Factor the expression completely:
2x² + 5x - 12
Answers
2x^2+5x-12
x^2+5x-24
(x+8)(x-3)
(x+8/2)(x-3/2)
(x+4)(2x-3)
Final answer: (2x-3)(x+4)
Related Questions
8.51 is what percent of 18.5
Answers
dive the two numbers:
8.51 / 18.5 = 0.46
0.46 = 46%
Let f (x) = ax + b and g(x) = cx + d, where a, b, c, and d are constants. determine necessary and sufficient conditions on the constants a, b, c, and d so that f ◦ g = g ◦ f
Answers
[tex]g(x)=cx+d[/tex]
[tex]f\circ g(x)=a(cx+d)+b=acx+ad+b[/tex]
[tex]g\circ f(x)=c(ax+b)+d=acx+bc+d[/tex]
In order for [tex]f\circ g=g\circ f[/tex] to hold, we require [tex]ad+b=bc+d[/tex], which can be rearranged slightly as [tex](a-1)d=(c-1)b[/tex] or [tex]\dfrac{a-1}{c-1}=\dfrac bd[/tex], etc.
The necessary and sufficient conditions for f ◦ g = g ◦ f are that a and c must be non-zero and have the same sign, while b and d can be any values.
Explanation:To determine the necessary and sufficient conditions for f ◦ g = g ◦ f, we need to find the values of a, b, c, and d that satisfy this equation.
a and c must be non-zero, as dividing by zero is undefined in functions.If a and c have different signs, f ◦ g and g ◦ f will have different slopes, which means they will not be equal. Therefore, a and c must have the same sign.If a and c have the same sign, b and d can be any values, as they won't affect the slopes of the functions.Therefore, the necessary and sufficient conditions for f ◦ g = g ◦ f are that a and c must be non-zero and have the same sign, while b and d can be any values.
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It takes Awan 8 1/3 minutes to run a mile, it takes Kate 1 1/5 time longer. How long does it take Kate to run one mile?
Answers
Answer:
10 minutes
Step-by-step explanation:
Given: It takes Awan [tex]8\frac{1}{3}[/tex] minutes to run a mile, it takes Kate [tex]1\frac{1}{5}[/tex] time longer.
To Find: How long does it take Kate to run one mile.
Solution:
Time taken by Awan to run a mile = [tex]8\frac{1}{3}[/tex] [tex]\text{minutes}[/tex]
= [tex]\frac{25}{3}[/tex] [tex]\text{minutes}[/tex]
Time taken by Kate to run a mile = [tex]1\frac{1}{5}\times\text{time taken by Awan}[/tex]
= [tex]\frac{6}{5}\times\text{time taken by Awan}[/tex]
Therefore,
on putting values
The time taken by Kate = [tex]\frac{6}{5}\times\frac{25}{3}[/tex] [tex]\text{minutes}[/tex]
= [tex]\frac{6\times25}{5\times3}[/tex]
= [tex]10[/tex] [tex]\text{minutes}[/tex]
Hence, the time taken by Kate to complete one mile is [tex]10[/tex] [tex]\text{minutes}[/tex]
Kalesha is purchasing a laptop. The original price of the laptop is $900. The store is offering 10% off on all computers. Kalesha has a $100 gift card.
How should Kalesha determine the amount she will pay for her computer?Subtract $100, then take 10% off.Take 10% off, then subtract $100.Kalesha will pay
The answer is : $710
Answers
The amount Kalesha will pay for her computer is:
$ 710
Step-by-step explanation:It is given that:
The original price of the laptop is $900.
The store is offering 10% off on all computers.
Kalesha has a $100 gift card.
Now in order to calculate the amount Kalesha will pay we first have to find the cost that will be reduced on a offer of 10% provided by the store and subtract this reduced price from the original price ; and finally we again subtract $ 100 from this resulting price.
When a offer of 10% is applied to the computer we have:
Price reduced on offer=10% of original price
i.e.
Price reduced on offer=10%×900
i.e.
Price reduced on offer=0.10×900
i.e.
Price reduced on offer=$ 90
Cost of Computer= Original price-Price reduced on offer
i.e.
Cost of computer= 900-90
i.e.
Cost of Computer=$ 810
Now, when Kalesha uses her gift card of $ 100 then,
Amount Kalesha will pay= $ (810-100)
i.e.
Amount Kalesha will pay= $ 710
If 12 less than 4 times a number is 8, the number is 5. What difference sentence where the unknown number is also 5?
Answers
Tina and Bruce are each rolling a 1 to 6 number cube . they are looking for different ways to roll two factors whose product is greater than 14. how many different ways will they find ?
Answers
Final answer:
To find the different ways to roll two factors whose product is greater than 14, we list the different outcomes when rolling a number cube twice.
Explanation:
To find the different ways to roll two factors whose product is greater than 14, we need to consider the possible outcomes when rolling a number cube twice.
First, we look at the factors of 14 and determine that they are 1, 2, 7, and 14.
Now, we can list the different ways to roll two factors:
If Tina rolls a 1 and Bruce rolls a 15 (6 + 9), the product is 15 which is greater than 14.
If Tina rolls a 2 and Bruce rolls a 10 (3 + 7), the product is 20 which is greater than 14.
If Tina rolls a 7 and Bruce rolls a 3, the product is 21 which is greater than 14.
If Tina rolls a 14 and Bruce rolls a 2, the product is 28 which is greater than 14.
Therefore, there are 4 different ways for Tina and Bruce to roll two factors whose product is greater than 14.
Which number sentence correctly solves this problem?
Jill's dad spent $783 for home repairs and $390 for car repairs. How much did Jill's dad spend on the repairs?
A.
783 – 390 = 393
B.
783 + 390 = 1,073
C.
783 + 390 = 1,173
D.
783 – 390 = 493
Answers
783+390=1173.
Find an equation of the sphere that passes through the origin and whose center is (â2,2,3). be sure that your formula is monic.
Answers
I am not sure about this sorry.
Can someone help me understand why the mean travel for women is greater than the mean travel for men?
Problem Words:
"In San Jose, the amount of time it took each person to get to work was recorded and rounded up to the nearest 555 minutes. The data collected for men and women are shown in the bar graph to the left"
Answers
To ascertain why mean travel time for women could be greater than for men, one would analyze commuting data for both genders and possibly use hypothesis testing to determine if any observed difference is statistically significant.
Explanation:Understanding the differences in mean travel time between men and women requires analysis of provided data and consideration of statistical methods. For instance, if in San Jose, the recorded commuting times were higher for women, this could be a result of many factors including job location, availability of transportation, or societal roles affecting women's work commute. In the hypothetical scenario provided, it appears there were no actual data points or a graph to refer to, but typically, one would calculate the average commute time for each gender groups and then compare the two means.
For example, if you have a dataset and you're trying to establish whether the mean travel time for women is greater than that for men, you could perform a hypothesis test. The null hypothesis would state there is no difference in the commuting times between men and women, while the alternative hypothesis would state that There is a significant difference in mean commute times. You would then use the data findings, such as sample means and standard deviations, to perform an appropriate statistical test, like a t-test, to determine if there is a statistically significant difference between the mean commute times of the two groups.
Concluding if this difference is significant would involve looking at a predefined significance level (like 5% or 10%) and comparing the p-value from the test to this level. If the p-value is less than the significance level, we reject the null hypothesis and can claim there is a significant difference in the mean travel times between men and women.
What is the volume of the frustum?
Answers
depending on the value used for PI the answers vary
but attached picture is solution
Answer is A.503.77
a number is double and than increased by nine. the result is ninety-one. what is the original number?
Answers
A store is giving away a $10 to every 7th person to enter the store and a $25 coupon to every 18th person to enter the store . which person will be the first to get both coupons?
Answers
So, it's the 126th customer
Which number is 1/10 as great as 0.7?
Answers
Answer:
Step-by-step explanation:
It’s actually 7.
help me with this I don't get it help4help?
Answers
3/4 x 2/1 = 3/2 (so you could only have 1 and 1/2 servings with 1/2 pound of chicken in each serving.
2) Set up a little algebra problem. Let x = the multiplier of the original 3/4 pounds of chicken needed to make two full servings with 1/2 pound of chicken in each.
(3/4)x = 2(1/2) (Found this online V(0-0)v)
Three fourths of college students use the Internet more than the library. Nine hundredths use the library more. How many times more students use the internet?
Answers
4/3X 100/9 = 8 1/3
You are a contractor and charge $45 for a site visit plus an additional $24 per hour for each hour you spend working at the site.Write and solve an equation to determine how many total hours you have to work
Answers
45+(24x)=h
I feel this is the best I can do with the given information ... hope this helps
in a sale there is 25% off all prices a bed costs £33 in the sale what was the original price
Answers
Set up a proportion.
33/x= 75/100
Cross multiply
33*100=3300
3300/75=44=x
Final answer: $44
99 Point question - Consider the graph of f(x) below. (See attachment)
Write the equation of f(x), and classify the function as linear, quadratic, cubic, exponential, or logarithmic.
Answers
A quadratic function has one point where is switches from going up to going down (or down to up), but this has two, so that's not it.
A cubic function has 2 points where it goes from down to up or up to down, so this may just work.
An exponential function has a constant to the power of something, so it's either staying constantly up or down after 0 or jumping up and down with every x value, which it isn't doing.
Logarithmic functions are similar to exponential functions in that it usually stays either going up or down the whole time.
Using our definitions, a cubic function is the only one that fits
Explain why the function is differentiable at the given point then find the linearization of x/(x+y)
Answers
The box office manager said about 5,000 people attended the show. Write a number that could be the actual attendance if he correctly rounded to the nearest hundred
Answers
hope this helps
a movie club charges a one time fee of $25 it allows members to purchase movies for $7 each another club does not charge a membership fee and sells movies $12 how many movies must a member purchase for the total cost of the two clubs to be equal
Answers
No membership club = $12 per movie(x)
We need to know how many movies must each purchase to equal in costs.
Set up both equations to equal each other and solve for x=movies.
25 + 7x= 12x
25 + 7x -7x = 12x - 7x
25= 5x
25/5=5x/5
5=x it will take them both 5 movies each to have equal costs.
The number of movies in which the total cost of the two clubs should be equal is 5.
Given that,
The one-time fee is $25.The other club should be $7.The selling price of the movies should be $12.Let us assume the number of movies be x.25 + 7x= 12x
Now put -7x in both sides
So,
25 + 7x -7x = 12x - 7x
25= 5x
x = 5
Therefore we can conclude that the number of movies in which the total cost of the two clubs should be equal is 5.
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What number can be written as 40 plus 5
Answers
add them together: 40+5 = 45
the number is 45
What is the factored form of x2 − 4x − 5?
(x + 5)(x − 1)
(x + 5)(x + 1)
(x − 5)(x − 1)
(x − 5)(x + 1)
Answers
If you used the foil method for (x-5)(x+1) and combined like terms you would get the same as
The factored form of the equation x² − 4x − 5 is ( x - 5 )( x + 1 ). The correct option is D.
What is a quadratic equation?A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given that the quadratic equation is x² − 4x − 5. The value of x will be calculated as:-
x² − 4x − 5 = 0
x² - 5x + x - 5 = 0
x( x - 5 ) + 1 ( x - 5 ) = 0
( x - 5 ) ( x + 1 ) = 0
Hence, the factored form of the equation x² − 4x − 5 is ( x - 5 )( x + 1 ).
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4/9 divided by what equals 12
Answers
Multiply both sides by x
4/9=12x
Divide both sides by 12
(4/9)*(1/12)= 4/108
4/108= 1/27
Final answer: 1/27
An arithmetic sequence has this recursive formula
Answers
This is because 7 is standing in place for a1 and -4 is standing in place for d in the explicit equation: an=a1+(n-1)d
Answer:
[tex]\text{The explicit formula is }a_n=7+(n-1)(-4)[/tex]
Option B is correct.
Step-by-step explanation:
Given the recursive formula of arithmetic sequence
[tex]a_1=7[/tex]
[tex]a_{n}=a_{n-1}-4[/tex]
we have to find the explicit formula for the above sequence.
[tex]a_{n}=a_{n-1}-4[/tex]
[tex]a_{n}-a_{n-1}=-4[/tex]
which is the common difference, d=-4
The explicit formula for A.P is
[tex]a_n=a_1+(n-1)d[/tex]
[tex]a_n=7+(n-1)(-4)[/tex]
Option B is correct.
A construction firm is trying to decide which of two models of a crane to purchase. Model A costs $100,000 and requires $4,000 per year to maintain. Model B has an initial cost of $78,000 and a maintenance cost of $13,000 per year. For how many years must model A be used before it becomes more economical than B? (Round your answer to one decimal place.)
Answers
The functions are as follows:
A(x)=100,000+4,000x (dollars)
B(x)=78,000+13,000x (dollars)
Model A becomes more economical than Model B when A(x)<B(x),
so we solve:
100,000+4,000x<78,000+13,000x
100,000-78,000<13,000x-4,000x
22,000< 9000x
22<9x
x>22/9=2.444
Model A becomes more economical in the third year, that is after the first 2 years.
I am not sure how to solve this
Answers
We're simply just trying to get "x" by itself :)
So, we have to add 2x to both sides.
2x + 2x + 1 - 4 = -3
Add like terms.
(2x + 2x) + (1 - 4) = -3
Simplify.
4x - 3 = -3
Then, we must add 3 to both sides.
4x = -3 + 3
Simplify.
4x = 0
Divide both sides by 4.
x = 0 ÷ 4
Simplify.
x = 0
~Hope I helped!~
or parallelogram ABCD, A(0, 0), B(a, b), and D(c, 0) are three of its vertices. Find the coordinates of C in terms of a, b, c.
Answers
Because ABCD is a parallelogram, therefore
(i) AD = BC, so that
x - a = c - 0
x = a + c
(ii) AB = DC, so that
y - 0 = b - 0
y = b
he coordinates of C are (a+c, b).
Answer: (a+c, b)
Answer:
(a + b, c)
Step-by-step explanation:
I did this is school and this was the correct answer!
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What is the area of a circle with a diameter of 8 meters (use 3.14 for O
)
Answers
Michael plays 1/5 of a song in 1/15 pf a minute. How many minutes will it take to play whole song
Answers
now, he only plays 1/5 in 1/15, how many minutes will it take to play the whole 5/5 of the song?
[tex]\bf \begin{array}{ccll} \stackrel{part}{song}&\stackrel{part}{minutes}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \frac{1}{5}&\frac{1}{15}\\\\ \frac{5}{5}&m \end{array}\implies \cfrac{\frac{1}{5}}{\frac{5}{5}}=\cfrac{\frac{1}{15}}{m}\implies \cfrac{\frac{1}{5}}{\frac{5}{5}}=\cfrac{\frac{1}{15}}{\frac{m}{1}}\implies \cfrac{1}{5}\cdot \cfrac{5}{5}=\cfrac{1}{15}\cdot \cfrac{1}{m}[/tex]
[tex]\bf \cfrac{1}{5}=\cfrac{1}{15m}\implies 15m=5\implies m=\cfrac{5}{15}\implies m=\stackrel{\textit{minutes}}{\cfrac{1}{3}}[/tex]