how do i factorise x^2+6x-40 ?
Answers
9514 1404 393
Answer:
(x +10)(x -4)
Step-by-step explanation:
Compare the factored and expanded forms:
(x +p)(x +q) = x^2 +(p+q)x +pq = x^2 +6x -40
That is, the constants in the binomial factors will be factors of -40 that have a sum of 6. This is where your knowledge of multiplication tables is helpful.
-40 = -1×40 = -2×20 = -4×10 = -5×8
The sums of these factor pairs are 39, 18, 6, 3, respectively. So, the one we want is (-4)(10) = -40. Now that we know the values of 'p' and 'q', we can write the factorization ...
x^2 +6x -40 = (x -4)(x +10)
Related Questions
3x – 2y = -6
y = 1.5x + 3
What is the solution to the system
Answers
Answer:
The answer is D infinitely many
Step-by-step explanation:
A store sells oranges and apples. Oranges cost $1.00 each and apples cost $2.00 each. In the first sale of the day, 15 fruits were sold in total, and the price was $25. How many of each type of frust was sold?
Answers
A store sells 5 oranges and 10 apples.
What is the cost amount?
The cost of an asset to you often serves as its basis. The cost is the sum that you pay for it using money, debt, other goods, or services. Sales tax and other purchase-related costs are included in the price.
Here, we have
Given: A store sells oranges and apples. Oranges cost $1.00 each and apples cost $2.00 each. In the first sale of the day, 15 fruits were sold in total, and the price was $25.
We have to determine how many of each type of fruit were sold.
We, let the oranges be x.
let the apples be y.
x + y = 15...(1)
1x + 2y = 25...(2)
We subtract equation(2) from equation(1), we get
y = 10
Now we put the value of y in equation (1) and we get
x + 10 = 15
x= 5
Hence, a store sells 5 oranges and 10 apples.
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Abby is filling a 100 quart dog bath using a 2 gallon bucket. how many buckets will it take to fill the dog bath?
Answers
( or 12.5 buckets)
Step by step
We know the bath holds 100 quarts
We know 100 quarts is equal to 25 gallons
( 4qts to 1 gallon)
If Abby is using a 2 gallon bucket, divide 25 gallons by 2
25/2 = 12 1/2 buckets to fill the bath
Overview question 2 of 20, 17 complete
2
When members of the military are in a combat zone, they often eat meals-ready-to-eat (MRES). A typical MRE contains 1,000 calories. If the average soldier eats 3
MREs per day and is deployed for 12 months, approximately how many calories will be consumed by a 43-member platoon of soldiers?
The platoon will consume million calories
(Round to the nearest hundredth as needed.)
Answers
Answer:
Step-by-step explanation:
I am getting the ans wait
The function f(x)=4^x-6 is transformed to function G through a vertical compression by a factor of 1/2. Complete the equation of function G .  enter the correct answer in the box. Substitute  numerical values into the equation for a and k.
g(x) = a(4)^x-k
Answers
The equation for the transformed function g(x) is: g(x) = 2.323 (4) raise to the power x-0.872/2
How to solve a function?
If the function f(x) is vertically compressed by a factor of 1/2, the equation for the new function g(x) is given by:
g(x) = a(4) raise to the power x-k/2
where "a" and "k" are constants that need to be determined. To find these constants, we can use the fact that the original function f(x) is equal to g(x) when the compression is applied:
f(x) = g(x)/2
Substituting the expression for g(x) into this equation and simplifying, we get:
4raise to the power x - 6 = a(4)raise to the power x-k/2
To solve for "a" and "k", we need to find two equations involving these variables. One way to do this is to evaluate the expression for f(x) at two different values of x, and then set those equal to the corresponding values of g(x)/2. For example, we can choose x = 0 and x = 1:
f(0) = 4 - 6 = -5
f(1) = 4- 6 = -2
Using the equation g(x)/2 = f(x), we can write:
g(0)/2 = -5
g(1)/2 = -2
Substituting the expression for g(x) into these equations, we get:
a(4) raise to the power -k/2 = -10
a(4) raise to the power 1-k/2 = -4
Taking the ratio of these two equations, we can eliminate the variable "a" and solve for "k":
(4)raise to the power -k/2 / (4) raise to the power 1-k/2 = -10 / -4
Simplifying this equation, we get:
4.raise to the power(1-k/2) = 5
Taking the logarithm of both sides (with base 4), we get:
1-k/2 = log4(5)
Solving for "k", we get:
k = 2 - 2 log4(5)
Substituting this value of "k" back into one of the equations we derived earlier, we can solve for "a":
a = -10 / (4) raise to the power -k/2
Substituting the numerical value of "k", we get:
k = 2 - 2 log4(5) ≈ 0.872
a = -10 / (4) raise ti the power -k/2 ≈ 2.323
Therefore, the equation for the transformed function g(x) is:
g(x) = 2.323 (4)raise to the power x-0.872/2
or equivalently:
g(x) = 1.1615 (4) raise to the power -x0.872
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Answer:
g(x) = 1/2 (4)^x - 3
Step-by-step explanation:
A vertical compression by a factor of 1/2
means that the entire function f is multiplied by 1/2:
1/2 f (x) = 1/2 (4^x - 6)
= 1/2 (4)^x - 3
Find the volume of a sphere with a diameter of 6.2 in.
Answers
Answer: its 23 meters
Step-by-step explanation:
The volume of a sphere with a diameter of 6.2 in is 39.72π
What is the volume of the sphere?The volume of a sphere is defined as the total amount of capacity applied in a sphere that can be calculated using the volume formula for the sphere which is V = (4/3)πr3.
The radius of the sphere is;
\(\rm Radius =\dfrac{Diameter}{2}\\\\Radius=\dfrac{6.2}{2}\\\\Radius=3.1\)
The volume of the sphere is;
\(\rm Volume =\dfrac{4}{3}\pi r^3\\\\Volume =\dfrac{4}{3}\pi (3.1)^3\\\\Volume = 39.72\pi\)
Hence, the volume of a sphere with a diameter of 6.2 in is 39.72π.
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A recipe calls for 2 tsp of oatmeal to make 7 protein bars.
How much oatmeal is needed to bake 27 protein bars?
A) 3 1/3 tsp
B) 9 tsp
C) 21 tsp
D) 81 tsp
Answers
Answer:
3 1/3 is the answer im pretty sure
Hudson went shopping for a new pair of sneakers. The listed price of the pair of sneakers was $29, but the price with tax came to $31.61. Find the percent sales tax.
Answers
Answer:
18
Step-by-step explanation:
multiply then add a all together
Proving Triangles Congruent: ASA AAS
Answers
The congruence theorem required for each figure are
1. AAS
2. ASA
3. ASA
4. ASA
5. ASA
6. ASA
What is ASA congruence theorem?ASA (Angle-Side-Angle) congruence theorem states that if two triangles have two angles and the included side in common, then they are congruent.
That is to say, if two angles and the included side of one triangle are congruent to the corresponding two angles and included side of another triangle, then the two triangles are congruent.
AAS (Angle-Angle-Side) congruence theorem states that if two angles and a non-included side of one triangle are congruent to the corresponding angles and non-included side of another triangle, then the two triangles are congruent.
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Consider the equation 5 +x=n.
What must be true about any value of x if n is a negative number?
Explain your answer.
Provide an example that would satisfy this condition.
Explain how you know your equation is correct.
Answers
Answer:
It's C.
Step-by-step explanation:
Any value of x must have a bigger negative number than 5. In this case, formally you say that all x values must be LESS than 5 only.
What is the vertex of the parabola
y = (x+3)^2 -4?
A. (-3,4)
B. (-3,-4)
C. (3,4)
D. (3,-4)
Answers
Answer:
D. X=-3(y + 3) - 4
Step-by-step explanation:
pls help me i’ll give ty brainlist
Answers
\(\sqrt{25*7x^{4}*x^{1} } \\=\sqrt{25*x^{4}*7 *x^{1} } \\=\sqrt{25x^{4} } *\sqrt{7x}\\=5x^{2} \sqrt{7x}\)
Option B is the answer.
Answer: C
i hope you can see my handwriting
You measure a foam roller in the shape of a cylinder. The foam roller has a diameter of 5.9375 inches and a height of 53.5 inches. About how many cubic inches of foam were used to make the roller?
Answers
Answer:
Volume V ≈ 1481.3269 cubic inches
Step-by-step explanation:
Volume V of a cylinder is given by the formula
V = πr²h where r = radius of the base of the cylinder and h the height
Here we are given the diameter, d = 5.9375 inches
Radius r = d/2 = 5.9375/2 = 2.96875 in
Height h = 53.5 in
V = π x 2.9685² x 53.5 ≈ 1481.3269 cubic inches
Answer V ≈ 1481.3269 cubic inches
find all solutions
36x²+12x=0
Answers
Answer:
x = -1/3 or 0
Step-by-step explanation:
Given equation:
\(36x^{2} + 12x = 0\)We can factor 12x on the L.H.S since 12x is divisible by 36x² and 12x.
\(\implies 36x^{2} + 12x = 0\)
\(\implies 12x(3x + 1) = 0\)
This can lead to two solutions. I have listed them below!
Solution 1:Divide 12x on both sides to open the parentheses.
\(\implies 12x(3x + 1) = 0\)
\(\implies \dfrac{12x(3x + 1)}{12} = \dfrac{0}{12}\)
Note: zero divided by any non-zero number is 0.
\(\implies \dfrac{12x(3x + 1)}{12} = \dfrac{0}{12}\)
\(\implies 3x + 1 = 0\)
Isolate 3x on one side of the equation.
\(\implies 3x + 1 = 0\)
\(\implies 3x = 0 - 1\)
\(\implies 3x = -1\)
Divide 3 both sides to determine the value of x.
\(\implies 3x = -1\)
\(\implies \dfrac{3x}{3} = \dfrac{-1}{3}\)
\(\implies \boxed{x = \dfrac{-1}{3}}\)
Solution 2:Divide (3x + 1) on both sides to isolate 12x.
\(\implies 12x(3x + 1) = 0\)
\(\implies \dfrac{12x(3x + 1)}{(3x + 1)} = \dfrac{0}{(3x + 1)}\)
Note: zero divided by any non-zero number is 0.
\(\implies \dfrac{12x(3x + 1)}{(3x + 1)} = \dfrac{0}{(3x + 1)}\)
\(\implies 12x = 0\)
Divide 12 both sides to determine the value of x.
\(\implies 12x = 0\)
\(\implies \dfrac{12x}{12} = \dfrac{0}{12}\)
\(\implies \boxed{x = 0}\)
Therefore, the solutions for x are -1/3 or 0.
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Answer:
x = 0 or x = -1/3
Step-by-step explanation:
In the equation 36x²+12x=0 we have :
36x² = 6x × (6x)
12x = 2 × (6x)
This means that 6x is a common factor,so let’s factor :
36x²+12x=0
⇔ 6x × (6x) + 2 × (6x) = 0
⇔ 6x × (6x + 2) = 0
⇔ 6x = 0 or 6x + 2 = 0
⇔ x = 0 or x = -2/6
Find the value of 3a when a = -4.
(b)- 7
(d) -12
(a) 7
(c) 12
Answers
Answer:
(d) -12
Step-by-step explanation:
3a = _____
a = -4
3(-4) = ___
3(-4) = -12
The answer is (d) -12
The cost of Nate's dinner including a 15% tip was $43.70. What was the cost of dinner alone?
Answers
Answer:
The cost of dinner alone was $37.145
Step-by-step explanation:
15%=0.15----Convert your percentage into a decimal
43.70*0.15=6.555----Multiply the cost of dinner with the decimal
$43.70-$6.555=$37.145----Subtract the last number(6.555) from the total(43.70) to get the cost of dinner alone of $37.145 -This is making you subtract the percentage from the total!
I hope this helped!
How to apply the distributive property to
\( - 9x(5j + k) = \)
create an equivalent expression-9
*(5j+k)=
Answers
Answer:
-9x(5j) + -9x(k)
Step-by-step explanation:
distribute -9x by multiplying it with the different numbers in the parenthesis
please help lolol.....
Answers
Answer:
2
Step-by-step explanation:
cuz
Answer:
What is the area of the polygon given below? Please explain how
Someone help with this equation
Answers
The answer is:
g(x + 1) = 6x + 1
g(4x) = 24x -5
Work/explanation:
To evaluate, I plug in x + 1 into the function:
\(\sf{g(x)=6x-5}\)
\(\sf{g(x+1)=6(x+1)-5}\)
Simplify
\(\sf{g(x+1)=6x+6-5}\)
\(\sf{g(x+1)=6x+1}\)
------------------
Do the same thing with g(4x)
\(\sf{g(4x)=6(4x)-5}\)
\(\sf{g(4x)=24x-5}\)
Hence, these are the answers.
The House of Pizza say that their pizzas are 14 inches wide, but when you measured it, the pizza was 12 inches. What is your percent error? Make sure to include your percent sign! (Round to 2 decimals)
Answers
The percent error of the house of the pizza would be 2.
How to calculate the percent error?Suppose the actual value and the estimated values after the measurement are obtained. Then we have:
Error = Actual value - Estimated value
To determine the percent error, we will measure how much percent of the actual value, the error is, in the estimated value.
We have been given that House of Pizza says that their pizzas are 14 inches wide, but when measured, the pizza was 12 inches.
WE know that Error = Actual value - Estimated value
Then Error = 14 - 12 = 2
Therefore, the percent error would be 2.
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Which expression is always equivalent to sin x when 0° < x < 90°?
(1) cos (90°- x)
(3) cos (2x)
(2) cos (45° - x)
(4) cos x
Answers
The expression that is always equivalent to sin x when 0° < x < 90° is (1) cos (90° - x). Option 1
To understand why, let's analyze the trigonometric functions involved. In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Since we are considering angles between 0° and 90°, we can guarantee that the side opposite the angle will always be the shortest side of the triangle, and the hypotenuse will be the longest side.
Now let's examine the expression cos (90° - x). The cosine of an angle is defined as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. In a right triangle, when we subtract an angle x from 90°, we are left with the complementary angle to x. This means that the remaining angle in the triangle is 90° - x.
Since the side adjacent to the angle 90° - x is the same as the side opposite the angle x, and the hypotenuse is the same, the ratio of the adjacent side to the hypotenuse remains the same. Therefore, cos (90° - x) is equivalent to sin x for angles between 0° and 90°.
On the other hand, options (2) cos (45° - x) and (3) cos (2x) do not always yield the same value as sin x for all angles between 0° and 90°. The expression cos x (option 4) is equivalent to sin (90° - x), not sin x.
Option 1 is correct.
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Arrange the steps in order to simplify the expression
Answers
Answer:
Step-by-step explanation:
For step explanation:
1. write the problem
2. distinguishing the neg sign
3. distributing 3
4. moving like terms next to each other through commutative property
5. Combining like terms
6. getting rid of parentheses
the area of a circle is 144m2 What is the diameter of the circle
Answers
Step-by-step explanation:
AREA = pi r^2
144 = pi r^2 shows r = 6.77 m ( or sqrt ( 144/pi) )
then diameter = 2 * r = 13.54 m (or 2 sqrt (144/pi) )
Answer:
7.64
Step-by-step explanation
This is what I did so I take the root of 144 = 12 and 12/3.14 = roughly 3.82 thats the radius and that times 2 = 7.64 have a great day success to homework yay! Have a great day!!! :D
Jesus Christ is our lord and savior he died for us on the Christ because he loves us and wants entirety hapiness for us❤️Amen
Answers
Answer:
AMEN YOU PREACH!!!!1
Step-by-step explanation:
SPREAD THE GOOD NEWS!!!
Answer:
praise him let him know that we are here
Step-by-step explanation:
AMEN!!!!!
go to world harvest next year
Church school
Find the area and perimeter
Answers
Answer:
A = 31.36
P = 22.4
Answer:
31.36 cm 2 : 22.4 cm 2
Step-by-step explanation:
Perimeter: 5.6*4=22.4
Area: 5.6*5.6=31.36
hacmin birimi ...... ve ......dır
Answers
Answer:
?
Step-by-step explanation:
don't get your question
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*..
IM GIVING 40 POINTS !! DONT SKIP :((.
Answers
Answer:
Step-by-step explanation:
Part A: Maci made $170 grooming dogs one day with her mobile dog grooming business. She charges $60 per appointment and earned $50 in tips. Write an equation to represent this situation and solve the equation to determine how many appointments Maci had.
Part B: Logan made a profit of $235 as a mobile groomer. He charged $75 per appointment and received $40 in tips, but also had to pay a rental fee for the truck of $10 per appointment. Write an equation to represent this situation and solve the equation to determine how many appointments Logan had.
Answers
Maci and 2 appointments and Logan had 3 appointments.
How many appointments did Maci and Logan have?The linear equation that represents the total amount earned by Maci is:
Total amount earned = (amount per appointment x number of appointments) + tips
$170 = ($60 x a) + $50
$170 = $60a + $50
$170 - $50 = $60a
$120 = $60a
a = $120 / $60
a = 2
The linear equation that represents the total amount earned by Logan is:
Profit = total revenue - total cost
Profit = (fee per appointment x number of appointments) + amount received in tips - (rental fee x number of appointments)
$235 = ($75 x a) + $40 - ($10 x a)
$235 = $75a + $40 - $10a
$235 = $65a + $40
$235 - $40 = $65a
$195 = $65a
a = $195 / 65
a = 3
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are ratios 15:20 and 1:10 equivalent
Answers
If you simplify 15:20 by dividing 15 and 20 by 5, you’ll get 1:4.
And 1:4 is not equal or proportional to 1:10.
Therefore, the given ratios are not equivalent.
a carpenter has 6 boards that are each 7/8 yard long. how many 3/4 yard sections of board can he construct
Answers
The number of sections of board that he can construct will be equal to 7.
We are given that:
A carpenter has 6 boards.
Length of each board = 7 / 8 yard long
Now, we will use multiplication.
Total length of cardboards available = 7 / 8 × 6 yards
Total length = 42 / 8 yards
Total length = 21 / 4 yards.
Now, 3/4 yard sections of board that he can construct will be:
Number of sections of board = 21 / 4 ÷ 3 / 4
Number of sections of board = 21 / 3
Number of sections of board = 7
Therefore, the number of sections of board that he can construct will be equal to 7.
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