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Work Shown:
5x^3 + 14x^2 + 9x
x( 5x^2 + 14x + 9 )
To factor 5x^2 + 14x + 9, we could use the AC method and guess and check our way to getting the correct result.
A better way in my opinion is to solve 5x^2 + 14x + 9 = 0 through the quadratic formula
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(14)\pm\sqrt{(14)^2-4(5)(9)}}{2(5)}\\\\x = \frac{-14\pm\sqrt{16}}{10}\\\\x = \frac{-14\pm4}{10}\\\\x = \frac{-14+4}{10} \ \text{ or } \ x = \frac{-14-4}{10}\\\\x = \frac{-10}{10} \ \text{ or } \ x = \frac{-18}{10}\\\\x = -1 \ \text{ or } \ x = \frac{-9}{5}\\\\[/tex]
Then use those two solutions to find the factorization
x = -1 or x = -9/5
x+1 = 0 or 5x = -9
x+1 = 0 or 5x+9 = 0
(x+1)(5x+9) = 0
So we have shown that 5x^2 + 14x + 9 factors to (x+1)(5x+9)
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Overall,
5x^3 + 14x^2 + 9x
factors to
x(x+1)(5x+9)
A square box lid has an area of 40 square inches. Which is the best estimate of the length of one side?
Answer:
10 OR 8
Step-by-step explanation:
Area is length times width, so with that being said you could say 10 times 4 is 40 or you can say 8 times 5 is 40
2x+4=2x+5 ( YOU CAN ONLY CHANGE ONE TERM). MAKE THIS EQUATION INFINITELY MANY SOLUTIONS AND ONE SOLUTION
Answer & Step-by-step explanation:
2x + 4 = 2x + 5
To make this equation have infinitely many solutions, you would change the 5 on the right side of the equation to be a 4. This would cause both the expressions to be exactly the same, changing the solution to be infinitely many solutions. You could also change the 4 on the left side of the equation to be a 5.
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To make the equation have only one solution you would change the 2x on the left (or right) side of the equation to be anything other than 2x. For example, you could change the 2x on the right side of the equation to be 3x, making x equivalent to -1, which means that x only has one solution.
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Hope this helps!!!
Mateo invested $4100 in a savings account with a yearly interest rate of 5%
for 15 years. How much simple interest did he earn?
A. $205.00
B. $307.50
C. $3075.00
$2050.00
Answer:
c
Step-by-step explanation:
Determine the value of the variables when simplifying and evaluating the expression (302)0 .
What is the value of m in the simplified power?
(302)0= 30m
m =
What is the value of (302)0?
(302)0 =
Any value that is raised to the power of zero is 1. The value of the expression given in its simplified form is 1
Exponents and functionsAny value that is raised to the power of zero is 1. Given the expression
(30^2)^0
Simplify
30^2 = 900
Substitute into the original function to have:
(30^2)^0 = 900^0
(30^2)^0 = 1
Hence the value of the expression given in its simplified form is 1
Learn more on exponents here: https://brainly.com/question/11975096
Please help me on this: it’s 10 points pls help me
Answer:
10^4 ---------------- 10,000
10^-4* 10^2 ------- 1/10^2 = 0.01
10^-4 ---------------- 1/10^4 = 0.0001
10^-4/10^2 -------- 1/10^6 = 0.000001
step by step explanition for all pleasee
I'll do the first three problems to get you started
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Problem 40
Plug in x = 0 to find the y intercept
x+y = 5
0+y = 5
y = 5 is the y intercept
Plug in y = 0 to find the x intercept
x+y = 5
x+0 = 5
x = 5 is the x intercept
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Answer: The x intercept is 5. The y intercept is 5.=====================================================
Problem 41
Use the same idea here as well
Plug in x = 0 to get
x-y = 5
0-y = 5
-y = 5
y = -5 is the y intercept
Now plug in y = 0 to solve for x
x-y = 5
x-0 = 5
x = 5 is the x intercept
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Answer: The x intercept is 5. The y intercept is -5.=====================================================
Problem 42
Plug in x = 0 and solve for y
3x+4y = 12
3(0)+4y = 12
0+4y = 12
4y = 12
y = 12/4
y = 3 is the y intercept
Plug in y = 0 and solve for x
3x+4y = 12
3x+4(0) = 12
3x+0 = 12
3x = 12
x = 12/3
x = 4 is the x intercept
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Answer: The x intercept is 4. The y intercept is 3.‼️WILL LIST BRAINLIEST ‼️Nick ran 4.8 miles on the treadmill in 0.6 hours. What is the average number of miles he ran per hour?
Answer:
4.8 divided by-____ is 8 i think lol
Step-by-step explanation:
Answer:
The average number of miles he ran per house is 8.
Step-by-step explanation:
4.8 divided by 0.6 = 8
15. Before oil is added to a certain road surface material, the other ingredients are mixed. The mixture contains
45% 3/4 inch stone and 32% % inch stone. The balance of the mixture is made up of sand. If the mixture weighs
15,000 pounds before the oil is added, how many pounds of each ingredient are in the mixture?
Answer:
sand = 3450 pounds
3/4 inch stones =6750 pounds
1 inch stones =4800 pounds.
Step-by-step explanation:
The mixture composition is :
45% three-quarter inch stones
32% inch stones and
sand for balance
The percent here is by mass of material used.
Weight of mixture is 15,000 pounds before oil addition.
Use the percent by weight for the two types of stones and calculate real values in pounds
Formula to apply is:
Mass percent = (mass of a material/ total mass of mixture) * 100
For 3/4 inch stones it will be:
[tex]0.45= \frac{x}{15000} *100\\\\0.45=\frac{x}{150} \\0.45*150=x\\x=6750[/tex]
The 3/4 inch stones weigh 6750 pounds
The 1 inch stones will be
[tex]32/100 * 15000 =4800[/tex]
The 1 inch stones weigh = 4800 pounds
Total for the two items : 4800+6750 =11550 pounds
The sand used weighs : 15000 - 11550 = 3450 pounds
GIVEN:MN is an angle bisector of ∠JMK
Prove:m∠JMN=1/2m∠JMK
Answer:
Step-by-step explanation:
Statements Reasons
1. MN is an angle bisector of ∠JMK 1. Given
2. ∠JMN ≅ ∠NMK 2. Definition of an angle bisector
3. m∠JMN ≅ m∠NMK 3. Definition of congruent angles
4. m∠JMN + m∠NMK = m∠JMK 4. Angle addition postulate
5. m∠JMN + m∠JMN = m∠JMK 5. Substitution property
6. 2(m∠JMN) = m∠JMK 6. Addition property of equality
7. m∠JMN = [tex]\frac{1}{2}(m\angle JMK)[/tex] 7. Division property of equality
Find an
equation for the perpendicular bisector of the line segment whose endpoints
are (-1, -2) and (-5,4).
Answer:
[tex]y=\frac{2}{3}x+3[/tex]
Step-by-step explanation:
Perpendicular Bisector
It's defined as a line that divides another line into two equal parts. The bisector passes through the midpoint of the line forming any angle, but if that angle is exactly 90°, then the bisector is also perpendicular.
We need to find the equation of the line that divides into equal parts the line with endpoints (-1, -2) and (-5,4) and is perpendicular to it.
First, let's find the slope of the line segment. The slope can be calculated with the formula:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\displaystyle m=\frac{4-(-2)}{-5-(-1)}=\frac{6}{-4}=-\frac{3}{2}[/tex]
The line for the perpendicular bisector has a slope m2. Two perpendicular lines with slopes m1 and m2 must comply:
[tex]m_1.m_2=-1[/tex]
Solving for m2:
[tex]\displaystyle m_2=-\frac{1}{m_1}[/tex]
[tex]\displaystyle m_2=-\frac{1}{-\frac{3}{2}}=\frac{2}{3}[/tex]
The equation of the perpendicular bisector has the form:
[tex]y=\frac{2}{3}x+b[/tex]
Now we find the coordinates of the midpoint of the segment:
[tex]\displaystyle \bar x=\frac{-1-5}{2}=-3[/tex]
[tex]\displaystyle \bar y=\frac{4-2}{2}=1[/tex]
The midpoint is (-3,1). Using this point will allow us to find the value of b:
[tex]1=\frac{2}{3}(-3)+b[/tex]
[tex]b=1+2=3[/tex]
Thus, the equation for the perpendicular bisector is
[tex]\boxed{y=\frac{2}{3}x+3}[/tex]
1. (02.05)
Choose the missing step in the given solution to the inequality -x - 10 > 14 + 2x (1 point).
-X-10 > 14 + 2x
-3x -10 > 14
X<-8
-3x > 24
-3x < 4
-3x > -4
8
Answer:
-3x > 24
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
The length of one leg 20 inches and the hypotenuse is 52 inches
Answer:
48 inches
Step-by-step explanation:
Remember the Pythagorean theorem, where a and b are legs and c is the hypotenuse
a^2 + b^2 = c^2
a= 20
c = 52
now substitute in the given values
20^2 + b^2 = 52^2
400 + b^2 = 2704
solve using inverse operations
400 + b^2 = 2704
-400 -400
b^2 = 2304
b= sqrt(2304)
b=48
PLEASE HELP I WILL MARK YOU BRAINLIEST
Answer:
C. $17.00
Step-by-step explanation:
rational number?
square root 97square root 98, square root 99, square root 100
Answer:
square root 97 is 100, square is root 98 is 100, square root 99 is 100, square root 100 is 100
Seven times a number is greater than 28.
Answer:
Inequality would be
7x>28
The answer to the inequality would be
X>4
Step-by-step explanation:
Divide 7 on Both sides
x>4
check
7(5)>28?
35>28☑️
solve the equation 5(x-3) = 11 -3 (x-2)
Answer:
x = 4
Step-by-step explanation:
5 multiplied by x and 5 multiplied by -3
5x - 15 = 11 -3(x - 2)
-3 multiplied by x and -3 multiplied by -2
5x - 15 = 11 - 3x + 6
Add 15 to both sides
5x = 26 - 3x + 6
Add 3x to both sides
8x = 26 + 6
Add 26 + 6
8x = 32
Divide 32 by 8
x = 4
State whether each function is a linear function. Write yes or no. Explain. f(x)=5/x+6
Answer:
yes
Step-by-step explanation:
its in y= mx+b form or f(x)= mx+b
Answer:
No, it is a non linear function.
Step-by-step explanation:
As the equation says:
f(x)=5/x+6
Demonstrating 5 in the numerator and x+6 in the denominator it is not a linear function. This is because the x variable is in the denominator which makes it fail to become a linear function. Have a wonderful dayy!!
-_-
7. What Is the volume
of the rectangular
prism shown below
Greetings! Hope this helps!
Answer
D) 5633.712
__________
13.8 x 12.6 x 32.4
Have a good day!
_______________
A brainliest would help tons! :D
what is 7.63x19pls help
Answer:
144.97
Step-by-step explanation:
Use long multiplication to evaluate.
factor 10x^3-12x^2+5x-6
Answer:
(5x-6)(2x²+1)
Step-by-step explanation:
10x³-12x²+5x-6
2x²(5x-6)+5x-6
(5x-6)(2x²+1)
Abby is adopting kittens from the pet store. if there are 18 kittens, how many ways can she choose 2 kittens?
Answer:
I think its 32
pls help -
Caleb types 100 words in 5 minutes. What is the unit rate? 100 words to 5 minutes 5 minutes per 100 words 20 words per minute 1 minute to 20 words
Answer:
Unit rate= 20
words per minute/ 0.3
words per second
Step-by-step explanation:
We could work out the unit rate in 2 ways:
Per Minute or Per second.
First we will start of with per minute:
Rate=Word/minute=100/5=20
Answer:
100 words to 5 minutes
Step-by-step explanation:
what is the answer to 4 (-5.4)?
Answer:
-21.6
Step-by-step explanation:
When a number, like 4 in your equation, is next to parentheses without a sign (ex. plus or minus) it means to multiply. 4(-5.4) is equal to 4x5.14 which is -21.6
WILL MARK BRAINLIEST! Marla bought one necklace and two bracelets for $67.50. Use the following information to determine the amount she paid for each bracelet: • The price of the necklace was $27. • The bracelets were both the same price.
I need help with #13, with an explanation...please help <3
Answer:
Step-by-step explanation:
d= c/ pi
multiply both side by pi
d*pi = c
divide by d
pi= c/d
help pleaseeee . i’m not good
The picture above should help
PLEASE GIVE AN EXPLANATION WITH YOUR ANSWER! 6 cm are cut from a 24 cm board. What is the percent decrease in length?
Answer:
75%
Step-by-step explanation:
24/6=4
1/4=6
4*6=24
24-6=18
3/4 of 24=18
3/4=75%
The percentage decrease in length of the board is 25%
From the given statement we can deduce the following:
original length of the board = 24 cmnew length after cutting 6 cm = 24 cm - 6 cm = 18 cmThe change in the length of the board is calculated as:
Change in length = original length - new lengthChange in length = 24 cm - 18 cmChange in length = 6 cmThe percentage decrease in the length is calculated as;
[tex]Percentage \ decrease = \frac{change \ in \ length }{original \ length} \times 100\%\\\\Percentage \ decrease = \frac{6}{24} \times 100\%\\\\Percentage \ decrease = 25\%[/tex]
Thus, the percentage decrease in length of the board is 25%
Learn more here: https://brainly.com/question/2140235
What would be the anwser
Find the domain and range of each relation. Then determine if the relation is a function.
Answer:
There is no fixed domain, meaning it is ongoing
The range is from -1 ≤ x ≤ 3
It is a function
Step-by-step explanation:
Domain refers to the x values. If there was a domain then there would be a dot or a point signalling that there is a fixed domain, however, there are arrows meaning that it will keep going.
The range refers to the y-values. The lowest y-value is -1 and the highest is 3.
It is a function because, when you do the vertical line test, each x-value has its own y-value.
Which situation involving Raul’s bank account would be modeled by a positive number?
Raul deposited his paycheck.
Raul wrote a check to his grandmother.
Raul withdrew cash from an ATM.
Raul paid for groceries with his debit card.
Answer: deposited
Step-by-step explanation:
That means that he put in
Everything is was a withdrawal(taking out)
Answer:
Raul deposited his paycheck.
Step-by-step explanation:
The reason it's 'A' is because when you deposit your paycheck, you are depositing money.
I hope this helps!
