The zero of polynomials is -2. The polynomials is p(y) = [tex]3y^{3} - 16 y - 8[/tex].
According to the question,
The polynomials is p(y) = [tex]3y^{3} - 16 y - 8[/tex]. In order to find the zero of polynomials only if we substitute the value and polynomials become zero.
p(-2) = [tex]3(-2)^{3} - 16 (-2) - 8[/tex]
= 3(8) + 32 -8
= 0
Hence, the zero of polynomials is -2. The polynomials is p(y) = [tex]3y^{3} - 16 y - 8[/tex].
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From Belmont, how much farther is it to Riverside than to Yardley? Use paths shown below
On solving the provided question, we can say that by addition, the distance between Belmont and Yardley is by adding all distances in between them = 9.75+8324 = 17.99 mils
what is addition?The other three fundamental operations are subtraction, multiplication, and division. Addition is one of the four basic operations. The sum or total of these combined values is obtained by adding two integers. The process of merging two or more numbers is known as addition in mathematics. Numbers are added together to form addends, and the outcome of this operation, or the final response, is referred to as the sum. This is one of the crucial mathematical operations we employ on a regular basis. You would add numbers in a variety of circumstances. Combining two or more numbers is the foundation of addition. You can learn the fundamentals of addition if you can count.
by addition,
the distance between Belmont and Yardley is
by adding all distances in between them = 9.75+8324 = 17.99 mils
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If UT and VS biscect each other at W, EHAT method could you use to prove the triangles congruent?
Answer: Where they bisect each other at W the 2 lines are split in the center by one another which means both of those lines are 180
Step-by-step explanation:
Answer:
SAS
Step-by-step explanation:
You have segments UT and VS bisecting each other at point W, and you want to show triangles UWV and TWS ae congruent.
SASEach half of the segment is congruent to the other half:
UW≅TW and VW≅SW
The angles between them are vertical angles so are congruent:
∠UWV ≅ ∠TWS
So, you have congruent corresponding sides and the angle between. The triangles UWV and TWS are congruent by the SAS congruence postulate.
__
Additional comment
You can use substantially the same argument to say triangles UWS and TWV are congruent. The proof above shows UV≅TS. The congruence of triangles UWS and TWV shows US≅TV. Hence the figure TSUV is a parallelogram.
Please answer ill give extra points and brainiest please im begging you, answer both questions please all i need is the answer and a small explanation
(Ignore what i wrote on the paper btw)
The school biology club member want to buy matching shirts to wear on a field trip they needed to determine from which of two stores to purchase the shirts these tables show the total cost including set up fee for purchasing different numbers of the shirt
If you want to buy fewer than 25 shirts, then prefer Shirts By Sam shop. If you want to buy more than 25 shirts, then prefer Might T Shirt shop.
What is an equation?
A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.
Given that:
Shirts By Sam
The cost of 10 shirts is $127.5
The cost of 15 shirts is $168.75.
Assume the equation that represents total cost is y = ax+b
Putting x= 10 and y=127.5 in y = ax+b:
127.5 = 10a+b.....(i)
Putting x= 15 and y=168.75 in y = ax+b:
168.75 = 15a+b.....(ii)
Use elimination method to solve equation (i) and (ii).
Subtract equation (i) from (ii)
15a+b = 168.75
10a+b = 127.5
____________
5a = 41.25
a = 8.25
Putting a=8.25 in equation (i)
127.5 = 10×8.25+b
b = 40
The equation is y = 8.25x+40.
Might T Shirt
The cost of 8 shirts is $137
The cost of 12 shirts is $163
Assume the equation that represents total cost is y = ax+b
Putting x= 8 and y=137 in y = ax+b:
137 = 8a+b.....(iii)
Putting x= 12 and y=163 in y = ax+b:
163 = 12a+b.....(iv)
Use elimination method to solve equations (iii) and (iv).
Subtract equation (iv) from (iii)
8a+b = 137
12a+b = 163
____________
4a = 26
a = 6.5
Putting a=6.5 in equation (iii)
137= 8×6.5+b
b = 85
The equation is y =6.5x+85.
The solution of the system of equations:
y = 8.25x+40 .....(vi)
y =6.5x+85 ......(vii)
Use substitution method to solve equations (vi) and (vii).
Subtract equations:
8.25x+40 - 6.5x-85=0
1.75x - 45 =0
x = 45/1.75
x = 25.71
Putting x = 26 in equations (vi) and (vii)
y = 8.25×26+40 = 254.5
y = 6.5×26+85 = 254
Putting x = 24 in equations (vi) and (vii)
y = 8.25×24+40 = 238
y = 6.5×24+85 = 241
Thus if you buy more than 25 shirts, then prefer Might T Shirt shop.
if you buy fewer than 25 shirts, then prefer Shirts By Sam.
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What should be added to 2x2 xy 2y2 to obtain 3x2 5xy?
To obtain 3x² + 5xy from 2x² + 2xy², you would need to add the polynomial x² + 5xy to the original expression.
In order to add two polynomials together, the terms must have the same degree and variable. In this case, we see that 2x^2 and 2xy^2 have different degrees and variables. So, we need to find a polynomial that when added to 2x² + 2xy² will give us 3x² + 5xy.
To do this, we can start by looking at the x² term in 3x² + 5xy. We can see that we need to add x² to our original polynomial. Next, we can look at the xy term in 3x² + 5xy. We can see that we need to add 5xy to our original polynomial.
So by adding x² + 5xy to 2x² + 2xy², we get the desired polynomial of 3x² + 5xy.
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What should be added to 2x² + 2xy² to obtain 3x² + 5xy.
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Square each binomials and place them into perfect square trinomial form, then subtract the trinomial
1 (x + 3) 2 - (x - 4) 2
2 (7b2 - 7) 2 - (2b2 - 11) 2
3 (5ab2 + 3) 2 - (6ab2 - 7) 2
The results of subtractions between perfect square trinomials are listed below:
(x + 3)² - (x - 4)² = 14 · x - 7 (7 · b² - 7)² - (2 · b² - 11)² = 45 · b⁴ - 54 · b² - 72 (5 · a · b² + 3)² - (6 · a · b² - 7)² = - 9 · a² · b⁴ + 114 · a · b² - 40How to simplify subtractions of perfect square trinomials
In this problem we have three cases of subtractions between two perfect square trinomials that must be simplified. According to algebra, perfect square trinomials can be expanded by means of the following definition:
(a + b)² = a² + 2 · a · b + b²
Where a, b are real constants.
The procedure is summarized below:
Expand the perfect square trinomials.Add and subtract similar terms.Arrange the resulting polynomial in standard position.Case 1
(x + 3)² - (x - 4)²
(x² + 6 · x + 9) - (x² - 8 · x + 16)
x² + 6 · x + 9 - x² + 8 · x - 16
14 · x - 7
Case 2
(7 · b² - 7)² - (2 · b² - 11)²
(49 · b⁴ - 98 · b² + 49) - (4 · b⁴ - 44 · b² + 121)
49 · b⁴ - 98 · b² + 49 - 4 · b⁴ + 44 · b² - 121
45 · b⁴ - 54 · b² - 72
Case 3
(5 · a · b² + 3)² - (6 · a · b² - 7)²
(25 · a² · b⁴ + 30 · a · b² + 9) - (36 · a² · b⁴ - 84 · a · b² + 49)
25 · a² · b⁴ + 30 · a · b² + 9 - 36 · a² · b⁴ + 84 · a · b² - 49
- 9 · a² · b⁴ + 114 · a · b² - 40
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match each system of equations with the number of solutions the system has
solutions are :
one solution
no solution
infinitely many solutions
What is the residual for five?
-1.6 is the residual value of 5 for given regression table.
What is residual?A residual value is the difference between the observed and expected y-values (as determined by the regression equation).
Here,
In this case, the given regression equation for the line,
y = 5.2 x - 0.4
As a result, for x = 5, the anticipated value is y = 5.2 5 - 0.4 = 26.0 - 0.4 = 25.6.
Now, according to the table,
The observed value of y = 24 for x = 5.
As a result, the residual for 5 = Observed y for 5 - Predicted y for 5
= 24 - 25.6 = - 1.6
The first option is the correct one.
The residual value of 5 for the provided regression table is -1.6.
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The complete question:
The line of best fit to model the data in the table is y = 5.2x – 0.4.
What is the residual for 5?
–1.6
–0.6
0.6
1.6
The temperature in Coldspot is 4 Fand is increasing 2.5 Fper hour The temperature in Frostberg is 30 and is decreasing 4 Fper hour a, How long will it be until the temperatures are the same? What will the temperature be then?
Answer:
Step-by-step explanation:
Bong's savings in February was P9,500 and his savings in May was
P7,300. What was the percentage decrease in Bong's savings? Solution:
Answer: 23.16%
Step-by-step explanation: 7300/9500 can be simplified to 73/95 which gives us 76.84%. subtract that from 100 and you get 23.16
27x9+57+5 / 9
(psst, lets talk about something lol-)
Answer:
27x9+57+5 / 9 = 243 + 57 + 5 / 9 = 305 / 9 = 33.89
Step-by-step explanation:
Answer:
33.89
Step-by-step explanation:
(27*9+57+5)/9=33.89
(6x -7) +(-4x - 8) simplified
Answer:
2x−15
Step-by-step explanation:
6x−7−4x−8
=6x+−7+−4x+−8
Combine Like Terms:
=6x+−7+−4x+−8
=(6x+−4x)+(−7+−8)
=2x+−15
How do you solve linear inequality step by step?
Solving a linear inequality step by step involves several steps including isolating the variable on one side of the inequality sign, simplifying the inequality, graphing the inequality, shading the region that include the solutions and representing the solutions in the form of an interval.
1. Isolate the variable on one side of the inequality sign: This can be done by adding or subtracting the same value from both sides of the inequality, or by multiplying or dividing both sides by the same non-zero value.
2. Simplify the inequality: This can include combining like terms, or simplifying fractions or decimals.
3. Graph the inequality: This can be done by plotting the inequality on a number line or a coordinate plane, using a solid line for "greater than" or "less than" and a dotted line for "greater than or equal to" or "less than or equal to"
4. Test a point: To test whether a point is a solution of the inequality, substitute the coordinates of the point into the inequality, and check if the statement is true.
5. Shade the region that includes the solutions: The solutions of the inequality are all the points that make the inequality statement true. The solutions of the inequality are all the points that are in the shaded region.
6. Write the solution in interval notation: Write the solution in interval notation, if needed.
Here is an example:
Solve the inequality 2x - 3 > 5.
Step 1: Isolate the variable by adding 3 to both sides: 2x > 8
Step 2: Divide both sides by 2: x > 4
Step 3: Graph the inequality on a number line. Using a solid line, draw a line at x = 4 and shade the region to the right of the line, including 4.
Step 4: Test a point, e.g. x = 5, if 5 > 4 is true.
Step 5: The solution is x > 4.
Step 6: if needed, the solution can be written in interval notation as (4, +inf)
It's important to note that solving inequalities is not always straightforward, and some inequalities may require multiple steps to be solved.
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Write an equation in standard form with an x-intercept of 5 and a y-intercept of -4
An equation in standard form with an x-intercept of 5 and a y-intercept of -4 is,
⇒ 5x + 4y = 20
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The x - intercept = 4 ,
So, ( 4,0) is a point on the line.
And, The y - intercept = 5,
So, ( 0, 5) is a point on the line.
Now, Slope of the line passing through the point (4, 0) and (0, 5) is,
⇒ m = (5 - 0) / (0 - 4)
⇒ m = - 5/4
So, The slope intercept form of an equation is,
⇒ y = mx + b
Where, m = slope and b = y- intercept.
Hence, We get;
⇒ y = - 5/4x + 5
We know that;
An equation in standard form is,
⇒ Ax + By = C
So, We get;
⇒ y = - 5/4x + 5
⇒ 4y = - 5x + 20
⇒ 5x + 4y = 20
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which number is a factor of the prime factorization of 60?
Answer:
Step-by-step explanation:
So, the prime factorisation of 60 is 2 × 2 × 3 × 5 or it can be written as 22 × 3 × 5. where 2, 3 and 5 are prime numbers.
What are the types of substitutions?
Answer:
"Substitution comes in three flavors: nominal, verbal, or clausal, depending on the item being substituted.
Step-by-step explanation:
Hope it helps!
The spring musical cost $600 for costumes and $450 for the stage materials.
If the spring musical cost $600 for costumes and $450 for the stage materials. the number of tickets is 56 tickets.
How to find the number of tickets?Total ticket = $600 + $450
Total ticket = $1050
Now let find the number of tickets that they have to sell to profit.
Number of tickets = $1,050 - $375 / $12
Number of tickets = $675/$12
Number of tickets = 56 tickets
Therefore the number of tickets is 56 tickets.
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The complete question is:
The spring musical cost $600 for costumes and $450 for the stage materials.
Students raised $375 from advertisements in the program. Tickets cost $12 each.
How many tickets do they have to sell to profit?
Given the function defined in the table below, find the average rate of change, in simplest form of the interval 12 < x < 24
Therefore , as a result the solution of the given problem of expressions comes out to be the typical rate of change is -2/5 in its simplest form.
How is the expression chosen?An algebraic equation must be checked by replacing each variable with a number and performing arithmetic operations. Since 8 plus 6 = 14, the reply variable in the above example is equivalent to 6. In order to test the expression, we can replace the values of the variables with ones we already know.
Here,
Simply said, the median rate of change is -2/5.
The function's gradient or slope is its rate of change.
The slope of a function can be calculated using the formula:
=> D = dy/dx = y2, -y1, and x2, -x1.
Using the coordinates (0, 41) from the table and (15, 35)
Replace the expression with the coordinate:
=>m = 35-41/15-0
=>m = -6 /15
=>m =-2/5
As a result, the typical rate of change is -2/5 in its simplest form.
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3. 53°C below zero
write an integer for each situation
Answer:
See below
Step-by-step explanation:
52 degrees C below 0 ° C is just - 53 °C
What value of x will make the triangles similar by the sss similarity theorem brainly.
The value of x is not given in the question, and it's not possible to determine the value of x that will make the triangles similar by the SSS similarity theorem.
The SSS similarity theorem states that if three corresponding sides of two triangles are proportional, then the two triangles are similar. This applies to all triangles, regardless of their size or shape.
To use the SSS similarity theorem, you must know the length of at least three corresponding sides of the two triangles. Once you have this information, you can use the theorem to determine if the two triangles are similar.
It's important to note that to use the SSS similarity theorem, you must know the length of at least three corresponding sides of the two triangles. Without this information, it's not possible to determine if the two triangles are similar.
Therefore the value of x is not given in the question, and it's not possible to determine the value of x that will make the triangles similar by the SSS similarity theorem.
The SSS similarity theorem only states that the two triangles are similar, it doesn't tell anything about the angles of the triangles.
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If a₁ = 7 and an = an-1 - 1 then find the value of a5.
Answer:
a₅ = 3--------------------
Given AP with recursive formula:
a₁ = 7 and aₙ = aₙ₋₁ - 1As per recursive formula the first term is a₁ = 7 and common difference is d = -1.
Use the nth term formula to find the 5th term:
aₙ = a₁ + (n - 1)da₅ = 7 + (5 - 1)*(-1) = 7 - 4 = 3Alex is applying for positions at two different electronic stores in neighboring towns. The first job offer is a $200 weekly salary plus 5% commission on sales. The second job offer is a $75 weekly salary plus 10% commission.
The amount of sales at which Company A's offer is the same as Company B's is $600
How to calculate the amount?The given parameters that will help us to understand the question are
Company A:
Base = $200
Commission = 10% of sales = .1*S
A = .1S + 200
Company B:
Base = 400
Commission = .05*S
B = .05S + 400
We're looking for the point where they're equal.
200 + .1S = 400 + .05S
Multiply by 100 to get rid of decimals
20000 + 10S = 40000 + 5S
Subtract 20000 from both sides
10S = 20000 + 5S
Subtract 5S from both sides
5S = 20000
Divide both sides by 5
S = 4000
So, at $4000 sales, the two jobs pay the same.
You have to always check your work. This can be done by plugging the values into the basic equations and determining if they check. Or we can graph the two lines and see where they cross.
Company A:
200 + .1(4000) = 200 + 400 = 600
Company B:
400 + .05(4000) = 400 + 200 = 600
Conclusively Alex (A) offers $600 as same as Company B
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Complete question:
A salesperson has two job offers. Company A offers a weekly salary of $200 plus commission of 10% of sales. Company B offers a weekly salary of $400 plus commission of 5% of sales. What is the amount of sales at which Company A's offer is the same as Company B's?
how do I find out if a table is linear or non linear
Answer:
In the case of the classification problem, the simplest way to find out whether the data is linear or non-linear (linearly separable or not) is to draw 2-dimensional scatter plots representing different classes. Here is a picture that represents the linearly and non-linearly separable dataset and how one can use scatter plots to visualize them.
Step-by-step explanation:
26. PICTURE FRAME Aston is making a wooden picture frame
in the shape of a parallelogram. He has two pieces of
wood that are 3 feet long and two that are 4 feet long.
a. If he connects the pieces of wood at their ends to each other, in
what order must he connect them to make a parallelogram?
b. How many different parallelograms could he make with these
four lengths of wood?
c. Explain something Aston might do to specify precisely
the shape of the parallelogram.
To make a parallelogram, Aston must connect the pieces of wood in the following order: 3 feet, 4 feet, 3 feet, 4 feet.
How many different parallelograms could he make with these
four lengths of wood?He must connect the 3 foot pieces of wood first, and then the 4 foot pieces of wood.There are two different parallelograms he could make with these four lengths of wood.To specify the shape of the parallelogram, Aston could measure the angles of each corner and the lengths of the sides. He could also measure the distance between each corner.Aston could make several different parallelograms with these four lengths of wood. For example, he could arrange the pieces to make a trapezoid, a rectangle, or a rhombus.To specify precisely the shape of the parallelogram, Aston could measure the angles of the four corners to ensure that they are all equal. He could also measure the lengths of each side to make sure that the opposite sides are of equal length.Additionally, he could measure the diagonals of the parallelogram to ensure that they are of equal length. This will guarantee that the shape of the frame is a proper parallelogram.To learn more about parallelogram refer to:
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Is it possible to construct a triangle whose sides are 3.5 cm 9.2 cm and 5.3 cm Why or why not?
The triangle can be constructed from sides of triangle measuring 3.5 cm 9.2 cm and 5.3 cm due to side rule of triangle.
The possibility to construct the triangle will be found out through the sum of any two sides of triangle. If the sum is greater than the remaining side of the triangle, the construction is possible. Let us assume the side a, b and c of triangle to be 3.5, 9.2 and 5.3 cm.
Now, using the side-side-side rule of triangle -
Side a + side b > side c
3.5 + 9.2 > 5.3
Add the values
12.7 > 5.3
Side b + side c > side a
9.2 + 5.3 > 3.5
Add the values
14.5 > 3.5
side c + side a > side b
5.3 + 3.5 > 9.2
Add the values
8.8 not greater than 9.2
Based on the results, the construction of triangle from mentioned sides is possible according to length rule of the triangle.
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The sum of two numbers is 10 and the difference of those two
numbers is 18. (Usef to represent the first number and s to represent
the second number.)
Number of Houses Sold
The graph below shows the number of houses sold over x days. What is the average rate of change from day 2 to day
10?
y
(2,8)
(0,0)
2
House Sales
(6.6)
f(x)
(12,4)
(10,2)
4
6 8 10
Number of Days
12
INING
X
02:39:25
The average rate of change from day 2 to day 10 is given as follows:
-0.75 houses sold per day.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output divided by the change in the input.
The points of interest are given as follows:
(2,8) and (10,2).
The change in the output is of:
2 - 8 = -6.
The change in the input is of:
10 - 2 = 8.
Hence the average rate of change is obtained as follows:
r = -6/8
r = -3/4
r = -0.75 houses sold per day.
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Suppose the x and y vary inversely and x=1 when y=3. wrote a function that models that models the inverse variation. graph the function and find when x=5
The value of y= 1.6667 when x= 5.
The graph is attached below.
What is proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
x= 1 when y=3, if x and y vary inversely.
Then, x = k/y
where is proportionality constant
So, k = x y
k = 3
Using Proportion
x/ y = k
5/y= 3
y= 5/3
y= 1.6667
Hence, y= 1.6667 when x= 5.
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What is quotient formula?
A quotient is a number created when two numbers are divided. The formula for this is Quotient = Dividend ÷ Divisor.
The division is the process of dividing one number by any other number to produce a different number. Consequently, the dividend is the number that is divided in this instance. A number's divisor is the one that divides the given number. The quotient is the number that we get as a result.
Then, the quotient formula is given by Quotient = Dividend ÷ Divisor. For example, 50÷5=10. Here, 50 is the dividend, 5 is the divisor, 10 is the quotient, and 0 is the remainder.
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Is 4 6 and 2 3 equivalent?
So we can write 4/6 as equivalent to 2/3
What is Equivalent ?Equal is not the same as equivalent. While comparable indicates similar but not the same, equal means the same in all respects. For instance, 1 + 1 is comparable to 2, even if 2 is supposed to be equal to 2.
Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.
The fractions with distinct numerators and denominators but the same value are said to be equivalent fractions. For instance, since 2/4 and 3/6 both equal the 1/2, they are identical fractions. An element of a whole is a fraction. The same amount of the whole is represented by equivalent fractions.
So , 4/6 can be written as 2*2/3*2 = 2/3
So we can write 4/6 as equivalent to 2/3
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Write a formula to find the number of sides N in a regular polygon given that the measure of one interior angle is x
N= ?
N = (360/x) - 2
This formula finds the number of sides N in a regular polygon when given the measure of one interior angle x.
The formula is derived from the fact that the sum of all interior angles in a regular polygon is equal to (N-2)*180, where N is the number of sides.
Therefore, it can be rearranged to be N = (360/x) - 2.
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