Option A is the correct answer. The expression is (x+3)(x+7).
The given equation is x²+10x+21
we have to find the roots of the equation
x²+10x+21 =0
x²+3x+7x+21
x(x+3)+7(x+3)
(x+3),(x+7)
Now, we need to remember to factorize the given expression, x²+10x+21, and have to choose two numbers when you add them you get "10" and when you multiply them you get "21".
These numbers are:
7 and 3
Because:
7+3=10
7*3=21
Therefore, you get that the factorization of the expression is the following:
(x+3)(x+7)
We can conclude that this factorization matches the first option.
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Solve the system of linear equations by substitution.
y=4x
x+y=-10
We may determine that the values of x and y are -2 and -8, respectively, by replacing the linear equations.
What are linear equations?
A linear equation is a first-order (linear) term and a constant in an algebraic equation of the type y=mx+b, where m is the slope and b is the y-intercept.
The previous equation, which has the variables y and x, is sometimes referred to as a "linear equation with two variables."
The typical form for linear equations with two variables is Ax+By=C.
For instance, the linear equation 2x+3y=5 is in standard form.
Finding both intercepts of an equation in this style is quite easy (x and y).
The following is the equation:
y=4x ...(1)
x+y=-10 ...(2)
Now change equation (2) to y = 4x:
x+y=-10
x+4x=-10
5x = -10
x = -10/5
x = -2
Then, change equation (1) to read x = -2:
y = 4x
y = 4(-2)
y = -8
Therefore, we may determine that the values of x and y are -2 and -8, respectively, by replacing the linear equations.
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Write an equation that passes through the points (1,8) and (3,4)
Answer:
[tex]y = -2x + 10[/tex]
Step-by-step explanation:
The slope-intercept form of equation of line:
y = mx + c
where:
m = slope
c = y-intercept
Slope, m: [tex]\frac{y_{2} - y_{1}}{x_{2} -x_{1}}[/tex]
= [tex]\frac{4 - 8}{3 - 1}[/tex]
= [tex]-\frac{4}{2}[/tex]
= [tex]-2[/tex]
[tex]y = -2x +c[/tex]
Substitute the coordinates of either of the two points in this equation to calculate the value of c:
8 = [tex]-2[/tex](1) + c
8 = [tex]-2[/tex] + c
c = 8 + 2
c = 10
Therefore, the equation is:
[tex]y = -2x +10[/tex]
50 points to whoever can answer this question w/ explanation.
Answer:
2/ c, e
Step-by-step explanation:
A graph can only be a function if one x only has one y.
If you use the line test, you see that only graphs C and E pass the test.
So, the answers are C and E.
if sammy has 900 fish and 200 dies and then he gets 500 × 8090 and gets divided by 2 how many fish dose sammy have
On solving the provided question, we can say that Sammy has 900 fish and 200 dies and equation will be => x - y = 700
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
Sammy has 900 fish and 200 dies
equation will be
x - y = 700
x = alive fishes
y = died fishes
remaining fishes are 700
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[tex]\lim_{x \to } 0 \frac{1-cosx\sqrt{cos2x} }{x^2} }[/tex]
Find the limit.
The limit of the function in this problem is given as follows:
lim x->0 f(x) = 1/2.
How to obtain the limit of the function?Following the standard procedure to obtain the limit of the function, merely obtaining the numeric value at x = 1, the limit is undetermined at x = 0, as follows:
0/0.
Hence the can apply the L'Hospital Rule, trying to find the derivative at the numerator and the denominator, hence:
[cos(x)sqrt(cos(2x))]' = [-sin(x)sqrt(cos(2x)) - 2sin(2x)cos(x)/sqrt(sin(2x))].[x²]' = 2x.At x = 0, the limit would again assume an undetermined value of 0/0, hence the L'Hospital Rule is applied again, hence:
[-sin(x)sqrt(cos(2x)) - 2sin(2x)cos(x)/sqrt(sin(2x))]' = cos(2x)sqrt(cos(2x)).[2x]' = 2.Now the function is:
f(x) = cos(2x)sqrt(cos(2x))/2.
Since cos(x) = 0, the numeric value at x = 0 is given as follows:
f(0) = 1/2.
Which is the limit.
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The mathematical constant pi is needed when calculating the area of a
When computing the area of a circle, the mathematical constant pi () is required. Pi is the circumference-to-diameter ratio of a circle and is approximately equal to 3.14159.
The area of a circle is calculated by multiplying pi by the radius squared (r2). To estimate the area of a circle, utilize pi in the calculation since it is a vital aspect of the relationship between the circumference and diameter of a circle.
Pi is not required when determining the area of a square, rectangle, or cube since the formulas for these shapes are different.
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The question is -
The mathematical constant pi is needed when calculating the area of a _.
a. circle
b. square
c. rectangle
d. cube
Hasan plans to choose a book from a section of the store where everything is 25% off. He writes the expression d−0.25d to find the sale price of the book if the original price is d dollars.
Bella correctly writes another expression, 0.75d, that will also find the sale price of the book if the original price is d dollars.
Drag each description to explain each part of both expressions.
Dragging each description to explain each part of Hasan's and Bella's expressions is as follows:
Hassan's Expression of d - 0.25d:d = Original price of book
0.25 = Percent Discount
0.25d = Amount of Discount
d - 0.25d = Sale price of book
Bella's Expression of 0.75d:0.75 = Percent of original price Bella will pay
d = original price
0.75d = Sale price of book
What is an algebraic expression?An algebraic expression is a combination of variables, constants, numbers, and values using the mathematical operands, including addition (+), subtraction (-), division (÷), and multiplication (×).
An algebraic expression does not have the equal symbol (=) unlike an equation.
Thus, the correct descriptions has been dragged to each part of both Hasan's and Bella's expressions.
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Function g can be thought of as a scaled version of f(x) = x².
f
-5 -4 -3
Y
5.
4+
3.
2-
1
234
-4+
-5
Write the equation for g(x).
g(x) =
345
(2,-1)
B
Answer:
g(x) = -1/4x²
Step-by-step explanation:
Given f(x) = x² and point (2, -1) on the graph of g(x), which is a scaled version of f(x), you want the equation for g(x).
Scale factorThe scale factor k will satisfy ...
g(x) = k·f(x)
g(2) = k·f(2) . . . . . . true at the given point
-1 = k·2² = 4k . . . . use the coordinates of the given point
k = -1/4 . . . . . . . . . divide by 4
The equation of g(x) is ...
g(x) = -1/4x²
a fast food shop sells ham sandwiches and egg sandwiches only. a ham sandwich is sold for 14 and an egg sandwich is sold for 9. in a morning, the shop sells 50 sandwiches and recieves 640. find the number of egg sandwiches sold
Answer:
Correct, the inequality y ≥ 0.8x + 1.5 accurately describes the relation between the duration of the hike (x) and the amount of water needed (y). This inequality means that for any duration of the hike (x), the amount of water needed (y) must be greater than or equal to 0.8x + 1.5.
Find the midpoint of A and B
where A has coordinates (2, 7)
and B has coordinates (6, 3).
Answer:
(4, 5)
Step-by-step explanation:
Add the two x values and divide by two, add the two y values and divide by two. Then put them in brackets and those are your coordinates.
Pls help. Look at photo
Note that the line of Best fit is attached accordingly. See the definition below.
What is a Line of Best Fit and why is it important?A line of best fit is a straight line that represents the trend of a set of data.
It is used to summarize and analyze the relationship between two variables in a scatter plot. Note that the line of best fit can be used to approximate the trend or pattern of the data and make predictions for new observations that fall within the range of the data.
The line is drawn in a way that minimizes the distance between the observed data points and the line.
The line of best fit can be used to make predictions and identify outliers. It is important because it helps to reveal patterns and trends in data and allows us to make informed decisions based on the information.
Note that the line takes a position that gives an approximately equal amount of variables or data points on either side.
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Enlarge triangle T by a scale factor 1/2, centre (2, 0).
Answer:
To enlarge a triangle by a scale factor of 1/2 with the center (2, 0), each vertex of the triangle should be multiplied by 1/2 and then shifted so that the center of the new triangle is (2, 0).
Step-by-step explanation:
For example, if the original triangle has vertices at (a, b), (c, d), and (e, f), the vertices of the new triangle would be at ((a-2)/2 + 2, (b-0)/2 + 0), ((c-2)/2 + 2, (d-0)/2 + 0), and ((e-2)/2 + 2, (f-0)/2 + 0).
If you flip a coin 12 times, what is the best prediction possible for the number of times it will land on heads?
The best prediction that the coin would land on heads wold be 6
If you flip a coin 12 times, what is the best prediction possible for the number of times it will land on heads?If you flip a fair coin 12 times, the best prediction for the number of times it will land on heads is 6. This is because each flip has an equal chance of landing on heads or tails, and if you flip a fair coin 12 times, the expected number of heads is 6. This is because each flip has a 50% chance of landing on heads.
In the coin, there are going to be 6 changes foe head and also 6 chains for tails. This is a 50 50 chance
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Happy Party Rental rents tables for $4 per
table plus a delivery fee of 60. Budget
Party Rental rents tables for $8 per table
plus a $20 delivery fee. How many tables
do you have to rent to have the cost of the
rental be the same. Write and solve an
equation.
The equations are H = 4x + 60 and P = 8x + 20. We need to rent 10 tables to ensure that the cost of the rental will be the same.
What is system of equations?A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."
Let us suppose tables as x.
Given that,
The happy party rents tables for $4 per table plus a delivery fee of 60. This is expressed as:
H = 4x + 60
Party Rental rents tables for $8 per table plus a $20 delivery fee.
P = 8x + 20
To get the same cost of the rent:
H = P
4x + 60 = 8x + 20
60 - 20 = 8x - 4x
40 = 4x
x = 10
Hence, we need to rent 10 tables to ensure that the cost of the rental will be the same.
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PLSSS HELP IF YOUR TURLY KNOW THISSS
Answer:
The value of x =10
Step-by-step explanation:
2x+ 5 = 25
Subtract 5 from each side.
2x+5-5 = 25-5
2x = 20
Divide each side by 2.
2x/2 = 20/2
x =10
The value of x =10.
Answer:
10
Step-by-step explanation:
Move the 5 to the right so the equation is 2x = 25 - 5
Then its 2x = 20 and 20/2 is 10.
Find the inverse of the function f(x)=∛(x+2)-5. Please show all work in finding the inverse.
Answer:
Step-by-step explanation:
Let [tex]f(x) = y[/tex]
∴ [tex]y = \sqrt[3]{x + 2} -5[/tex]
x has to be isolated and made the subject of the formula:
[tex]y + 5 = \sqrt[3]{x + 2}[/tex]
Cube is applied to both sides of the equation to get rid of the cube root:
[tex](y + 5)^{3} = x + 2[/tex]
x = [tex](y + 5)^{3} -2[/tex]
Substitute [tex]f^{-1} (y) = x[/tex]:
[tex]f^{-1} (y) = (y + 5)^{3} - 2[/tex]
Replace y with x:
[tex]f^{-1} (x) = (x + 5)^{3} -2[/tex]
what is the reflection of the point (-8,7) across the x and y axis?
Step-by-step explanation:
We have the point (-8, 7)
When we reflect across the X-AXIS, then the Y coordinate changes signs
When we reflect across the Y-AXIS, then the X coordinate changes signs
So when we reflect (-8, 7) across the x-axis, it becomes (-8, -7) since we change signs for the Y coordinate from +7 to -7
Reflecting across the Y, it becomes (8, 7), because we change signs from -8 to +8
i need help asap please i beg of you
Answer:
p = 150 - 65
Step-by-step explanation:
We know
p is the amount he has left to raise
The target is $150
He has $65
So, the equation is
p = 150 - 65
Jeremiah spins a spinner with 5 equal-sized section twice,
rolls a six-sided dice, and flips a coin. How many possible
outcomes there can be?
The total number of possible outcomes is the product of the number of outcomes for each event.
The spinner can land on any of its 5 sections on the first spin, and on any of the 5 sections again on the second spin. So there are 5 x 5 = 25 possible outcomes for the spinner.
The dice can land on any of its 6 sides.
The coin can land either heads or tails.
Therefore, the total number of possible outcomes is:
25 (spinner) x 6 (dice) x 2 (coin) = 300 possible outcomes.
suppose that DEF is isosceles with base DF
suppose that m
Answer: An isosceles triangle is a triangle with two sides that are congruent (equal in length). If DEF is isosceles with base DF, then DE and EF are congruent and have the same length. This means that the two sides of the triangle are equal in length, and that the angle formed by DE and EF is equal to each other (since they are congruent sides, they must also be congruent angles). The two equal angles are called the base angles of the isosceles triangle.
Step-by-step explanation:
Leonardo purchases a car for $18,995. The car depreciates at a rate of 18% annually. After 6 years, Manuel offers to buy the car for $4500. Should Leonardo sell the car to Manuel? Explain.
18,995 × 0.82^(6) = $5,774 so he should not sell
if the percentage decrease is 18% then do 100% - 18% which is 82. divide by 100 = 0.82. if it does this for 6 years then do 18,995 × 0.82^(6) because it's 6 years. the number is larger than Manuel's offer therefore he shouldnt sell
systems of two equations to solve systems of three equations.
Students are baking shortbread, croissants, and pound cakes.
• One group of students used a total of 3,525 grams of flour to make
5 batches of shortbread, 4 pound cakes, and 2 batches of croissants.
• Another group of students used 1,020 grams of flour to make one
batch each of shortbread and croissants and one pound cake.
• There is the same amount of flour in 4 pound cakes as there is
in 2 batches of croissants.
1. Let s = the amount of flour in a batch of shortbread, let c = the
amount of flour in a batch of croissants, and let p = the amount
of flour in a pound cake. Write an equation for each of the
3 statements above.
2. Multiply one equation, then add or subtract it with another
equation you wrote in Exercise 1 to eliminate the variable p.
3. Use the third equation and your result from Exercise 2 to write a
system of two equations with the variables p and c. Solve your system
and find the values for p and c.
4. What is the value of s? Explain what you did.
Step-by-step explanation:
Let s = the amount of flour in a batch of shortbread, let c = the amount of flour in a batch of croissants, and let p = the amount of flour in a pound cake.
The first statement can be written as 5s + 4p + 2c = 3525.
The second statement can be written as s + c + p = 1020.
The third statement can be written as 4p = 2c.
Multiplying the third equation by 2, we get 8p = 4c.
Subtracting this from the first equation, we get 5s + 4p + 2c - 8p = 3525 - 8p.
Simplifying, we get 5s - 6c = 3525 - 8p.
Now we have a system of two equations with the variables c and p:
5s - 6c = 3525 - 8p
s + c + p = 1020
We can use substitution to eliminate c. Solving the second equation for c, we get c = 1020 - s - p.
Substituting this into the first equation, we get 5s - 6(1020 - s - p) = 3525 - 8p.
Expanding the second equation and simplifying, we get 11s = 4545 - 8p.
Solving for s, we get s = (4545 - 8p) / 11.
Substituting the value of s into the second equation, we get c + p + (4545 - 8p) / 11 = 1020.
Expanding and simplifying, we get c + p + (4545 - 8p) / 11 = 1020.
Expanding, we get c + p = 1020 - (4545 - 8p) / 11.
Solving for c and p, we find that c = 664 grams and p = 356 grams.
Finally, the value of s is (4545 - 8 * 356) / 11 = 735 grams.
A teacher has 60 students in her class.she wants to form equal groups for project,what different groups she can make
The divisors of 60 are the numbers that evenly divide 60 without leaving a remainder. In other words, if we divide 60 by one of its divisors, the result will be a whole number.
For example, if we divide 60 by 2, we get 30. If we divide 60 by 3, we get 20. And so on.
When the teacher wants to form equal groups of students, she needs to ensure that the number of students in each group is one of the divisors of 60. This way, she can divide the class into groups with an equal number of students in each group.
So, in this case, the different groups the teacher can make are:
1 group of 60 students
2 groups of 30 students each
3 groups of 20 students each
4 groups of 15 students each
5 groups of 12 students each
6 groups of 10 students each
10 groups of 6 students each
12 groups of 5 students each
15 groups of 4 students each
20 groups of 3 students each
30 groups of 2 students each
60 groups of 1 student each
These are the 12 different options for forming equal groups of students.
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eleven bands are to perform at a weekend festival. how many different ways are there to schedule their appearances?
It depends on the length of the festival, the length of each band's performance, and other factors. There could be any number of ways to schedule their appearances.
The number of ways to schedule the bands' appearances at the weekend festival depends on a variety of factors such as the length of the festival, the length of each individual band's performance, and the number and type of stages available.
For example, if the festival runs for two days and each band's performance is one hour, there could be a total of 22 hours of music, so eleven bands could each perform twice, once on each day.
Alternatively, if the festival has three stages and two of the stages are dedicated to different genres of music, then the bands could be scheduled to perform on those stages, with each stage hosting five bands each day.
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can you do it by telling
Answer:
Step-byoooooooooooo
-step explanation:
this function represents the relationship between the radius of cylinders with a height of feet and their volume. why is this relationship between radius and volume nonlinear?
The relationship between the radius and volume of a cylinder with a height of 4 feet is nonlinear because the volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. In this case, the height is fixed at 4 feet. As we change the radius, the volume changes in a nonlinear manner.
The volume increases much faster as the radius increases. This can be seen from the exponential nature of the formula, as the radius is squared. Therefore, even a small increase in the radius results in a substantial increase in the volume, making the relationship between radius and volume nonlinear.
In contrast, if the height were to be proportional to the radius, then the relationship between radius and volume would be linear. This is because the volume would be proportional to the product of the radius and height, which is a linear relationship.
Therefore, the nonlinear relationship between radius and volume, in this case, is due to the exponential nature of the formula for the volume of a cylinder and the fixed height of 4 feet.
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--The given question is incomplete; the complete question is
"This function represents the relationship between the radius of cylinders with a height of 4 feet and their volumes. Why is this relationship between radius and volume nonlinear?"--
PLS HELP I NEED THIS ASAP
Answer:
(-3, 9)
2
Step-by-step explanation:
Photo attached in the description below
The reduction of the fraction is (y-3)/4.
How to interpret the fraction?Suppose the fraction is proper (the numerator is smaller than the denominator).
Let it be [tex]\dfrac{a}{b}[/tex]
Then, we can interpret it as:
[tex]\dfrac{a}{b}[/tex]= a parts out of b parts of a thing.
There is a fraction, containing numerator(upper value) and denominator(lower value).
When the numerator is less than the denominator, the fraction is called proper fraction, otherwise it is called improper fraction.
A proper fraction is also called fraction which is less than 1.
And an improper fraction is ≥ 1
A mixed fraction contains a sum of whole number and a proper fraction.
Given;
=y^2-9/4y+12
=y^2-3^2/4(y+3)
=(y+3)(y-3)/4(y+3)
=y-3/4
Therefor, the answer of fraction will be (y-3)/4
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Tell me the explanation and the result of how to convert numbers into fractions Daisy is practicing trivia. She gets 12 out of 20 questions correct.
What percentage of the trivia questions do you get right? bone what is the percent of that
Answer:
60%
Step-by-step explanation:
12/20 = 0.6 multiply this by 100% = 60%
We know
5 x 4 = 20
So, which of the following statements are also true?
(Choice A, )
5 is a factor of 20
(Choice B)
5 is a multiple of 20
(Choice C)
20 is a multiple of 4
Options A and C are correct for the condition 5 x 4 = 20.
What Is a Factor?A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.
Factors can be found using either division or multiplication. Rules of divisibility can also be applied.
Given 5 x 4 = 20
factors of 20 are 2*2*5
so 5 is the factor of 20,
A is correct.
now multiples of 20 are 20, 40, 60.......
since all values are greater than 5,
so 5 is not a multiple of 20.
B is not correct.
now multiples of 4 are 4, 8, 12, 16, 20, 24 .......
so 20 is a multiple of 4,
C is correct.
Hence A and C are correct statements.
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