Use distributive property to factor method 1. Use distributive property to expand method 2.
Answers
Step-by-step explanation:
I guess method 1 means to deal with whole factors.
x + 5 = (x - 2)(x + 5)
for (x + 5) <> 0 we can divide both sides by this factor :
1 = x - 2
x = 3
for the second solution we deal with
x + 5 = 0
x = -5
so, for x = -5 and x = 3 both functions deliver the same output, and these are the intersection points.
method 2 : we multiply the expression out and solve it then
x + 5 = (x - 2)(x + 5)
x + 5 = x² + 5x - 2x - 10 = x² + 3x - 10
0 = x² + 2x - 15
the general solution to such a square equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = 2
c = -15
x = (-2 ± sqrt(2² - 4×1×-15))/(2×1) =
= (-2 ± sqrt(4 + 60))/2 = (-2 ± sqrt(64))/2 = (-2 ± 8)/2 =
= -1 ± 4
x1 = -1 + 4 = 3
x2 = -1 - 4 = -5
and you get the 2 solutions again. as expected, they are the same as with method 1, of course.
Related Questions
solve for m:
y=3mx-8
Answers
Answer: m= y/3x + 8/3x
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Find the volume of the cylinder. Find the volume of the cylinder with the same radius and double the height
Answers
Answer:
πr² x h and πr² x 2h
Step-by-step explanation:
Volume of Cylinder = base area x height
Volume of Cylinder = πr² x h
Volume with same radius but double the height:
Volume = πr² x 2h
Please really need the correct answer for this or I'll fail algebra 3
Answers
Answer:
[tex]4\pi[/tex]
Step-by-step explanation:
S = Arc Lenth
θ = Radians
R = Radius
S = θR
So, now that we understand the formula, we will convert 72° into radians by introducing the equation [tex]x*\frac{\pi }{180}[/tex], x = 72
S = [tex]72*\frac{\pi }{180} * R[/tex]
given that R = 10
S = [tex]\frac{72*10*\pi }{180}[/tex]
S = [tex]\frac{720*\pi }{180}[/tex]
We simplify 720 as 180 goes into 720 4 times and we get
S = [tex]4\pi[/tex]
Hope this helps
PLEASE HELP !!!!!!!!!
Answers
Answer:4/5
the angle of elevation to the sun is 24°. what is the length of the shadow cast by a person 1.82 m tall?
Answers
Answer:
4.089
Step-by-step explanation:
24 degree is the Angle of elevation. SO we can use in this triangle Tan.
So tan 24 = AB/BC because tan is the ratio of height over adjacent.
So we can say it is tan 24 = (1.82)/BC
So BC = (1.82)/tan(24) = 4.089m
BC is representing shadow of men. So shadow of men is 4.089m
please help this is urgent i will give brainliest
Answers
2. $12.5
3. 20%
4. 120%
5. 30%
6. 39
7. 900
8. 60%
9. 30%
10. 39
hope this helped!!
Problem number 26 of the Rhind Papyrus says: Find a quantity such that when it is added to StartFraction 1 Over 4 EndFraction of itself the result is a 15. The modern day equation that models this problem is x plus StartFraction 1 over 4 EndFraction x equals 15.. What is the solution to the equation? x = 10 x = 12 x = 15 x = 30 What is the fee Michael charges each new subscriber?
Answers
Answer:
x=12
Step-by-step explanation:
For the given situation , a quantity x is added to [tex]\frac{1}{4} x[/tex] gives 15.
We can set up equation as
[tex]x+\frac{1}{4}x=15[/tex]
Multiply each term by 4 on both sides to get rid the denominator.
It gives,
4 x+x=60
Now, combine like terms
5 x=60
Divide both sides by 5
x=12.
help pls first correct answer gets brainleist
Answers
2x=16
x=8
Hope that helps :3
I’ll add the questions they are 14 plz solve them I’ll mark u as u want
Plz plz I need them after 18 minutes
Answers
Step-by-step explanation:
3.3rd option
4.1st option
5.x=-10
6.x=6
7.109
8.75
9.24
10.19
you and 13 of your friends play on a softball team.a sponsor paid for the league fee each player's t-shirt new box for the team and tuna softballs for each game of the season does expression that represents the total amount (in dollars) paid by the sponsor is 14x + 20 (2 y +) + 5 Z + 120.
a. which at a represents the league fee? Explain your reasoning
b. Which added represents the T-shirt? Explain your reasoning.
c. What does y represent?
Answers
The expression of the league fee is an algebraic expression
The expression that represents the league fee is 14x
How to determine the league fee?The expression is given as:
14x + 20(2y + ) 5z + 10
The expression is not properly stated;
Only the league fee can be deducted from the given expression.
From the question, we understand that there are 14 players in total
i.e you (1) and (13) others
This means that the total league fee for the 14 players is:
Total = 14 * League fee for each player.
One of the terms of the expression is 14x.
So, we have:
14 * League fee for each player. = 14x
Hence, the expression that represents the league fee is 14x
Read more about algebraic expressions at:
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Mrs Atkins is going to choose two students from her class to take part in a competition.
She can choose from 16 girls and 14 boys.
(a)
Work out the number of different ways of choosing one girl and one boy.
Answers
Given:
Total number of girls in her class = 16
Total number of boys in her class = 14
To find:
The number of different ways of choosing one girl and one boy.
Solution:
We have,
Total number of girls = 16
Total number of boys = 14
So,
Total number of ways to select one girl from 16 girls = 16
Total number of ways to select one boy from 14 boys = 14
Now, number of different ways of choosing one girl and one boy is
[tex]16\times 14=224[/tex]
Therefore, the required number of different ways is 224.
a. The number of different ways of choosing one girl and one boy is 226
Calculation:Total number of ways to select one girl from 16 girls = 16
Total number of ways to select one boy from 14 boys = 14
So, the number should be
[tex]= 16 \times 14[/tex]
= 224
Find out more information about the Number here : https://brainly.com/question/17429689?referrer=searchResults
Write a linear equation that passes through
the point (2, -9) and has a slope of -5 in
slope-intercept form.
Answers
Answer:
f(x)=-5(2)-9
Step-by-step explanation:
linear equation- f(x)=m(x)-y
x- the x intercept
y- the y intercept
m- slope
x=-5, y=-9 , m=-5
WILL MARK YOU BRAINLIEST!!!!! Please help me with my geometry.
Answers
Answer: i believe your answer is c! i hope that helps!
Step-by-step explanation: im sorry ifs not, im not the gratest at this:(
Which type of motion is this an example of?
150 m/sec
1.acceleration
2.velocity
3.speed
Answers
Answer:
3. Speed
Step-by-step explanation:
acceleration is measured in m/s^2
velocity is speed plus direction
speed in measured in m/s
could u vote me brainliest plz, im trying to level up. thx:)
solve the equation 4-t+=3(t-1)-5
Answers
Answer:
use the picture to solve the equation
Answer:
Step-by-step explanation:
4-t=3t-3-5
-t-3t= -8-4
-4t=-12
t=12/4
t=3
Good luck!
HELP!!! WILL MARK BRAINLIST!!!! AND A 5 STAR REVIEW!!!
Answers
Answer:
8
Step-by-step explanation:
32 is equivalent to 32/1. So you can treat this as 1/4 x 32/1. Then, multiply the numerators together and then the denominators together. You will get 32/4. Simplified, this is equal to 8.
Is the square root of 105 closer to 10 or 11. Explain?
Answers
11 times 11 is 121
Answer:
You can say that √105 is somewhere between 10 and 11 because 105 lies between the squares of 10 and 11 (100 and 121, respectively). However, 105 isn't a perfect square, so you can't really find its exact square root. If you have a calculator with you, you can solve for an approximate of √105 which is 10.246950766.
Step-by-step explanation:
A soccer goalie kicks the soccer ball. The quadratic function y = −16t2 + 64t gives the time t seconds when the soccer ball is at a height 0 feet. How long does it take for the soccer ball to return to the ground?
Answers
Answer:
The correct answer is 4 sec
Step-by-step explanation:
The soccer ball returns to the ground after 4 seconds, got from solving the quadratic function y = -16t² + 64t.
What is a polynomial function?A polynomial function is a relation where a dependent variable is equal to a polynomial expression. A polynomial expression is an expression including numbers and variables, where variables are raised to non-negative powers.
The general form of a polynomial expression is:
a₀ + a₁x + a₂x² + a₃x³ + ... + aₙxⁿ.
The highest power to a variable is the degree of the polynomial expression.
When degree = 2, the function is a quadratic function.
When degree = 1, the function is a linear function.
How do we solve the given question?We are given a quadratic function representing the height of the ball after a goalie kicks it. The function is y = −16t² + 64t, where y is the height in feet of the ball at time t seconds.
We are asked how long it takes for the soccer ball to return to the ground.
To calculate the time for the ball to return to the ground, we take height y = 0.
Our equation therefore is,
0 = -16t² + 64t
or, 16t² - 64t = 0
or, t² - 4t = 0
or, t(t-4) = 0
∴ Either, t = 0; Or, t-4 = 0 ⇒ t = 4.
∴ The height of the ball is 0 when time t is 0 and 4. Time 0 is before the goalie kicked the ball, so we take t = 4 seconds.
∴ The ball takes 4 seconds to return to the ground.
Learn more about Quadratic Functions at
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#SPJ2
Triangle JKL is similar to triangle MNO. Find the measure of side NO. Round your
answer to the nearest tenth if necessary.
O
11
K
15
M
58.8
Answers
Answer:
43.1
Step-by-step explanation:
Similar shapes have sides of the same proportions. This means that one shape is just an enlargement of the other.
In this case, triangle MNO is an enlargement of triangle JKL so we can work out a scale factor.
To work out the scale factor, we can do 58.8 ÷ 15 = 3.92. To find side NO, all we have to do is multiply 11 by 3.92 to get 43.12 ≈ 43.1 (rounded to the nearest tenth).
Hope this helps!
3x+6 and 2x+14 find value of x
Answers
Answer:
Step-by-step explanation:
3x+2x is 5x
6+14 is 20
5x+20
if you are looking for this answer
x=4
divide 5 by 5x and 20 by 5
Can some one help
It is about a scatter plot
Answers
Answer:
1: 3 billion
2: 1/1/14
Step-by-step explanation:
Hope this helps! Have a nice day!
Randy is checking to determine if the expressions 2 x + 2 + 4 x and 2 (3 x + 1) are equivalent. When x = 3, he correctly finds that both expressions have a value of 20. When x = 2, he correctly evaluates the first expression to find that 2 x + 2 + 4 x = 14.
Answers
Please find attached full question
Answer and explanation:
Find attached answer and explanation
Please help I need it asap!!!!! The equation of line k is y=ax+b. Which could be the equation of line l?
A. y=−2a(x+4)+b
B. y=−2ax+4+b
C.y=−2a(x−4)+b
D. y=−2ax−4+b
Answers
Answer:
Option D
Step-by-step explanation:
See attached image
Using Euclid's algorithm, find the HCF of 1651 and 2032. Express
the HCF in the form (1651m + 2032n) for some integers m and n.
Answers
Answer:
Since 2032 gt 1651, we divide 2032 by 1651 to get 1 as quotient and 381 as remainder. step 2. Since the remainder 381≠0 , we divide 1651 by 381 to get 4 as quotient and 127 as remainder.
Step-by-step explanation:
Euclid algorithm lemma, a = bq + r where 0 ≤ r < b
From Euclid algorithm lemma, 2032 = 1651 × 1 + 381
Using lemma for 1651 and 381, e.g., 1651 = 381 × 4 + 127
Similarly, use lemma for 381 and 127, e.g., 381 = 127 × 3 + 0
Hence, HCF = 127
Now, 127 = 1651M + 2032 N
⇒127 = (127 × 13)M + (127 × 16)M
⇒1 = 13M + 16 N
Here many solutions possible because we have one equation contains two variable.
Assume M = 5 and N = -4
Then, 13 × 5 + 16 × -4 = 65 – 64 = 1
So, HCF of 1651 and 2032 in the form of 1651M + 2032 N is [1651(5) + 2032(-4)]
Help me. The topic is Maths, please.
Answers
Answer:
7
3
Step-by-step explanation:
First Solution
X=7
4= 12
Making X Subject of the formula
we have,
X= 7×4 = 28 = 14 = 7
12 12 6 3
OR
You cross multiply
X multiplies 12= 12X
7 multiplies 4= 28
you now have 12X=28
divinding both sides by 12,
12 cancels 12 and leave X
Answer:
x = [tex]\frac{7}{3}[/tex]
Step-by-step explanation:
[tex]\frac{x}{4}[/tex] = [tex]\frac{7}{12}[/tex] ( cross- multiply )
12x = 28 ( divide both sides by 12 )
x = [tex]\frac{28}{12}[/tex] = [tex]\frac{7}{3}[/tex] ← in simplest form
Cuál de los siguientes es un triángulo rectángulo?
A
2 cm - 3 cm - 4 cm
B
4 cm - 5 cm - 6 cm
C
6 cm - 8 cm - 12 cm
D
5 cm - 12 cm - 13 cm
Answers
Step-by-step explanation:
B
Question 1 (1 point) A locksmith charges $25 to make a house call and $15 for each lock re-keyed. Another locksmith charges $10 to make a house call and $20 for each lock that is re-keyed. Write a system of equations and use them to determine the number of locks where the total cost is the same. What will be the total cost? (Hint: write 2 equations of the form y = mx + b)
Answers
Answer:
The number of locks will be 3
The total cost = $50
Step-by-step explanation:
We are trying to write the equations of the cost in the form of the equation of a straight line
The equation will be;
C = F + 15r
where F is the price for house lock , C is total cost and r is the amount per rekey
For the first locksmith;
His equation will be ;
C = 25 + 15r
For the second
C = 10 + 20r
If the total cost is the same for both;
then;
10 + 20r = 25 + 15r
20r - 15r = 25 - 10
5r = 15
r = 15/5 = 3
For the total cost to be same, number of locks is 3
The total cost will be ;
C = 20 + 10(3) = 20 + 30 = $50
help with functions and relations
Answers
Answer:
It does NOT represent a function
Step-by-step explanation:
This DOES NOT represent a function because in the diagram 1 is connected to 8 and -3. If it was a function the number would connect to only one of them.
1,000 to 1200 what is the percentage difference?
Answers
Answer:
20%
Step-by-step explanation:
200÷1000×100
.......
Which table shows a constant rate of change?
Answers
Answer:
C
Step-by-step explanation:
It goes up by 225 each time. The others go up by different numbers each time.