Answer:
x = 3 or x = 6/5
Step-by-step explanation:
The zero product property (or rule) tells you the product will only be zero if one (or more) of the factors is zero. Here, that means the solutions are values of x such that ...
x -3 = 0 ⇒ x = 3
5x -6 = 0 ⇒ x = 6/5
Elijah and Jonathan play on the same soccer team. They have played 3 of their 15,
games. They each create a model to represent x, the number of games their team has left
to play. Their models are shown below. Explain whether each model is correct.
Who is correct
Answer:
Only Elijah's model is correct
Step-by-step explanation:
The data given in the question tells us they have 12 games left on their soccer team. Each one of them tried to simulate the fact by creating some model which look like a balance between quantities.
Elijah placed 3 cubes of value 1 and a cube of value x on one side of a balance. On the other side, he placed 15 cubes of value 1. He was obviously modeling the fact that 15 cubes (games due to play in our case) should be equal to 3 cubes (games already played) plus the x numbers left to play
This model if perfect, since the only way to equilibrate the balance is setting x to 12, the games left to play
Jonathan used a table with 3 x's in a row and a 15 in the second row, trying to model the same situation. To our interpretation, this table doesn't show the number of games left to play. If we equate 3x = 15, we get x=5 which has nothing to do with the situation explained in the question, so this model is not correct.
Elijah's model is correct .
Elijah and Jonathan play on the same soccer team. They have played 3 of their 15 games.
x is the number of games that are left to be played.
Elijah and Jonathan have 12 games left on their soccer team.
Elijah and Jonathan both try to simulate the situation which are shown in figure.
Creating some model which look like a balance between quantities.
Elijah placed 3 cubes of value 1 and a cube of value x on one side of a balance.
On the other side Elijah placed 15 cubes.
The value of each cube = 1
so 15 [tex]\times 1 = 15[/tex] which are equal to total number of games.
Since 3 games are already played so on the left hand side
3 boxes of magnitude 1 each are placed.
[tex]x[/tex] is the number of games that are left.
Jonathan uses a table with three x values in a row and a 15 is the total number of games to be played are represented in the second row trying to model the same situation.
This table doesn't show the number of games left to play.
Which are 12 in number
According to Jonathan's model
[tex]3x = 15 \\x =5[/tex]
This does not model the number of games left which are 12 in number and hence
Jonathan's model does not explains the situation
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Help with question 1 please.
Answer:
x is more than or equal to 35
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.
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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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
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.
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.Richard paints a picture on a rectangular canvas that is 3 feet by 2.64 feet. What is the area in Richards painting?
Answer:
7.92 Feet
Step-by-step explanation:
Since area is Length × Height in comparison to perimeter being Length + Length + Height + Height, the equation is simply:
3 × 2.64 = 7.92 Feet
Final answer:
The area of Richard's painting is calculated by multiplying the length of 3 feet by the width of 2.64 feet, which equals 7.92 square feet.
Explanation:
To calculate the area of Richard's rectangular painting, we use the formula for the area of a rectangle, which is the product of its length and width. In this case, the length of the canvas is 3 feet and the width is 2.64 feet. So, the calculation to find the area will be as follows:
Area = Length × Width
Area = 3 feet × 2.64 feet
Area = 7.92 square feet
Therefore, the area of Richard's painting is 7.92 square feet.
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.
A line segment has endpoints of (-3, 2) and (5, -2). Find the distance between the endpoints.
Round your answer to the nearest tenth (one number past the decimal). If the second number past the decimal is 5 or greater, round up.
Answer:
[tex]d=8.9\ units[/tex]
Step-by-step explanation:
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
(-3, 2) and (5, -2)
substitute the values in the formula
[tex]d=\sqrt{(-2-2)^{2}+(5+3)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(8)^{2}}[/tex]
[tex]d=\sqrt{80}\ units[/tex]
[tex]d=8.94\ units[/tex]
Round to the nearest tenth
[tex]d=8.9\ units[/tex]
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%.
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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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.
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
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.
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.
If h(x) = 5 + x and k(x)= 1/x, which expression is equivalent to (kxh)(X)?
Answer:
It can be solve this in two ways,
1) as if the h(x) = 5x and 2) as if h(x) = 5 + x
1) If h(x) = 5x and k(x) = 1/x
Then (k o h) (x) = k ( h(x) ) = k(5x) = 1/(5x)
2) If h(x) = 5 + x and k (x) = 1/x
Then (k x h)(x) =k ( h(x) ) = k (5+x) = 1 / [5 + x]
1/(5+x) is the correct answer
Step-by-step explanation:
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.
Which of the following is a step in simplifying the expression (see first image)
(the second image is the options for multiple choice)
Please be serious and don't joke around! <3 I really need help.
Answer:
D) (x^-3*y^-12)/(x^15*y^-15)
Step-by-step explanation:
If you simplify that further, then you'll get x^(-18)*y^3.
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
HELP ME YOU MUST EXPLAIN THE ANSWER
Answer: 4) 7c ^2d - 7c + 4d - 10
Explanation:
First write equastion as seen:
5c^2d - 4c + 3d - 3 + 2c^d - 3c+ d - 7
Next add the c^2d’s together:
7c^2d - 4c + 3d - 3 + 3c + d - 7
Add the c’s together:
7c^2d - 7c + 3d - 3 + d - 7
Add the d’s:
7c^2d - 7c + 4d - 3 - 7
Lastly add the normal numbers:
7c^2d - 7c + 4d - 10
Thus, that is your answer!
Hope this helps! :)
Does the arrow show a vertex,face,or edge?
Answer:
Face, beacuse it's pointing at the flat surface
The function shown below was created to track the different intervals of speed that an automobile travels over a period of 28 seconds. Use the graph of the function to complete Parts 1-3. After traveling for 16 seconds, the automobile begins to slow its speed at a steady rate. Use the coordinates on the graph to determine the rate at which the car is slowing down, in miles per hour per second. During which interval of time does the automobile experience the greatest change in its speed? What is the change in the automobile’s speed during this interval? For a time period of approximately 10 seconds, the automobile experiences no change in its speed. During which interval of time does the automobile’s speed remain constant? At what speed is the automobile traveling during this interval?
Answer:
1. The car is slowing down at a rate of 2.5mph/s
2. The greatest acceleration is 10 mph/s.
3. In the interval 4s to 16s the speed remains constant and has magnitude 25 mph.
Step-by-step explanation:
1. The deceleration of the car is from 16 seconds to 24 seconds is the slope [tex]m[/tex] of the graph from 16 to 24:
[tex]m=\dfrac{\Delta speed }{\Delta time } = \dfrac{5-25}{24-16} =-2.5mph/s[/tex]
the negative sign indicates that it is deceleration.
2. The automobile experiences the greatest change in speed when the slope is greatest because that is when acceleration/deceleration is greatest.
From the graph we see that the greatest slope of the graph is between 28 and 24 seconds. The acceleration the interval is the slope [tex]m[/tex]:
[tex]m= \dfrac{45-5}{28-24}= 10mph/s[/tex]
3. The automobile experiences no acceleration in the interval 4 s to 16 s—that's the graph is flat.
The speed of the automobile in that interval, as we see from the graph, is 25 mph.
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
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.
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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What is the solution set of 4x^2-36= 0?
(-3)
(3)
(-3,3)
Answer:
(-3, 3).
Step-by-step explanation:
4x^2-36= 0
4x^2 = 36 Taking square roots of both sides:
2x = +/- 6
x = +/- 3.
Answer:
(-3, 3)
Step-by-step explanation:
The equation is:
[tex]4x^2-36=0[/tex]
to clear for x, first we move the -36 to the right as a +36 (or you can also say that we add 36 to both sides):
[tex]4x^2=36[/tex]
dividing by 4:
[tex]x^2=36/4\\x^2=9[/tex]
taking the square root:
[tex]x=[/tex] ± [tex]\sqrt{9}[/tex]
we add the ± because a square root has two solutions, a positive one, and a negative one.
Then we get:
[tex]x=[/tex] ± 3
The solutions are -3 and +3
which is represented in the option (-3, 3)
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
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.