3 × √2 + √2 × 4 + ( √2 )²
y = 12 + 3√2 + 4√2 + 2
y = 14 + √2( 3 + 4 )
y = 14 + 7√2
The value of the expression ( 3 + √2)( 4 +√2 ) when simplified is 14 + 7√2.
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2+2 (free easy answer)
Answer:
5-1, known colloquially as four, 4, or 1+3.
Step-by-step explanation:
A laptop has a listed price of $887.99 before tax. If the sales tax rate is 9.75%, find the total cost of the laptop with sales tax included.
The total cost of the laptop, including the sales tax, is $974.57.
How is the total cost determined?The total cost of the laptop is the addition of the listed price and the sales tax (dollars).
The listed price refers to the retailer's (seller's) price before the addition of the sales tax.
After adding the sales tax to the listed price, the total cost is obtained.
Therefore, sales tax, which is a proportional tax, increases the cost of goods and services to consumers.
Data and Calculations:Listed price before tax = $887.99
Sales tax rate = 9.75%
Total cost after tax = $974.57 ($887.99 x 1.0975)
Thus, the total cost of the laptop after factoring in the sales tax is $974.57.
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What is 16,504÷55. Using 2 digit divisors write the remainder as a fraction.
16504 divided by 55 equals
300+ 4/55.
First we know about -
Divisor: The number by which the dividend is divided.
Quotient: The result of division.
Remainder: The amount that is left over after division.
Rules for the Division -
1. Take the first digits of the dividend, the same number of digits that the divisor has. If the number taken from the dividend is smaller than the divisor, you need to take the next digit of the dividend.
2. Divide the first number of the dividend (or the two first numbers if the previous step took another digit) by the first digit of the divisor. Write the result of this division in the space of the quotient.
3. Multiply the digit of the quotient by the divisor, write the result beneath the dividend and subtract it. If you cannot, because the dividend is smaller, you will have to choose a smaller number in the quotient until it can subtract.
4. After subtraction, drop the next digit of the dividend and repeat from step 2 until there are no more remaining numbers in the dividend.
0 0 3 0 0
5 5 ) 1 6 5 0 4
− 0
1 6
− 0
1 6 5
− 1 6 5
0 0
− 0
0 4
− 0
4
16504 divided by 55 equals
300 with a remainder of 4
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There are 6 circles and 3 squares. what is the simplest ratio of squares to circles? : attempt 1 out of 2 da'kyra jordan simplifying ratios (basic) sep 26, 7:01:57 pm there are 6 circles and 3 squares. what is the simplest ratio of squares to circles?
Given that there are 6 circles and 3 squares, the simplest ratio of squares to circles is 1 : 2 or 1 to 2 or 1/2.
Ratio is the relationship between two quantities, normally expressed as the quotient of one divided by the other.
It can be expressed in different ways:
1) Use the ":" to separate the values : a : b
2) Use the word "to" : a to b
3) Write it in fraction: a / b
If there are 6 circles and 3 squares. then the ratio of squares to circles can be written as:
3 : 6 or 3 to 6 or 3/6
To simplify the ratio, divide both numbers in the ratio by the same number until they cannot be divided any more.
Divide both number by 3.
3 : 6 = 1 : 2
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Can I please have answers to this question
Answer:
6. Slope = 2
7. y-intercept = 5
8. Equation: y = 2x + 5
Step-by-step explanation:
Question 6To find the slope of a line, define two points on the line:
(x₁, y₁) = (0, 5)(x₂, y₂) = (1, 7)Substitute these values into the slope formula and solve for m:
[tex]\implies \textsf{slope}\:(m)=\dfrac{7-5}{1-0}= \dfrac{2}{1}=2[/tex]
Therefore, the slope of the graph is [tex]\boxed{2}[/tex].
Question 7The y-intercept is the y-value of the point at which the line crosses the y-axis.
From inspection of the given graph, the y-intercept is [tex]\boxed{5}[/tex].
Question 8Slope-intercept form of a linear equation:
[tex]y=mx+b[/tex]
Where:
m = slopeb = y-interceptSubstitute the found slope and found y-intercept into the formula to create an equation for the line:
[tex]\boxed{y=2x+5}[/tex]
The formula for the area A of a trapezoid
A = 1/2 (b + b,)h. Solve for b
[Mathematical Situation]
Solve for [tex]b_1[/tex]; [tex]A=\frac{1}{2} (b_{1} + b_2)h[/tex]
Solution:
[tex]b_1=\frac{2a}{h}-b_2[/tex]
Hope this helps!
Find an equation in point-slope form for the line having the slope m=5 and containing the point (7,1).
[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ 5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ 5}(x-\stackrel{x_1}{7})[/tex]
PLS HELP
Look at the picture I attached, please help!
The expression which models the maximum number of days in which she can rent the car is 20x + 10 ≤ 80
How to illustrate the information?The maximum amount to spend = 80
Fixed charge per day $20
Charge per mile = $0.10
The inequality which represents the number of days Can be expressed thus :
(Charge per day × number of days) + (charge per mile × number of miles) ≤ 80
20x + 0.10 × 100 ≤ 300
20x + 10 ≤ 300
Hence, the required inequality expression is 20x + 10 ≤ 80.
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Is
f(x)
f(n)
f(a number)
Does all of them mean y?
help im homschooled n nun of the teachers help
Answer:
2
Step-by-step explanation:
What is the side length of a square house with an area of 9 kilometers?
Answer:
3
Step-by-step explanation:
[tex]\mathrm{a = \sqrt{A} = \sqrt{9} = 3}[/tex]
Simplify 5√12xm³
Assume x and m are nonnegative.
O 60√xm³
O 60m³√x
O 10m³√3x
O 10m√3xm
Answer:
[tex]\sf 10m\sqrt{3xm}[/tex]
Step-by-step explanation:
To simplify the expression, factorize 12. For every two items inside the square root, take one outside.
[tex]\sf 5\sqrt{12xm^3} = 5\sqrt{2*2*3*x*m*m*m}[/tex]
[tex]\sf = 5*2*m\sqrt{3xm}\\\\=10m\sqrt{3xm}[/tex]
Amari and ethan planned an end-of-season soccer party. they purchased 45 hot dogs and 30 individual bags of chips.
15 is the greatest number of people they can be without having any leftovers
Given data
45 hotdogs in 30 individual bags of chips
How to solve for the greatest number of people they can be without having any leftoversGiven data
45 hotdogs in 30 individual bags of chips
The greatest common factor of 45 and 30 is 15
using ratio
45 : 30
3 : 2
This means that one person will receive 3 hotdogs in 2 bags. Also 15 people will get the equal amount without left overs
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complete question
Amari and Ethan planned an end of season soccer party to purchase 45 hotdogs in 30 individual bags of chips which person will receive the same amount of food what is the greatest number of people they can be without having any leftovers
35° 91° 65° 28 What anglemeasures is this?
The angles 35° 65° and 28° are acute angles and the angle 91° is an obtuse angle
How to identify each of the angle measures?The angle measures are given as:
35° 91° 65° 28°
As a general rule:
Angles that are less than 90 degrees are acute angles
This means that
The angles 35° 65° and 28° are acute angles
Also, we have
Angles that are between 90 degrees and 180 degrees are obtuse angles
This means that
The angle 91° is an obtuse angle
Hence, the angles 35° 65° and 28° are acute angles and the angle 91° is an obtuse angle
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Complete question
What angle measure is this? 35° 91° 65° 28°
acute, right, obtuse, straight, or reflex
Find the distance between each pair of points.
25, 8, 10, 35, 5, 45, 40, 30, 20 What is the median of the given data set?
Answer:
25
Step-by-step explanation:
Arrange numbers to ascending order :
5,8,10,20,25,30,35,40,45
Cross of the smallest and biggest number until you left with one in the middle
Describe the difference between perfect square roots and non-perfect squares. Write at least two complete sentences.
Answer:
In this particular type of question we need to understand that perfect squares are the squares of the integers numbers and perfect square always end in 0,1,4,5,6,9.A perfect square number never ends with 2,3,7 or 8 .This is the first observation you will make to check if the number is a perfect square or not.
Step-by-step explanation:
15. Given the following relation {(2, 1), (-4,5), (1,7), (2, -3), (-1,2)), determine if it is a function.
We get that the relation { ( 2 , 1) , ( - 4 , 5 ) , ( 1 , 7 ) , ( 2 , - 3 ) , ( - 1, 2 ) } is a function.
We are given a relation as:
{ ( 2 , 1 ) , ( - 4 , 5 ) , ( 1 , 7 ) , ( 2 , - 3 ) , ( - 1, 2 ) }
We need to find that whether it is a function or not.
A relation is a set that shows a relationship between two values. A function is from a set X to a set Y assigns to each element of X exactly one element of Y.
Here, we can see that it is a function as one value of x only has one image in the set y.
Therefore, we get that the relation { ( 2 , 1) , ( - 4 , 5 ) , ( 1 , 7 ) , ( 2 , - 3 ) , ( - 1, 2 ) } is a function.
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40PTS. When you are getting dressed, you put your socks on first and then your shoes on second. But to undo this, you take your shoes off first and your socks off second. Why do you have to reverse the order? Use this scenario to help you explain why it is helpful to work backward when solving equations.
Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected. The probability that the sample contains 2 female voters is.
The probability that the sample contains 2 female voters is 0.31104
Binomial distribution uses two values; n and p. n represent the counts of sample that are being collected. On the other hand, p represents the chances of being successful on any trial. Using the two values, the probabilities are computed for binomial distribution.
Probability that a random voter is female is 0.40(p).
Sampled voters are 6(n).
Let X be the number of females in the sampled voters.
Then,
X∼ Bin (n, p)
∼Bin (6,0.4)
Probability that the sample contains exactly 2 female voters is,
P (X =2) = 6C2 (0.4)2 (1−0.4)6−2
=0.31104
Therefore, the probability that the sample contains exactly 2 female voters is 0.31104
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Multi-step k is the midpoint of _ jl , jl = 4x - 2, and jk = 7. find x, kl, and jl.
Answer:
K is the midpoint of JL, so it is halfway between J and L (see diagram). If JK is 7 units long, then so is KL. The length of the entire segment JL is 4x - 2, so
4x -2=14
Step-by-step explanation: