The expression of the statement is x³ - 7
How to determine the representation of the statement?The statement is given as
7 is subtracted from the cube of a number.
Represent the number as x
So, we have the following representation
"7 is subtracted from the cube of a number" ⇒ 7 is subtracted from the cube of x
The cube of x can be represented as x^3
So, we have
"7 is subtracted from the cube of a number" ⇒ 7 is subtracted from x³
"7 is subtracted" means minus 7
So, we have
"7 is subtracted from the cube of a number" ⇒ x³ minus 7
Rewrite as
"7 is subtracted from the cube of a number" ⇒ x³ - 7
Hence, the expression is x³ - 7
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2) Suve the following quadratic equations la, quadratic for naudas i) 2x²+7+3=0 ii) 6x²-5x=8
Answer: x = -1/2 and x = -3
Given the following quadratic function
[tex]2x^2\text{ + 7x + 3 = 0}[/tex][tex]\begin{gathered} \text{The standard form of a quadratic function is given as} \\ ax^2\text{ + bx + c = 0} \\ \text{a = 2 , b = 7 and c = 3} \\ \text{ find ac} \\ ac\text{ = 2 x 3} \\ ac\text{ = 6} \\ \text{ Find the factors of ac (6) when add that will give us 7x} \\ \text{The factor is 6 and 1} \\ 2x^2\text{ + 6x + x + 3 = 0} \\ 2x(\text{x + 3) + 1 (x + 3)} \\ (2x\text{ + 1) = 0 or (x + 3) = 0} \\ 2x\text{ + 1 = 0 or x+ 3 = 0} \\ \text{x = -1/2 or x = -3} \end{gathered}[/tex]The solution of the above quadratic function is x = -1/2 and x = -3
Izzy is calculating the amount of time it takes a rocket to get to the moon. The moon is around 239,000 miles from Earth. How many hours would it take a rocket that can travel at 500miles per minute to travel to the moon? Round to the nearest hour8 hours20 hours478 hours28,680 hours
8 hours
Explanation
Step 1
Let
distance = 239000 miles
speed = 500 miles per minute
time( hours) = t
Step 2
to find the time, use
[tex]\begin{gathered} \text{distance= speed }\cdot\text{ time } \\ \text{time}=\frac{dis\tan ce}{\text{speed}} \end{gathered}[/tex]replace
[tex]\begin{gathered} \text{time}=\frac{239000\text{ miles}}{500\frac{miles}{m\in\text{ute}}} \\ \text{time}=478\text{ minutes} \end{gathered}[/tex]Hence, time = 478
Step 2
convert the minutes into hours
if 1 hour = 60 minutes
then, x=hurs for 478 minutes
[tex]\begin{gathered} 1\rightarrow60 \\ x\rightarrow478 \\ \text{the ratio is the same, so} \\ \frac{1}{60}=\frac{x}{478} \end{gathered}[/tex]Now, solve for x
[tex]\begin{gathered} \frac{1}{60}=\frac{x}{478} \\ 1\cdot478=60\cdot x \\ x=\frac{478}{60} \\ x=7.96\text{ hours } \end{gathered}[/tex]Step 3
Round to the nearest hour
[tex]7.96\rightarrow8[/tex]8 hours
Solve m (a – 5) = 12 for the variable a.
name the property illustrated by each statement if a=4.75 and 4.75 = b, then a=b
Answer:
Symmetric Property
Step-by-step explanation:
Melinda ate 3/5 of the cookies and left the rest for Suzanne. What fraction of the cookies are left for Suzanne?
The fraction of cookies left for Suzanne will be equal to 2/5 of the total number of cookies.
What is fraction?In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. Example - 5/9. Here, (5) is called numerator and (9) is called denominator.
Given is Melinda who ate 3/5 of the cookies and left the rest for Suzanne.
Assume that the fraction of cookies left for Suzanne is represented by [x].
Fraction of cookies ate by Melinda = [y] = 3/5
The sum of the fractions representing the cookies eaten by both Suzanne and Melinda will be equal to 1. Mathematically -
x + y = 1
x + 3/5 = 1
x = 1 - 3/5
x = (5 - 3)/5
x = 2/5
Therefore, the fraction of cookies left for Suzanne will be equal to 2/5 of the total number of cookies.
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selected the ordered pair that represent solutions to the system of inequalities. A) (-6,3)B) (-3,3)C) (-5,0)D) (-4,2)E) (0,0)F) (-6,6)G) (-3,-6)H) (-4,0)PLEASE ANSWER FAST
To detremine the ordered pairs that represent the system of inequalities given, from the choices given, the corredct ordered pairs are:
(x, y) ==> (-6, 3), (-4, 2), (-6, 6), (-4, 0)
What is the value of y when x is 4/5 ?
According to the direct variation model, the value of the variable y is the mixed number [tex]3 \frac {1}{5}[/tex]. (Correct choice: C)
What is the value of a variable according to a direct variation model?If a variable y varies directly with the variable x, then we can derive the following relationship to find the missing value:
y₁ / x₁ = y₂ / x₂
Where:
x₁, x₂ - Value of the variable x.y₁, y₂ - Value of the variable y.If we know that x₁ = 3 / 5, y₁ = [tex]2 \frac{2}{5}[/tex] and x₂ = 4 / 5, then the value of y₂ is:
y₁ = 2 + 2 / 5 = 12 / 5
y₂ = (y₁ / x₁) · x₂
y₂ = [(12 / 5) / (3 / 5)] · (4 / 5)
y₂ = (12 / 3) · (4 / 5)
y₂ = 4 · (4 / 5)
y₂ = 16 / 5
y₂ = 15 / 5 + 1 / 5
y₂ = 3 + 1 / 5
y₂ = [tex]3 \frac{1}{5}[/tex]
The value of the missing variable is the mixed number [tex]3 \frac{1}{5}[/tex].
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11) Solve the system by the addition method.
5x + 15y = -80
0.1x = -4.1 -0.3y
"5x + 15y = -80" + "0.1x = -4.1 -0.3y" using the addition method given equation "5.1x + 15.3y = -12.1".
What is the addition method of equations?A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 = 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. Using the Addition Method to Solve Two-Variable Equation Systems The addition method, also known as the elimination method, is a third approach to solving systems of linear equations. In this method, the sum is zero by adding two terms with the same variable but opposite coefficients.So, "5x + 15y = -80" + "0.1x = -4.1 -0.3y" using addition method:
Change 0.1x = -4.1 -0.3y to: 0.1x + 0.3y = -4.1Now, "5x + 15y = -80" + "0.1x = -4.1 -0.3y" (refer to the image attached below for calculation)The resulting equation is: 5.1x + 15.3y = -12.1
Therefore, "5x + 15y = -80" + "0.1x = -4.1 -0.3y" using the addition method given equation "5.1x + 15.3y = -12.1".
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MATH PROBLEM HELP please make sure it correct
For the value of c = 0,c=1 then A is not invertible
For given matrix A is invertible if c≠ 0 and c≠ 1
[tex]Given \ $A=\left[\begin{array}{ll}1 & 1 \\ c & c^2\end{array}\right]$ \\A matrix $A$ is invertible if $|A|={det}(A) \neq 0$.\\Now consider $|A|={det}(A)=0$.[/tex]
[tex]$$\begin{aligned}&\Rightarrow\left|\begin{array}{ll}1 & 1 \\c & c^2\end{array}\right|=0 \\&\qquad \quad \text { If } A=\left[\begin{array}{ll}a & b \\c & d\end{array}\right] \text { then }|A|={det}(A)=a d-b c\end{aligned}$$[/tex][tex]$$\begin{aligned}&\Rightarrow c^2-c=0 \\&\Rightarrow c(c-1)=0 \\&\Rightarrow c=0, c=1\end{aligned}$If $c=0$ or $c=1$ then \A \is \\not \ invertible. \\$\therefore$ Given matrix $A$ is invertible iff $c \neq 0$ and $c \neq 1$. \\ie Given marix $A$ is invertible for $c \in \mathbb{R}-\{0,1\}$.[/tex]
What are matrix?Matrix, a collection of numbers arranged in rows and columns forming a rectangular array. The number is called the elements or entries of the matrix. Matrices have wide applications in engineering, physics, economics and statistics, as well as in various areas of mathematics. Matrices also have important applications in computer graphics, where they have been used to represent image rotations and other transformations.
Different types of matrices are
row matrixcolumn matrixzero matrixsquare matrixdiagonal matrix upper triple matrixlower triple matrixsymmetric matrix asymmetric matrix.To learn more about matrix, refer;
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According to Descartes's rule of sign, how many possible positive and negative roots are there for the equation 0=−4x6−3x5+2x2−4x+1?Drag the choices to the boxes to correctly complete the table.
According to Descartes’ Rule of Signs, if we let
[tex]f(x)=a_nx^n+a_{n-1}x^{n-1}+\cdot\cdot\cdot+a_1x+a_0[/tex]be a polynomial function with real coefficients:
then,
the number of positive real zeros is either equal to the number of sign changes of f(x) or is less than the number of sign changes by an even integer.
the number of negative real zeros is either equal to the number of sign changes of f(-x) or is less than the number of sign changes by an even integer.
In this case,
[tex]f(x)=-4x^6-3x^5+2x^2-4x+1[/tex]We will now check the number of sign changes of f(x)
There are 3 sign changes.
Therefore, f(x) has 3 or 1 positive real roots
Next we find f(-x),
[tex]\begin{gathered} f(-x)=-4(-x)^6-3(-x)^5+2(-x)^2-4(-x)+1 \\ \text{hence,} \\ f(-x)=-4x^6+3x^5+2x^2+4x+1 \end{gathered}[/tex]We will now check the number of sign changes of f(-x)
There are 1 sign changes.
Therefore, f(x) has 1 negative real root
Number of possible positive roots: 1 or 3
Number of possible negative roots: 1 only
The graph of an equation drawn through which two points would best represent therelationship between the number of miles and the cost of the trip?
(10,5) and (250, 120)
1) Since we don't have the exact points, all we can do is a visual approximation of the line that best fits in.
2) So let's draw a line, like this on that graph also known as the eye-ball method. We are going to make it half, or almost half of it for each side.
3)Hence, examining the options we pick (10,5) and (250,120) as the best options that could represent the relationship between the number of miles ad the cost of that trip.
Since the line represents an average cost, and those points are approximately the same distance from the line.
I7 < x + 13 And what it looks like on a number line
ok
7 < x + 13
7 - 13 < x
-6 < x
Darius was walking from one class to the other during the passing period when he realized his shoes were untied. He stopped to tie his shoes and then glanced at the clock. The clock read 11:52 AM. He had to get to his classroom by 11:55 or he would be counted tardy to class. His class is 30 feet away. How fast will Darius have to move to make it to class on time?
Darius has to move at a speed of 1.67 feet per second to make it to class on time.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
From 11:52 am to 11:55 am, 30 feet of distance has to be covered.
The distance:
= 11:55 - 11:52
= 3 minutes
This means,
In 3 minutes, 30 feet need to be covered
30 feet = 3 minutes
Dividing 3 into both sides.
10 feet = 1 minute.
1 minute = 60 seconds
10 feet = 60 seconds
Dividing 60 into both sides.
10/6 feet = 1 second
5/3 feet = 1 second
1.67 feet = 1 second
The speed is 1.67 feet per second.
Thus,
Darius has to move at a speed of 1.67 feet per second to make it to class on time.
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Help please if you can show your work
7
400 ÷ 64 = 6.25
This doesnt mean its 7 because if u multiply
6 x 64 =384
Multiply 64 x 7 it gives you 448 which means she has enough to go on the trip
can you please solve this practice problem for me I really need assistance.find the y-intercept.
Given the graph in the attached image.
we want to find the y-intercept b.
The y intercept b is the point at which the line graph intercept the y axis.
For the given graph the line touches the y axis at;
[tex]y=450[/tex]So, the y-intercept is;
[tex]b=450[/tex]Solve the system by graphing and determine the number of solutions it has. (Hint: to graph find the y-intercept and slope of the line.)-4x + y = 5-2y = -8x + 4
Given the system of equations:
-4x + y = 5
-2y = -8x + 4
To solve the system of equations by graphing, apply the slope-intercept form:
y = mx + b
Where m is the slope and b is the y-intercept.
Rewrite each equation to slope-intercept form
Equation 1:
-4x + y = 5
Add 4x to both sides:
-4x + 4x + y = 4x + 5
y = 4x + 5
Equation 2:
-2y = -8x + 4
Divide all terms by -2:
[tex]\begin{gathered} \frac{-2y}{-2}=\frac{-8x}{-2}+\frac{4}{-2} \\ \\ y=4x-2 \end{gathered}[/tex]We have the equations in slope intercept form:
y = 4x + 5
y = 4x - 2
From the slope intercept form of both equatios, we can see both equations have the same slope.
Slope = 4
Since they have the same slope, they are parallel lines.
The solution will be the points of intersections, but parallel lines do not intersect.
Therefore, we can say the system has no solution.
We have the graph below:
From the graph above, both lines do not intersect. Therefore, there is no solution.
ANSWER:
No solution
Find two circular objects. Measure the diameter and then make a prediction about the circumference of each circle. How could you check your predictions?
Let's say that the two objects have 5 centimeters and 7 centimeters of diameter.
The circumference of a circle is defined as
[tex]C=\pi d[/tex]Where d is the diameter. Using the measures above, we have
[tex]C_1=\pi(5cm)\approx5\cdot3.14\operatorname{cm}\approx15.7\operatorname{cm}[/tex][tex]C_2=\pi(7\operatorname{cm})=7\cdot3.14\operatorname{cm}=21.98\operatorname{cm}[/tex]Therefore, the circumferences of the measures obtained are 15.7 and 21.98 centimeters.Choose two pairs of alternate interrior angles.
D. <7 & <12
<6 & <9
A packing machine wastes 0.17 liters of fruit punch for every case of 36 juice boxes that it fills.
If each juice box contains 0.12 liters, how many liters of fruit punch is packaged per liter of fruit punch wasted?
Round your answer to the nearest tenth.
The quantity of liters of fruit punch that is packaged per liter of fruit punch after waste would be = 4.15 liters.
What is a packaging machine?A packaging machine is defined as the industrial equipment that is used package finished product of food and food products such as juice.
For every case of 36 juice boxes = 0.17 liter of wastes juice
The quantity of juice per box = 0.12 liter
This means that the 36 juice boxes = 36 × 0.12 = 4.32 liters
The quantity of juice that is packaged after the wastes has been removed would be;
= 4.32 - 0.17
= 4.15 liters
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A salsa recipe uses 14 ounces of peppers and 7 ounces of onions.which two statements correctly state the related unit ratio?A.Use 0.5 ounces of pepper for each ounce of onionB.Use 2 ounces of pepper for each ounce of onionC.Use 7 ounces of pepper for each ounce of onionD.Use 0.5 ounces of onion for each ounce of pepperE.Use 2 ounces of onion for each ounce of peppersF.Use 7 ounces of onion for each ounce of peppers
14 ounces of peppers ---------- 7 ounces of onions
wee need satisfy always this equivalence
B. satisfy the equivalence
2 ounces of peppers ---------- 1 ounce of onions
D. satisfy the equivalence
1 ounce of peppers ---------- 0.5 ounces of onions
we always need to have the relations 2:1
the correct statements are B and D
1. AMNO with M(-5,2), NO. 4), and O(4.5): (-6, -2) /1 a. What kind of transformation is this? /3 b. What are the vertices of the image after the transformation?
Answer:
a. Translation
b. M'(-11, 0)
N'(-6, 2)
O'(-2, 3)
Explanation:
<-6, -2> indicates that the triangle MNO will be translated 6 units left and 2 units down, so <-6, -2> is a translation.
On the other hand, to know the new vertices, we need to apply the following rule:
(x, y) ----> (x - 6, y - 2)
So, the vertices of the image after the transformation are:
M(-5, 2) ----> (-5 - 6, 2 - 2) = M'(-11, 0)
N(0, 4) ----> (0 - 6, 4 - 2) = N'(-6, 2)
O(4, 5) ----> (4 -6, 5 - 2) = O'(-2, 3)
Therefore, the answers are:
a. Translation
b. M'(-11, 0)
N'(-6, 2)
O'(-2, 3)
What is the volume, to the nearest tenth of a cubic inch, ofthe plastic object?
In order to calculate the volume of a cylinder, we can use the formula below:
[tex]V=\frac{\pi d^2h}{4}[/tex]If the base diameter is 6 in and the height is 8 in, we have:
[tex]\begin{gathered} V=\frac{3.14\cdot6^2\cdot8}{4}\\ \\ V=226.2\text{ in^^b3} \end{gathered}[/tex]Therefore the volume is 226.2 in³.
3. How do these values relate to Max and Mary's ages?
The numbers of the intersections of the two lines represent the solution for the problem
for this, the point is (5,3) since they are the corresponding ages of them
Arrange the numbers 5^3, 6^2, and 2^7 in order from least to greatest.
5^3 = 5x5x5 = 125
6^2 = 6x6 = 36
2^7 = 2x2x2x2x2x2x2 = 128
From least to greatest
36 - 125- 128
6^2- 5^3 - 2^7
divide (x3−8x2+2)÷(x−3)
Answer: -37
Step-by-step explanation:
standard: -13 -[tex]\frac{37}{x-3}[/tex]
quotient: -13
Remainder: -37
Answer:
[tex]x^{2} + \frac{-5x^{2} + 2}{x - 3}[/tex]
Step-by-step explanation:
Attached on file below.
how do i find the markup price and retail price
Price = 72.87
The markup is 30% or 30/100 = 0.3
Let's find the markup of the price:
[tex]72.87\cdot0.3=21.861[/tex]The retail price, or selling price, is the price + markup.
Thus, retail price is:
[tex]72.87+21.861=94.731[/tex]Answers:
Markup = $21.86Retail Price = $94.73Please help. Much Appreciated Please mark as a,b, & c. Thank you in advance.
a) We can see that an increase in the number of employees (x) also leads to an increase in the number of products produced monthly, thus we can say that there is a positive correlation between the number of employees in the plant and the number of products produced monthly.
A positive correlation occurs when one variable increases with respect to another variable.
b) The function that best fits.
Let's first Find the rate of change(slope).
Take the points;
(x1, y1) ==> (0, 120)
(x2, y2) ==> (10, 200)
Use the slope formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]We have:
[tex]m=\frac{200-120}{10-0}=\frac{80}{10}=8[/tex]Use the form:
y = mx + b
Where m is the slope and b is the y-intercept
We have:
y = 8x + b
Substitue 0 for x and 120 for y, to solve for b.
120 = 8(0) + b
120 = b
Thus, we have the function:
y = 8x + 120
f(x) = 8x + 120
c) The slope, m is = 8
The slope indicates that the avearge rate of change between both variables is 8.
The y-intercept can be said to be the point where the line of the plot crosses the y-axis. This means when the number of employees are is zero, the number of products will be 120.
It can also be called the constant value.
Please help I need this for a text ASAP.
Two lines are 2linese intersect to form linear pairs with equal measures one angle measures 2x other measure 11y+2. x is 45 and y is 8.
The sum of a linear pair of angles is 180 degrees.
Now, we are given two pieces of information. We will use these to develop equations and then solve the equations simultaneously.
First, we know that the two angles are equal, therefore:
2x = 11y+2-------.> equation 1
Second, we know that the two angles form a linear pair of angles, therefore:
2x +11y+2 = 180 -------.> equation 2
Substitute by equation 1 in equation 2:
2x +2x = 180
4x = 180
x = 45
Substitute with the value of x in equation 1 to get y as follows:
2x = 11y+2
2 (45) -2 = 11y
88 = 11y
y = 8
Therefore:
the first angle = 2x = 2(45) = 90 degrees
the second angle = 11(8)+2 = 90 degrees
The two angles are equal and their sum is 180 .
What are linear pair of angle?Line pairs of angles occur when two lines intersect at a single point. Angles are considered linear if they are adjacent after the intersection of these two lines. The sum of the angles of a linear pair is always 180°. Such angles are also called supplementary angles.
If there is a pair of adjacent angles, the pair is a linear pair if the sum of the two angles (their measures) is 180°. Thus, linear pairs of angles always add up to 180°.
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Kayla notices that she can buy snacksandcandy in bulk at the grocery store.Write a formula that helps Kayla determinehow much she'll have to pay if she buys thefood in bulk.Let's lett = total pricep = price per kilogramk = number of kilograms of foodEnter the correct answer.
In this problem the total price (p) will be equal to the price per kilogram (p) times the number of kilograms of food (k) so the equation will be:
[tex]t=p\cdot k[/tex]Many bank accounts never go below zero. But some banks will allow a negative balance, at least for a short time, called an overdraft. It means someone has taken out, or 'drafted', more money than was in the account to begin with. Chloe's account went into overdraft. To get back to a positive balance, she deposited money at steady rate of $30.84 per week. After 3 weeks, she had $44.21 in the account. What was the balance when the account went into overdraft?
When the overdraft occurred, the balance was -48.31.
What happens if a bank account balance falls to zero?Major Takeaways. When your account balance drops below zero, you have an overdraft. If you have overdraft protection, your bank may permit a negative balance on your account or may provide one-time exceptions, but they may charge you for each transaction. Bank clients are required by federal regulations to choose to participate in overdraft protection schemes.
Let x represent the balance at the time the account entered overdraft.
He consistently made deposits totaling $30.84 a week in order to return to a positive balance.
Amount deposited per week = $30.84
Amount deposited 3 weeks = 30.84 × 3 = 92.52
Now amount in account after 3 weeks =x+ 92.52
We are given that After 3 weeks, he had $44.21 in the account.
So,x+92.52=44.21
x=44.21-92.52
x=-48.31
Hence The balance when the account went into overdraft was -48.31
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