Parallel cross sections of a sphere look like circles with the same radius as the sphere, while perpendicular cross sections look like points. Cross sections taken at other angles will be ellipses.
What you understand by sphere?A sphere is a three-dimensional geometric shape that is perfectly round in shape, like a ball. It is defined as the set of all points in three-dimensional space that are at a constant distance (the radius) from a given point called the center.
If we take a cross section of a sphere, the resulting shape will depend on the angle at which the section is taken relative to the center of the sphere.
If we take a plane that is parallel to the base of the sphere, the cross section will be a circle with the same radius as the sphere. This is because the intersection of the plane with the sphere will be a circle, and since the plane is parallel to the base of the sphere, the circle will have the same radius as the sphere.
On the other hand, if we take a plane that is perpendicular to the base of the sphere, the cross section will be a point. This is because the plane will intersect the sphere at only one point, which is the point at which the plane is perpendicular to the sphere.
If we take a plane that is neither parallel nor perpendicular to the base of the sphere, the resulting cross section will be an ellipse. The size and shape of the ellipse will depend on the angle at which the plane intersects the sphere.
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Find the surface area of the cube if it is 3/4 cm wide. Enter your answer as a fraction, please. Just enter the number, not the unit.
The surface area of the cube is 3 6/16 cm²
How to determine the valueTo determine the value of the surface area of the cube, we need too know the formula
The formula for calculating the surface area of a cube is represented as;
Surface area = 6a²
Such that the variable 'a' is the length of the side of the cube
From the information given, we have that;
a = 3/4
Substitute the value, we get;
Surface area = 6 (3/4)²
find the squares
Surface area = 6(9/16)
Multiply the values
Surface area = 3 6/16 cm²
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Also they all should be one step equations: integers
Answer: 3. is 13
4. is 36
5. is 21
6. is 15
7. is 21
8. is 2
9. is 6
10. is 45
Step-by-step explanation:
the letters are there to just confuse you. i promise its all right <-- the answers
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Lesson 4.06
The number of people that enter a contest on the 1st day is 23. On the 2nd day 30 people entered, and 37
people entered on the 3rd day. This pattern continues and the contest lasts 28 days.
What is the total number of people that enter the contest? Write the arithmetic series formula you used
to determine the total number of people and show all steps used to find the solution.
Thus, 3290 persons in total have entered the contest. We calculated the sum using the following arithmetic series formula: [tex]S = (n/2) * [2a + (n-1)d][/tex]
what is arithmetic progression ?The phrase "arithmetic progression" (AP) describes a series of numbers in which every term—aside from the first—is derived by multiplying the previous term by a set value. The common difference is a constant number. The following equation can be used to symbolise an arithmetic progression: a n = a 1 + (n-1)d where d is the clear differentiation, a n is the n - th term, a 1 represents the initial term, and n is the total number of terms. For instance, an arithmetic progression with 5 terms and a common difference of 3 starting at 1 would be: 1, 4, 7, 10, 13
given
The formula for the sum of an arithmetic series can be used to determine the total number of contestants:
[tex]S = (n/2) * [2a + (n-1)d][/tex]
Here are the facts:
a = 23 (the first phrase) (the first term)
d = 7 (the usual difference, since each day 7 more participants enter the contest) (the common difference, since each day 7 more people enter the contest)
n = 28 (the number of terms, since the contest lasts 28 days) (the number of terms, since the contest lasts 28 days)
With these values entered into the formula, we obtain:
S = (28/2) * [2(23) + (28-1)(7)]
S = 14 * [46 + 189]
S = 14 * 235
S = 3290
Thus, 3290 persons in total have entered the contest. We calculated the sum using the following arithmetic series formula: S = (n/2) * [2a + (n-1)d].
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Carly wants to fly to Canada, rent a car, and drive 568 miles to visit her sister in a truck that gets 21 miles per gallon. If gas costs $1. 02 per liter, how much will the road trip cost her? There are 3. 79 liters in 1 gallon. Round your answer to the nearest cent
Carly will need to buy 27.05 gallons of gas for the trip, which will cost her $7.28.
To calculate the total cost of the road trip, we need to find out how many gallons of gas Carly will need and then multiply that by the cost per gallon.
First, we need to convert the distance from miles to gallons, using the truck's fuel efficiency of 21 miles per gallon
568 miles ÷ 21 miles per gallon = 27.05 gallons
So Carly will need approximately 27.05 gallons of gas for the trip.
Next, we need to convert the cost of gas from liters to gallons. There are 3.79 liters in 1 gallon, so the cost of gas is:
$1.02 per liter ÷ 3.79 liters per gallon = $0.269 per gallon
Finally, we can calculate the total cost of the road trip by multiplying the number of gallons of gas by the cost per gallon
27.05 gallons × $0.269 per gallon = $7.28
Therefore, the road trip will cost Carly approximately $7.28.
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The energy for a rigid rotator constrained to rotate in the x-y plane is given by 21 where the moment of inertia I is a constant. (a) What is the Hamiltonian? Show that the Hamiltonian and L commute. What are the allowed energies and normalized energy eigenfunctions of the rigid rotator?
a. The Hamiltonian is given by:
H = T + V = (p² / 2I) + 0 = p² / 2I
b. Since the commutator is zero, we can conclude that the Hamiltonian and L commute.
c. The energy eigenfunctions are given by:
ψ[tex]_{n}[/tex](θ, φ) = √((2n + 1) / (4π)) × [tex]e^{(inφ)[/tex] × P[tex]_{n}[/tex](cosθ)
What is Hamiltonian?When time is not explicitly included in the function, it is used to characterize a dynamic system (such as the motion of a particle) in terms of momentum components and coordinates of space and time, and it is equal to the total energy of the system.
(a) The Hamiltonian is given by:
H = T + V = (p² / 2I) + 0 = p² / 2I
where T is the kinetic energy and V is the potential energy. Since the rotator is constrained to rotate in the x-y plane, there is no potential energy.
b. To show that the Hamiltonian and L commute, we need to calculate their commutator:
[H, L] = HL - LH
where L is the angular momentum operator given by L = r x p, where r is the position vector and p is the momentum operator.
HL = (p² / 2I) × (r × p) - (r × p) × (p² / 2I)
= (1/2I) × (p² × r × p - r × p × p²)
= (1/2I) × [p², r x p]
LH = (r x p) × (p² / 2I) - (p² / 2I) × (r x p)
= (1/2I) × (r × p × p² - p² × r x p)
= -(1/2I) × [p², r x p]
Therefore, [H, L] = [p², r x p] / 2I - [p², r x p] / 2I = 0.
Since the commutator is zero, we can conclude that the Hamiltonian and L commute.
c. The allowed energies of the rigid rotator are given by:
E[tex]_{n}[/tex]= (n² × h²) / (8I)
where n is a positive integer and h is Planck's constant. The energy levels are quantized and spaced equally apart, with the energy increasing as n increases.
The energy eigenfunctions are given by:
ψ[tex]_{n}[/tex](θ, φ) = √((2n + 1) / (4π)) * [tex]e^{(inφ)[/tex] * P[tex]_{n}[/tex](cosθ)
where θ is the polar angle and φ is the azimuthal angle, and P_n(x) is the n-th order Legendre polynomial. The eigenfunctions are normalized and orthogonal, with each energy level having a unique set of eigenfunctions.
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Explica por qué las siguientes expresiones representan el mismo valor.
a) 10 - (-2)
b) -10 +2
after calculating both the expressions we can conclude that both expressions represent the same value of 12.
what is expression ?Mathematical operations including multiplication, division, addition, and subtraction are possible. The construction of an expression looks like this: Expression, number, and mathematical operator Numbers, variables, and functions are the elements of a mathematical expression (such as addition, subtraction, multiplication, and division, etc.). Expressions and phrases can be contrasted. Expressions are any equations that comprise numbers, variables, and an arithmetic operation. They are occasionally referred to as algebraic expressions. For instance, the value of m in the computation of 4m + 5 is the same as the word m in the provided equation, which has been separated from the figures 4m and 5 by the mathematical symbol +.
given,
Since subtracting a negative integer is equivalent to adding its positive counterpart, the expressions "10 - (-2)" as well as "-10 + 2" have the same meaning.
To be more precise, "10 - (-2)" denotes starting with a value of 10 and then deducting a negative value of -2. The positive value of an amount that is negative may be subtracted without affecting it, and vice versa. Therefore, "10 - (-2)" equals "10 + 2," making 12 the result.
The expression "-10 + 2" on the opposite hand suggests that we start with an amount of -10 and subsequently add a value of 2.
A positive number is equal to its negative counterpart when added to a negative number. Because of this, "-10 + 2" equals "-10 - (-2)", which also equals 12.
Therefore, both expressions represent the same value of 12.
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Raj writes a polynomial expression in standard form using one variable, a, that has 4 terms and is degree 5.
One possible polynomial expression in standard form using one variable, a, that has 4 terms and is degree 5 is:
$4a^5 - 3a^4 + 2a^3 - 7a^2$
Polynomials expression explained.
A polynomial expression is a mathematical expression that consists of variables and coefficients, combined using the operations of addition, subtraction, and multiplication. The term "polynomial" comes from the fact that the expression can be thought of as a sum of many terms, each of which is a product of one or more variables raised to a non-negative integer power.
For example, the expression 3x^2 + 4x - 1 is a polynomial in one variable, x, with three terms. The first term is 3x^2, the second term is 4x, and the third term is -1. The highest power of the variable in this expression is 2, which makes it a polynomial of degree 2.
Polynomial expressions can be written in standard form, where the terms are arranged in descending order of degree and the coefficients are written with the highest power of the variable first. For example, the expression above could be written in standard form as 3x^2 + 4x - 1.
One possible polynomial expression in standard form using one variable, a, that has 4 terms and is degree 5 is:
$4a^5 - 3a^4 + 2a^3 - 7a^2$
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11. What is the slope of the line y=1/2x-2
a.-2 b. -1/2
c.1/2
d. 2
ans. (c) 1/2
given line,
y = 1/2 x -2
we know that the slope form of the line is given by
y =mx+c
comparing both equations we get
m= 1/2
hence, the slope is 1/2
True or False: For a given mass of rising air, the dry adiabatic rate will always be higher than the wet adiabatic rate.
Answer:
true
Step-by-step explanation:
because there's less humidity
Find the value of x and y in each triangle
Answer:
x=4 y=3
Step-by-step explanation:
because y=3 and x=4
slope-reliability) with respect to the 3-sigma rule used in reliability analysis, studies have shown that even experts tend to under-predict the range in parameter values (max-min). however, this is conservative because it leads to a smaller estimate of reliability. true false
The statement "with respect to the 3-sigma rule used in reliability analysis, studies have shown that even experts tend to under-predict the range in parameter values (max-min). however, this is conservative because it leads to a smaller estimate of reliability" is true because studies have shown that experts tend to under-predict the range in parameter values when using the 3-sigma rule, leading to a conservative estimate of reliability.
The 3-sigma rule is a widely used method in reliability analysis that assumes the range of parameter values is within three standard deviations of the mean value. However, studies have shown that experts tend to under-predict the range of parameter values.
This under-prediction can result in a conservative estimate of reliability because it leads to a smaller range of possible outcomes. In other words, the estimated reliability is likely to be lower than the actual reliability. Therefore, it is important to take into account the potential for under-prediction when using the 3-sigma rule and to use other methods to estimate reliability as well.
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Please help I’ll mark brainly
1) Note that the rates of change (slope) are 4 and 30 respectively over (0,3). This mean that the slope of y=1+4^x is much higher. This is also evidenced in the graph.
Why is it important to compare slopes of linear equations?It is crucial to compare the slopes of linear equations because it can disclose vital information about how the dependent variable varies in relation to the independent variable.
It may also be used to find patterns or trends in data and forecast future behavior.
Note that to get the y values of each function, we just plugged in the value of x into the equation to solve. See the attached sheet showing the formula .
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Little Johnny's lemonade stand sells glasses of lemonade for 75 cents per class. If he sells 125 glass, how much money did he make?
$75.00
$93.75
$935.75
$9375.00
A trip to St. Louis from Atlanta will take 7¾ hours. Assuming you're two-thirds of the way there, how much longer, in hours, will the trip take?
Answer:
5 and 1/6 hours
Step By Step Explanation:
I am really stuck on this question please help!!!
Answer:
8 weeks
Step-by-step explanation:
Ok, so the equation given is y=8x+40
If the school needs 104 cabinets in total, we have to find x, the number of weeks to complete this order.
We can input 104 as y as that's the total:
104=8x+40
We have to isolate x, so first, subtract 40 from both sides
64=8x
Next, divide both sides by 8
8=x
So, it will take 8 weeks to fulfill this order.
3(6+b)-(2b+1).
Nothing else answer is just too short to submit
Answer:
b + 17
Step-by-step explanation:
Now we have to,
→ Simplify the given expression.
The property we use,
→ Distributive property.
The expression is,
→ 3(6 + b) - (2b + 1)
Let's simplify the expression,
→ 3(6 + b) - (2b + 1)
Applying Distributive property:
→ 3(6) + 3(b) - (2b) - (1)
→ 18 + 3b - 2b - 1
Combining the like terms:
→ (3b - 2b) + (18 - 1)
→ (1b) + (17)
→ b + 17
Hence, the answer is b + 17.
HELP PLEASE IM RLLY STRUGGLING
Answer:
1.6
Step-by-step explanation:
0.8×2=1.6
double radius to find diameter
Answer:
1.6ft
Step-by-step explanation:
We did a similar problem, except we had to go from diameter to radius.
Remember, to go from diameter to radius we divided by 2. Now, we do the inverse as we are going from radius to diameter.
We multiply 0.8 x 2 to get 1.6 ft
So the diameter of this object is 1.6ft
ris poll asked a random sample of 1,015 adults nationwide the following question: are you afraid of being alone in an elevator? 10% of the people in the in the sample answered yes. the se of the sample % is about 0.94%. a) an approximate 95% confidence interval for the percentage of all american adults who are afraid of being alone in an elevator is closest to incorrect 9.94%-10.06% correct: 8.12%-11.88%
Answer: The correct answer is 8.12%-11.88%.
We can use the formula for a confidence interval for a proportion:
p ± z*SE
where p is the sample proportion, z* is the z-score corresponding to the desired level of confidence (in this case, 1.96 for a 95% confidence interval), and SE is the standard error of the proportion.
SE = sqrt(p*(1-p)/n) = sqrt(0.1*0.9/1015) = 0.0094
Plugging in the values, we get:
0.1 ± 1.96*0.0094
= 0.1 ± 0.0184
So the 95% confidence interval is (0.0816, 0.1184), which is equivalent to 8.12%-11.88%.
Step-by-step explanation:
the area of a rectangle is 30 cm squared, what is the height of the rectangle if the base is 4 cm
Answer:
7.5 cm.
Step-by-step explanation:
The height of a rectangle can be calculated using the rectangle's base and area using the following formula:
height = area / base
This formula can be derived from the formula for the area of a rectangle:
area = base x height
By rearranging this formula, we get:
height = area / base
Therefore, if we know the area and base of a rectangle, we can use this formula to calculate its height.
1) rewrite
Height = are / base
2) plug in
h = 30 cm / 4 cm
3) solve (divide)
height = 7.5 cm
Therefore, the height of the rectangle is 7.5 cm.
HELP!! I am soooo lost!! And Ineed quick help! 20 points!
From the knowledge of vertical angle theorem, angle TXS is equal to angle RXU which is equal to
62 degreesWhat is vertical angle?Vertical angles are a pair of non-adjacent angles formed by the intersection of two straight lines.
When two lines intersect at a point, they form four angles around that point, and the vertical angles are the pair of opposite angles, which are across from each other and not adjacent.
Vertical angel theorem have it that Vertical angles are congruent, which means that they have the same measure or size. This theorem helps us in providing a correct answer for the problem
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I have 45 min 2 attempts help pls!!!
The missing points of the table at x = 5, y = 1 and y = 0 has been completed in the table attached.
How to complete the table of the graph?
In general, to complete a table based on a graph, you need to follow these steps:
Look at the graph carefully and identify the variables represented on each axis.Determine the range of values for each variable.Decide on the intervals or steps you want to use for the table, based on the level of detail required.Create a table with the appropriate number of columns and rows.Label the columns and rows with the variables and their corresponding units.Fill in the table by reading the values of the dependent variable (y-axis) for each value of the independent variable (x-axis) and recording them in the appropriate cell of the table.Learn more about completing graph tables here: https://brainly.com/question/29298329
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1. Describe the basic characteristics of an independent
measures, or a between-subjects, research study.
The main advantage of an independent measures design is that it reduces the risk of order or practice effects and minimizes the influence of individual differences between participant
Describing the basic characteristicsAn independent measures design, also known as a between-subjects design, is a type of research study in which different groups of participants are used for each condition being tested.
In other words, each participant is only exposed to one condition, and the data from each group is analyzed and compared to determine if there are any significant differences between the groups.
The main characteristics of an independent measures design are:
Participants are randomly assigned to one of the groups. Each group of participants is exposed to only one level of the independent variableData is collected from each group and compared to determine if there are any significant differences between the groups. The design requires a larger sample size compared to a within-subjects design because each participant can only be in one group.Read more about research study at
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What is the equation of this circle in general form?
Responses
x2+y2−2x−6y−26=0
x squared plus y squared minus 2 x minus 6 y minus 26 equals 0
x2+y2+2x+6y−26=0
x squared plus y squared plus 2 x plus 6 y minus 26 equals 0
x² + y² + 2x + 6y + 4 = 0
x, ² +, y, ² + 2, x, + 6, y, + 4 = 0
x2+y2−2x−6y+4=0
Answer: for future k-12 kids :)
Step-by-step explanation:
Answer:
(a) x² +y² -2x -6y -26 = 0
Step-by-step explanation:
You want the equation for the circle with center (1, 3) and radius 6 written in general form.
Circle equationThe standard form equation for a circle with center (h, k) and radius r is ...
(x -h)² +(y -k)² = r²
The radius and center are found from the graph, attached. For the circle centered at (h, k) = (1, 3) and radius r = 6, this is ...
(x -1)² +(y -3)² = 6²
Expanding this equation gives ...
x² -2x +1 +y² -6y +9 = 36
Written in general form, the equation becomes ...
x² +y² -2x -6y -26 = 0 . . . . matches choice A
__
Additional comment
There is an image of this question showing the correct answer choice is the third one. However, that answer choice shows up first on this instance of the question. You will need to read and compare answer content to make sure you have the correct choice. You cannot go by the order of the the answers.
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Suzy is shooting basketballs at Bob’s Gym. She makes 9 field goals. After 10 minutes, her friend Joshua joins her. They shoot basketballs together for another 20 minutes.
a. Write an expression for the total number of field goals Suzy and Joshua make during the 30 minutes they spend at the gym. Be sure to define the variable used in the expression.
b. Altogether, Suzy and Joshua made 27 goals. Use the expression you created to determine the number of field goals they made in the last 20 minutes. Explain your thinking.
The second term (20(S + J)) denotes the total number of field goals they both scored in the final 20 minutes.
what is expression ?An expression is a grouping of figures, symbols, and algebra (such as addition, reduction, multiply, and division) that expresses a value. Variables, that are symbols for unknowable values, are symbols that can be included in expressions. The statement can be evaluated to give a specific value after the contents of the variables are assigned. An expression using a variable x, for instance, is 3x + 5. When we give x a number of 2, the expression is evaluated to: 3(2) + 5 = 6 + 5 = 11 . As a result, the expression's value at x = 2 is 11.
given
a. Assume that "S" represents the number of field goals Suzy scores each minute and "J" represents the number of field goals Joshua scores each minute.
The calculation for the total number of field goals Suzy and Joshua score in their 30-minute workout is as follows:
[tex]Field goals total = (9 + 10 S) + (20 (S + J)[/tex]
The first term (9 + 10S) denotes Suzy's total number of field goals in the first 10 minutes, while the second term (20(S + J)) denotes the total number of field goals they both scored in the final 20 minutes.
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Mrs. Dundee wants to sell the rights to her new Cajun cookbook, and she has two offers. The first publisher has offered to pay $80,000 up front and a $3 royalty for every book sold. The second publisher has offered to pay $30,000 up front and $5 for every book sold. Over what range of sales will Mrs. Dundee make more from the second publisher than from the first?
Mrs. Dundee will make more from the second publisher than from the first if she sells more than $25,000 worth of books.
What is the rate?In mathematics, rate is a measure of the change in one quantity with respect to another quantity. It is typically expressed as a ratio between the two quantities.
According to the given information:Let's represent the number of books sold as "x". Then, the total amount of money that Mrs. Dundee will make from the first publisher is:
Total from first publisher = $80,000 + ($3 x x) = $3x + $80,000
Similarly, the total amount of money that she will make from the second publisher is:
Total from second publisher = $30,000 + ($5 x x) = $5x + $30,000
We want to find the range of values of x for which the total amount from the second publisher is greater than the total amount from the first publisher. In other words, we want to find the range of values of x for which,
$5x + $30,000 > $3x + $80,000
Simplifying this inequality, we get:
$2x > $50,000
x > $25,000
Therefore, Mrs. Dundee will make more from the second publisher than from the first if she sells more than $25,000 worth of books.
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Use the image to determine the type of transformation shown.
Horizontal translation
Vertical translation
Reflection across the x-axis
90° clockwise rotation
(Use Image added)
Answer:
Vertical translation
Step-by-step explanation:
Let's compare each point to its corresponding point in the image.
First, look at point A. Look at point A'.
With respect to the shapes ABCD and A'B'C'D', they are in the same position (in between B/B' and D/D'; across from C/C').
If you look at the image again, you'll find that the shape A'B'C'D' is not a rotated version of ABCD.
Thus, we can rule out the option "90° clockwise rotation."
A reflection across the x-axis indicates that A'B'C'D' and ABCD would be symmetrical across the x-axis (a horizontal line).
Because ABCD and A'B'C'D' are not symmetrical across a horizontal line, we can also rule out "Reflection across the x-axis."
Now, look at the position of A'B'C'D' with respect to ABCD. It's directly next to ABCD. In other words, it was shifted sideways.
Translations are basically just shifts.
Recall that horizontal means up and down, while vertical means side to side.
Since this is a sideways shift, we can conclude that the translation was:
a vertical translation.
What is the domain of the radical function shown below?
What is the domain of the radical function shown below?
The required domain of the given function f(x) = √x+4 is (D) {x|x ≥ -4} respectively.
What is a domain?The domain of a function is the set of values that we are allowed to enter into our function.
This collection includes the x values for functions like f(x).
The set of values that a function can accept as input is known as its range.
The function outputs this list of values once we enter an x value.
Think about the equation y = f(x), where x and y are the independent and dependent variables.
If a value for x successfully enables the creation of a single value y using another value for x, it is said to be in the domain of the function f.
Considering the function's expression:
f(x) = √x+4
We are aware that the set of input values for which the function is real and defined constitutes the function's domain.
We are aware that for the function to continue to be defined, the value included within the radical expression must be larger than or equal to 0.
x+4 ≥ 0
Take 4 off of both sides.
x+4-4 ≥ 0-4
x ≥ 4
Then, the domain is:
{x|x ≥ -4}
Therefore, the required domain of the given function f(x) = √x+4 is (D) {x|x ≥ -4} respectively.
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Correct question:
The graph of the function f(x)=V x+4 is shown below. The domain of the function?
write quadratic formula
Answer:
x=9,-2
Step-by-step explanation:
in this case [tex]x^{2} -7x-18[/tex]
you can chose if you want the -7x and -18 to be a or b because [tex]x^{2}[/tex] would be c.
can yall pls help me with this? i have been having a rlly bad day so this would help me alot.
The possible number of pounds of candy that Linda will buy can be shown as p > 5 .
How to find the possible number ?Let's use algebra to solve the problem. We know that Linda will spend more than $30 on candy, so we can write:
6p > 30
Dividing both sides by 6, we get :
p > 5
This means that Linda must buy more than 5 pounds of candy in order to spend more than $30. And this can be shown by the expression, p > 5.
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Help!! Drag each number to complete the steps of the equation
Here is the complete equation using the provided values
6x+8=2x+24
6x-2x+8=2x-2x+24
4x+8=24
4x+8-8=24-8
4x=16
x=4
Factorization of EquationFactorization is the process of finding the factors of a given number or expression. A factor is a number or expression that divides the original number or expression without leaving a remainder. In other words, factorization is the process of expressing a number or expression as a product of its factors.
For example, the number 12 can be factored into 2 and 6, or into 3 and 4, because 2 and 3 are factors of 12 and their product gives 12. Similarly, the expression x^2 - 4 can be factored into (x+2)(x-2), because if we multiply (x+2) and (x-2), we get x^2 - 4.
Factoring is an important tool in algebra, as it allows us to simplify expressions, solve equations, and work with polynomials in a more efficient way.
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