Answer: x=-1,-2
Step-by-step explanation:
X^2+3x+2=0
(x+1)(x+2)=0
x=-1,-2
A bathtub is filling with water at a rate of 60 liters per minute. How many liters of water are in the bathtub after t minutes? Write your answer as an expression.
Answer:
There are 60t liters of water in the bathtub after t minutes.
After t minutes, [tex]\( 60t \)[/tex] liters of water fill the bathtub.
The amount of water in the bathtub after t minutes can be expressed as the product of the rate of filling (60 liters per minute) and the time (t minutes):
[tex]\[ \text{Amount of water} = \text{Rate of filling} \times \text{Time} \][/tex]
[tex]\[ \text{Amount of water} = 60 \text{ liters/minute} \times t \text{ minutes} \][/tex]
[tex]\[ \text{Amount of water} = 60t \text{ liters} \][/tex]
So, after [tex]\( t \)[/tex] minutes, there will be [tex]\( 60t \)[/tex] liters of water in the bathtub.
A charity received a donation of 25.6 million. If this represents 54% of the charity‘s donated funds, what is the total amount of it’s donated funds. Round your answer to the nearest million
Answer:
Step-by-step explanation:
100%-54%=46%
46%*25.6m=11,776,000
25,600,000+11,776,000=
37,376,000 Answer
solve the system of equations y=x^2+3-6 y=2x-6
The solutions of the system of equations are (0 , -6) , (-1 , -8)
Step-by-step explanation:
To solve a system of equations, one 1st degree and the other 2nd degree, do that:
Use the 1st degree equation to find one variable in terms of other variableSubstitute this variable in the 2nd degree equation and solve it to find the other variableSubstitute the value of the other variable in the 1st degree equation to find the first variable∵ The system of equations is:
y = x² + 3x - 6 ⇒ (1)
y = 2x - 6 ⇒ (2)
Equate (1) and (2)
∴ x² + 3x - 6 = 2x - 6
- Add 6 to both sides
∴ x² + 3x = 2x
- Subtract 2x from both sides
∴ x² + x = 0
- Take x as a common factor in the left hand side
∴ x(x + 1) = 0
- Equate each factor by 0 to find the values of x
∵ x = 0
∴ The first value of x is 0
∵ x + 1 = 0
- Subtract 1 from each side
∴ x = -1
∴ The second value of x is -1
Substitute each value of x in equation (2) to find the values of y
∵ y = 2(0) - 6
∴ y = 0 - 6 = -6
The first value of y is -6
∵ y = 2(-1) - 6
∴ y = -2 - 6 = -8
∴ The second value of y is -8
∴ The solutions are (0 , -6) , (-1 , -8)
The solutions of the system of equations are (0 , -6) , (-1 , -8)
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Aiden and three of his friends were roasting pumpkin seeds. There were 236 pumpkin seeds. If each person wanted an equal portion, how many pumpkin seeds will each boy get
Answer:
Each boy would get 59 seeds
Step-by-step explanation:
Aiden and his three friends = 4 people
236 divided by 4 = 59
Each boy will get 59 pumpkin seeds.
Explanation:In this problem, Aiden and his three friends are sharing 236 pumpkin seeds equally. To find out how many pumpkin seeds each boy will get, we can divide the total number of seeds by the number of boys.
Divide the total number of pumpkin seeds, 236, by the number of boys, which is 4.
So, each boy will get 236 ÷ 4 = 59 pumpkin seeds.
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Write the expression in simplest form.
(-11/2 x + 3)-2(-11/4x-5/2
Answer:
The solution of expression in the simplest form is 8
Step-by-step explanation:
Given as :
The expression is written
( [tex]\dfrac{-11 }{2}[/tex]x + 3 ) - 2 ( - [tex]\dfrac{11 }{4}[/tex]x - [tex]\dfrac{5 }{2}[/tex])
Or, ( [tex]\dfrac{-11 }{2}[/tex]x + 3 ) +[tex]\frac{11\times 2}{4}[/tex]x+ [tex]\frac{5\times 2}{2}[/tex]
Now, separate the variable terms
Or, ( [tex]\dfrac{-11 }{2}[/tex] + [tex]\frac{11\times 2}{4}[/tex]) x + 3 + 5
Or, ( 0) × x + 8
or , 0 + 8
∴ 8
The simplest form if expression is 8
Hence The solution of expression in the simplest form is 8 . Answer
What is the length of the blue segment in A below?
Answer:
Step-by-step explanation:
L= 6.47 units is the answer for APEX
Answer:
B. 6.4
Step-by-step explanation:
We need to recall the theory of the chord distance to the center which tells that the two congruent chords are equidistant from the center of the circle.
In this situation, A is the center point, CR and BE are congruent with the length of 5,27. So, the distance from A to CR must be equal to the distance from A to BE. Hence, the length of the blue segment in A below is 6.4
Hope it will find you well.
Does the arrow show a vertex,face,or edge?
Answer:
Face, beacuse it's pointing at the flat surface
Which two mountain peaks combined are 56,190 feet tall?
Answer:
Everest and k2
Step-by-step explanation:
Answer:
its k2 and lhotse
Step-by-step explanation: 28,250 + 27, 940= 56, 190 because 0+ 0 =0
4+5 =9 9+ 2 = 11 carry the 1 8 + 7 +1 = 16 carry the 1 2+2+1 =5 so that equals 56,190 ft
The base of an isosceles triangle is one half as long as each of the congruent sides. The perimeter is 55 in. How long is the base?
Answer:
The base is 11 inches long
Step-by-step explanation:
we know that
An isosceles triangle has two equal sides and two equal interior angles
Let
y -----> is the length of the base of the isosceles triangle
x ----> is the length of each of the congruent sides
The perimeter of the triangle is equal to
[tex]P=y+x+x[/tex]
[tex]P=y+2x[/tex]
we have
[tex]P=55\ in[/tex]
so
[tex]55=y+2x[/tex] ----> equation A
[tex]y=\frac{x}{2}[/tex] ----> equation B
solve the system by substitution
substitute equation B in equation A
[tex]55=\frac{x}{2}+2x[/tex]
solve for x
[tex]55=\frac{5}{2}x[/tex]
[tex]x=55(2)/5\\x=22\ in[/tex]
Find the value of y
[tex]y=\frac{x}{2}[/tex] ----> [tex]y=\frac{22}{2}=11\ in[/tex]
therefore
The base is 11 inches long
Given that (3, 3, -2) is a solution to the given
system, which of the following statements are
possibly true of the system?
Check all of the boxes that apply.
The three planes represented by the
equations in the system are parallel.
The system is consistent.
The system is inconsistent.
The system is independent.
Answer: B & D
Step-by-step explanation:
The system is consistent.
The system is independent.
Svetlana’s hair is 3 cm long. Her hair grows 1.5 cm per month. Svetlana wanted her hair to be less then 18 cm long. Write an inequality to determine the number of months Svetlana can allow her hair to grow. Then, solve the inequality.
Svetlana can allow her hair to grow for 10 months.
Step-by-step explanation:
Current length of hair = 3cm
Growth per month = 1.5cm
Let, m be the number of months.
As she wants her hair no longer than 18cm, therefore, according to given statement;
1.5m + current length of her hair ≤ 18
[tex]1.5m+3\leq 18\\1.5m\leq 18-3\\1.5m\leq 15[/tex]
Dividing both sides by 1.5
[tex]\frac{1.5m}{1.5}\leq \frac{15}{1.5}\\m\leq 10[/tex]
Svetlana can allow her hair to grow for 10 months.
Keywords: linear inequality, division
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Choose the definition for the function.
Please need help badly!!!
Answer:
b
Step-by-step explanation:
Both graphs end or start at at x = 2
The lower graph has an open circle at 2 meaning that x cannot equal 2
Thus y = x + 1 for x < 2
The upper graph has a solid circle at x = 2 meaning that x can equal 2
Thus y = x + 2 for x ≥ 2
The arc length of a circle of radius 4 is 6.9813. What is the central angle created by the arc? Round
to the nearest whole number.
The central angle created by an arc length of 6.9813 in a circle with a radius of 4 is approximately 100 degrees when rounded to the nearest whole number.
The student is asking about the relationship between the arc length of a circle, the radius of the circle, and the central angle created by this arc. To find the central angle from the arc length and the radius, we use the formula:
arc length (As) = radius (r) x central angle (θ)
Here, we're given the arc length as 6.9813 and the radius as 4. Since the central angle is usually given in radians, we first perform the calculation in radians and then convert it to degrees if necessary.
The central angle in radians is:
θ (in radians) = arc length / radius
θ = 6.9813 / 4 ≈ 1.7453 radians
To convert radians to degrees, we multiply by,
(180/π).
Thus,
θ (in degrees) ≈ 1.7453 x (180/π) ≈ 100 degrees
And when rounded to the nearest whole number:
θ ≈ 100 degrees
So, the central angle created by the arc is approximately 100 degrees.
One of the solutions to the equation 5x^2+bx+12=0 is − 4/5 . Find the other solution.
Answer:
-3 is the other solution.
Step-by-step explanation:
As, [tex]\frac{-4}{5}[/tex] is One of the solutions of the equations , So, it should satisfy the equation.
Putting [tex]\frac{-4}{5}[/tex] in equation 5[tex]x^{2}[/tex] + bx + 12 = 0 ,
We get,
5×[tex]\frac{-4}{5}[/tex]×[tex]\frac{-4}{5}[/tex] + b×[tex]\frac{-4}{5}[/tex] + 12 = 0.
5×[tex]\frac{16}{25}[/tex] + [tex]\frac{-4b}{5}[/tex] + 12 = 0.
After solving , 16 - 4b + 60 = 0.
4b = 76
b = 19.
So, the equation is 5[tex]x^{2}[/tex] + 19x + 12 = 0.
After factorizing , 5[tex]x^{2}[/tex] + 15x + 4x + 12 = 0.
5x(x+3) + 4(x+3) = 0
(5x+4)(x+3) = 0
Clearly the roots of the equation are -3 and [tex]\frac{-4}{5}[/tex] .
So, the other solution is -3.
What is the first step in solving -5x-1/6>3/2
You add 1/6 to both sides
Step-by-step explanation:
Answer:
A is the correct answer
Step-by-step explanation:
Add 1/6 to both sides
Which is the graph of 3x-4y = 6
Note that this is the equation of a line, since you can rewrite it as
[tex]3x-4y=6 \iff 4y=3x-6 \iff y=\dfrac{3}{4}x-\dfrac{3}{2}[/tex]
Now just choose two values for x and compute the correspondent y values:
[tex]x=0 \implies y=-\dfrac{3}{2}[/tex]
So, the line passes through the point (0, -3/2).
[tex]x=2 \implies y=\dfrac{3}{2}-\dfrac{3}{2}=0[/tex]
So, the line passes through the point (2, 0)
Now, draw on a coordinate plane the two points and connect them, and you'll have the line.
Anyone help with linear inequalities?
Answer:
Yeah I'm here harmony plz tell
Step-by-step explanation:
Greenfield village is spread across 240 acres of land. Only 37% of the land is used for the exhibits, while the rest of the land consists of forest, rivers and pastures. How many acres are used for exhibits?
88.8 acres are used for exhibits
Step-by-step explanation:
Given
Total area of Greenfield = 24 acres
Percentage of lad for exhibits = 37%
Now,
[tex]Acres\ used\ for\ exhibits = 37\%\ of\ 240\\= \frac{37}{100} * 240\\=0.37*240\\=88.8\ acres[/tex]
Hence,
88.8 acres are used for exhibits
Keywords: Percentage, percent
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A 72,000 gallon water tower is being drained. Two thousand gallons are drained in the first hour. How many hours will it take to drain the water tower?
Answer:
To drain the water tower it will take 36 hours.
Step-by-step explanation:
Given:
A 72,000 water tower is being drained, and in an hour 2000 gallons are drained.
Now, to calculate the hours it would take to drain total 72,000 gallons of water, we should divide the gallons of water drained in one hour by total gallons of water in the tower.
Gallons of total water in the tower ÷ Gallons of water drained per hour
[tex]72000\div 2000[/tex]
[tex]=\ 36[/tex]
Therefore, to drain the water tower it will take 36 hours.
The sides of an equilateral triangle are 8 units long. What is the length of the altitude of the triangle?
5 StartRoot 2 EndRoot units
4 StartRoot 3 EndRoot units
10 StartRoot 2 EndRoot units
16 StartRoot 5 EndRoot units
Answer:The perimeter of parallelogram PQRS = 2\sqrt{10}+8\sqrt{2} ⇒
2nd answer
Step-by-step explanation:* Lets revise some properties of the parallelogram
- Each two opposite sides are parallel
- Each two opposite sides are equal
- Its perimeter is the twice the sum of two adjacent sides
* Lets solve the problem
∵ PQRS is a parallelogram
∵ The length of side SR is
∵ The length of side QR is
∵ SR and RQ are two adjacent sides
∵ The perimeter of parallelogram PQRS = 2(RQ + SR)
∴ The perimeter of parallelogram PQRS =
∵ =
∵ =
∴ The perimeter of parallelogram PQRS =
Answer:
Option B.
Step-by-step explanation:
It is given that the sides of an equilateral triangle are 8 units long.
Draw an altitude of the triangle.
Altitude of an equilateral triangle is perpendicular bisector.
Let x be the length of the altitude of the triangle.
According to the Pythagoras theorem
[tex]hypotenuse^2=base^2+perpendicular^2[/tex]
Using Pythagoras theorem we get
[tex]8^2=4^2+x^2[/tex]
[tex]64=16+x^2[/tex]
[tex]64-16=x^2[/tex]
[tex]48=x^2[/tex]
Taking square root on both sides.
[tex]\sqrt{48}=x[/tex]
[tex]4\sqrt{3}=x[/tex]
The length of the altitude of the triangle is 4√3 units.
Therefore, the correct option is B.
True or False: The given number is a solution to the corresponding equation
a=−3
4a+3=−9
Answer:
TRUE.
a = -3 is a Solution to the equation 4a + 3 = -9
Step-by-step explanation:
Given:
a = -3
4a + 3 = -9
Proof for Solution:
Let there be two part of the equation, left-hand side and right hand side.
If a = -3 is a solution ,
left-hand side = right hand side
left-hand side = 4a +3
= 4×-3 + 3...............{ For a = -3}
= -12 + 3
= -9
= right hand side
∴ left-hand side = right hand side
∴ a = -3 is a Solution to the equation 4a + 3 = -9
You pay $6 in tax on a $30 purchase. What is the tax percent.
Answer:
20%
Step-by-step explanation:
Help with hw due tomorrow plz help!!!!!!!!
Answer: see the explanation
Step-by-step explanation:
Add the price of the item and the tax on the item, or just multiply the price of the item by the tax rate plus 1 (to include the price of the item)
Let's say the cost of an item is
100 dollars and the tax rate is 5% or 0.05. To get the amount of tax that has to be paid on
the $100 item, multiply 100 by 0.05 to get 5 .
Add the amount of the tax ( $5 ) to the price of the item ( $100) to get a total cost of $100.
Or you could multiply 100 by 1+0.05 or 1.05 to get the same answer. The reason why the
1 can be added in is because the total cost includes the price of the item, not just the sales tax on it.
Which of the numbers 285, 629, 5490, 7392, 15708, 43695 are divisible by 3 but not by 9.
Answer:
285, 629, 7392, 15708,43695
Step-by-step explanation:
If you add the digits of the number together, it should be divisible by 9. If it isn't, then it must be a multiple of only 3, not 9.
Step-by-step explanation:
We need to find which of the numbers 285, 629, 5490, 7392, 15708, 43695 are divisible by 3 but not by 9.
285
285 ÷ 3 = 95 Divisible
285 ÷ 9 = 31.66 Not divisible.
Correct
629
629 ÷ 3 = 209.67 Not divisible
629 ÷ 9 = 69.89 Not divisible.
Not correct
5490
5490 ÷ 3 = 1830 Divisible
5490 ÷ 9 = 610 Divisible.
Not correct
7392
7392 ÷ 3 = 2464 Divisible
7392 ÷ 9 = 821.33 Not divisible.
Correct
15708
15708 ÷ 3 = 5236 Divisible
15708 ÷ 9 = 1745.33 Not divisible.
Correct
43695
43695 ÷ 3 = 14565 Divisible
43695 ÷ 9 = 4855 Divisible.
Not correct
Divisible by 3 and not by 9 are 285, 7392 and 15708.
There are 6 blades on each windmill. How many total blades are on 7 windmills? Use a five fact to solve
Answer:
42 Blades
Step-by-step explanation:
So 6 blades on each windmill
6=1 Windmill
so 7 windmills
so do
7 times 6 = 42 Blades
The total number of blades in 7 windmills is required.
42 blades are the total number of blades.
The number of blades in 1 windmill is 6 blades
[tex]1\ \text{windmill}=6\ \text{blades}[/tex]
There are 7 windmills
[tex]7\ \text{windmills}=7\times 6[/tex]
Using five fact
[tex]=(5\times 8)+(2\times 1) =42\ \text{blades}[/tex]
The total number of blades of the windmills are 42.
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For the following exercises, write the interval in set-builder notation
10. (-infinity, 6)
11. (4, infinity)
12. [-3,5)
13. [-4,1]U[9, infinity)
14. (-infinity, infinity)
Final answer:
Set-builder notation is a method to define intervals through a property shared by all members. The notation for the given intervals includes conditions that represent the endpoints or infinity, expressing the range of the variable in each set.
Explanation:
Writing intervals in set-builder notation involves describing a set through a property that its members share. Here is the set-builder notation for each interval provided:
10. (-infinity, 6) in set-builder notation is: [tex]\{x | x < 6\}[/tex]11. (4, infinity) in set-builder notation is:[tex]\{x | x > 4\}[/tex]12. [-3,5) in set-builder notation is: [tex]\{x | -3 \leq x < 5\}[/tex]13. [-4,1]U[9, infinity) in set-builder notation is: [tex]\{x | -4 \leq x \leq 1\} \cup \{x | x \geq 9\}[/tex]14. (-infinity, infinity) in set-builder notation is simply the set of all real numbers, which can be written as: [tex]\{x | x \text{ is a real number}\}[/tex]To express these sets, we use 'x' as our variable and conditions such as x < 6 that define the range of values 'x' can take. The 'U' symbol represents the union of two sets, indicating that the set includes all elements from both intervals.
A beverage company wanted to see if people in the United States liked their new logo. Which choice best represents a population? Every person in the United States. A selection of logo artists. 3,800 children age 5 - 15
Answer:
Every person in the US.
Step-by-step explanation:
If a selection of logo artists are asked whether they like or not the new logo, their answer will represent only the opinion of a specific group of artists of the US, and this is not the objective of the beverage company,who wants to know if people from the United States like their logo.If 3,800 children age 5-15 are asked whether they like the logo or not, their opinion will only represent the opinion of some children in the US, whose age is between 5 and 15, and again, this is not the objective of the beverage company,who wants to know if people from the United States like their logo.Finally, the population (which by definition includes all the elements under study, in this case, all the people in the US) will be defined by all people in the US: if the company wants to know if people from the US like their new logo, they must take into account that, the population under study is all people, and not a biased selection of it.Helene invested a total of $1,000 in two simple-interest bank accounts. One account paid 6% annual
interest; the other paid 7% annual interest. The total amount of interest she earned after one year was
$66. Enter and solve a system of equations to find the amount invested in each account. Enter the interest
rates in order as given in the problem. (Hint: Change the interest rates into decimals first.)
x+y = 1,000
0.06
x+ 0.07
y = 66
Helene invested $
at 6% and $
at 7%.
Answer:
Helene invested $ 400 at 6% and $ 600 at 7%.
Step-by-step explanation:
Let
x -----> the amount invested at 6%
y -----> the amount invested at 7%
we know that
The interest earned with the amount invested at 6% plus the interest earned by the amount invested at 7% must be equal to $66
Remember that
[tex]6\%=6/100=0.06\\7\%=7/100=0.07[/tex]
so
[tex]x+y=1,000[/tex] ----> equation A
[tex]0.06x+0.07y=66[/tex] ----> equation B
Solve the system of equations by graphing
The solution of the system is the intersection point both graphs
using a graphing tool
The solution is the point (400,600)
see the attached figure
therefore
Helene invested $ 400 at 6% and $ 600 at 7%.
What is the equation for the line?
Answer:
y=-4x+5
Step-by-step explanation:
the line goes down 4 for every 1 that x changes. the line crosses the y axis at 5.
(this might not be accurate, I can't really see if the line is on the exact point or not)
Answer:
[tex]\displaystyle y = -4x + 5[/tex]
Step-by-step explanation:
Starting from the y-intercept of [tex]\displaystyle [0, 5],[/tex]you do [tex]\displaystyle \frac{rise}{run}[/tex]by either moving four blocks north over one block west or four blocks south over one block east [west and south are negatives].
I am joyous to assist you anytime.
The sum of three consecutive integers is 105. What are the three integers?
Answer:
34, 35, 36
Step-by-step explanation:
34 + 35 + 36 = 105
Answer:
34
35
36
Step-by-step explanation:
Here we will use algebra to find three consecutive integers whose sum is 105.
We assign X to the first integer. Since they are consecutive, it means that the 2nd number will be X+1 and the third number will be X+2 and they should all add up to 105. Therefore, you can write the equation as follows:
X + X + 1 + X + 2 = 105
To solve for X, you first add the integers together and the X variables together. Then you subtract 3 from each side, followed by dividing by 3 on each side. Here is the work to show our math:
X + X + 1 + X + 2 = 105
3X + 3 = 105
3X + 3 - 3 = 105 - 3
3X = 102
3X/3 = 102/3
X = 34
Which means that the first number is 34, the second number is 34+1 and third number is 34+2. Therefore, three consecutive integers that add up to 105 are:
34
35
36