If f(x) = 2x³ + x - -4, then what is the remainder when f(x) is divided by x - 3?
Answer:
61
Step-by-step explanation:
A mountain cabin on 1 acre of land costs 30,000 dollars. If the land cost 4 times as much as the cabin, what was the cost of each?
The cost of each land is 120,000 dollars.
How to find the cost of each land?The mountain cabin on 1 acre of land costs 30,000 dollars.
The land cost 4 times as much as the cabin.
Therefore, the cost of each land can be calculated as follows:
cost of each land = 4 (30, 000)
cost of each land = 4 × 30000
cost of each land = 120,000 dollars
Therefore, the land that cost 4 times as much as the cabin cost 120000 dollars for each.
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The coordinates of quadrilateral JKLM are J (1,3), K(3, 1), L (-1, -3) and M(-3,-1). What is the perimeter of quadrilateral JKLM?
the coodrinates of JKLM is,
J(1,3) , K(3,1), L(-1,-3) and M(-3,-1)
the length JK is ,
[tex]\begin{gathered} JK=\sqrt[]{(1-3)^2+(3-1)^2} \\ =\sqrt[]{4+4} \\ =\sqrt[]{8} \\ =2\sqrt[]{2} \end{gathered}[/tex]length KL is,
[tex]\begin{gathered} KL=\sqrt[]{(-3-1)^2+(-1-3)^2} \\ =\sqrt[]{16+16} \\ =\sqrt[]{32} \\ =4\sqrt[]{2} \end{gathered}[/tex]Length LM is,
[tex]LM=\sqrt[]{(-3-(-1))^2+(-1-(-3))^2}[/tex][tex]\begin{gathered} LM=\sqrt[]{4+4} \\ LM=2\sqrt[]{2} \end{gathered}[/tex]length MJ
[tex]\sqrt[]{(-1-3)^2+(-3-1)^2}[/tex][tex]\begin{gathered} MJ=\sqrt[]{16+16} \\ MJ=4\sqrt[]{2} \end{gathered}[/tex]so, the perimeter = sum of sides,
= JK + KL + LM + MJ
= 2 root 2 + 4root2 + 2root2 + 4root2
= 12 root 2
thus, the perimeter is 12 root 2
Help me please with this question
The distance between the two points (2, 6) and (7, -6) will be 13 units.
What is the distance between two points?Let one point be (x, y) and another point be (h, k). Then the distance between the points will be
D² = (x - h)² + (y - k)²
A right triangle with the two points forming the hypotenuse. The two points are given below.
(2, 6) and (7, -6)
Then the distance between the points (2, 6) and (7, -6) will be given as,
D² = (7 - 2)² + (-6 - 6)²
D² = 5² + (-12)²
D² = 25 + 144
D² = 169
D = 13 units
The distance between the two points (2, 6) and (7, -6) will be 13 units.
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hey math genius can anyone help me out with these questions.. I will mark you brainlist if your answer is correct..
please:):):)
a) Because it is an equilateral triangle, all the sides must have equal lengths.
The perimeter = 24cm -> Each side = 8.
Area = 1/2 b.h = 8.8.1/2 = 32 cm2.
b) A square has all of its sides of equal lengths just like an equilateral triangle.
The perimeter = 24cm -> Each side = 6.
Area = side.side = 6.6 = 36 cm2.
c) Since they have equal perimeters and the same properties (all sides equal) BUT they have different number of sides and lengths, they won't have the same areas.
d) A rectangle. E.g :
A set of lengths of 5cm and 7cm makes a rectangle with a perimeter of 24cm : (5+7).2
But, its area equals 5 x 7 = 35cm2, which is greater than the triangle.
Answer:
a) 27.71 cm²
b) 36 cm²
Step-by-step explanation:
a) Perimeter of equilateral triangle = 3a
Here, a is the side of equilateral triangle.
Perimeter of equilateral triangle = 24 cm
3a = 24 cm
a = 24 ÷ 3
a = 8 cm
[tex]\sf Area \ of \ equilateral \ traingle = \dfrac{\sqrt{3}}{4}a^2[/tex]
[tex]\sf = \dfrac{\sqrt{3}}{4}*8*8\\\\ = 1.732*2*8\\\\ = 27.71 \ cm^2[/tex]
b) Perimeter of square = 4s
Here, s is the side of square.
Perimeter of square = 24 cm
4s = 24
s = 24 ÷ 4
s = 6 cm
Area of square = s*s
= 6 * 6
= 36 cm²
c) When the dimensions (length, width, height) of the shape changes, the area and volume changes.
d) Length of the rectangle is 10 cm and width is 2 cm.
Perimeter of rectangle = 2*length + 2* width
= 2*10 + 2*2
= 20 + 4
= 24 cm
Area of perimeter of rectangle = length *width
= 10 * 2
= 20 cm²
David needs to read 5 novels each month.
Let N be the number of novels David needs to read in M months.
Write an equation relating N to M. Then use this equation to find the number of novels David needs to read in 17 months.
which 2 number are distance 8 and -4
Answer: the answer is 6 and 7
Step-by-step explanation:
because never gonna give u up never gonna let u down yessir
What is the image point for the photo shown
I need the answer for step by step 823 divided by 13
PLS HURRY!!!!!
Answer: 63.30769 or 823/13 or 63 4/13
823 divided by 13 = 63.307692
The result of 823/13 is a non-terminating, repeating decimal.
The repeating pattern above, 307692, is called repetend, and denoted overlined with a vinculum.
This notation in parentheses is also common: 823/13 = 63.(307692): However, in daily use it’s likely you come across the reptend indicated as ellipsis: 823 / 13 = 63.307692… .
823 divided by 13 in decimal = 63.307692
823 divided by 13 in fraction = 823/13
823 divided by 13 in percentage = 6330.76923077%
number from least to greatest: 8.116, 8.119, 8.18, 8.03, 8.14, 8.1
The Number system from least to greatest of the given number 8.116, 8.119, 8.18, 8.03, 8.14, 8.1 is 8.03 , 8.1, 8.116, 8.119, 8.14, 8.11.
What is the arrangement of numbers?We were given the number 8.116, 8.119, 8.18, 8.03, 8.14, 8.1 so that we can arrange them from the smallest number to the highest number.
The first number will be 8.03 , then follow by 8.1, the after that we can see that the next number will be 8.116, which will be followed by the number 8.14, then this will be followed by 8.119 then followed by the number 8.18.
Therefore, the arrangement will be 8.03 , 8.1, 8.116, 8.119, 8.14, 8.11.
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Find the value of the exterior or interior angle
the values of both angles are
2x - 8 = 2*25 - 8
= 42 degree
x -7 = 25 - 7
= 18 degree
What is interior and exterior angles ?Both internal and external angles make up a triangle. The angle that forms between two of a triangle's adjacent sides is known as the interior angle. The angle created between a triangle's side and its next-to-furthest side extending outward is known as the exterior angle. Triangle Angle sum feature of triangle states for ABC that 180 degrees is the sum of the triangle's internal angles.
Calculation2x - 8 + x - 7 + 90 = 180
3x - 15 = 90
x = 25
therefore the values of both angles are
2x - 8 = 2*25 - 8
= 42 degree
x -7 = 25 - 7
= 18 degree
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What’s the value of x
In the given angle, the value of x is 18°.
What are angles?In Euclidean geometry, an angle is a shape created by two rays that share an endpoint and are referred to as the angle's sides and vertex, respectively. The plane that contains the rays contains the angles created by two rays. The meeting of two planes can also result in an angle. They are referred to as dihedral angles.So, first label the lines as A, B, C, and D as follows:
Refer to the image attached below.
As we can see that line ADB is a straight line, so ∠ADB will be 180°.Line DC cuts the angle ∠ADB in two parts, so the equation can be:
(6x + 5) + 67 = 180Now, solve for x as follows:
(6x + 5) + 67 = 1806x + 72 = 1806x = 180 - 726x = 108x = 108/6x = 18°Therefore, in the given angle, the value of x is 18°.
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Question 2(Multiple Choice Worth 2 points)
(Factoring Algebraic Expressions MC)
Rewrite 1/6x³y + 5/6xy² using a common factor.
xy(x² +5y)
xy(3x² +15y)
xy(x² +5y)
x³y²(y+5x)
Answer:
xy(x² +5y)
Step-by-step explanation:
Rewrite 1/6x³y + 5/6xy² using a common factor.
To simplify, multiple each term by 6:
6 × (1/6x³y) + 6 × (5/6xy²)
= [tex]x^{3} y+5xy^{2} \\[/tex]
take the common term xy and
= [tex]xy(x^{2} +5y)[/tex]
solve this for me pls
The x-intercepts of the function are 10, and -8.
y-intercept is: -80.
The zeros are: x = 10 and x = -8
f(2) = -80
f(x) = -65 when x = 5 or -3.
What is the Y-intercept and the X-intercept of a Function?The y-intercept of a function is the output (y) when the input value (x) is zero. On the other hand, the x-intercept is the input value (x), when the output value (y) is zero.
What are the Zeros of a Function?The zeros of a function are the x-intercepts of a function.
Given the function, f(x) = x² - 2x - 80, substitute f(x) = 0 to find the value of x, which is the x-intercept:
0 = x² - 2x - 80
x² - 2x - 80 = 0
Factorize
(x - 10)(x + 8)
x = 10 or x = -8
Substitute x = 0 into the function to find the y-intercept:
f(0) = 0² - 2(0) - 80
f(0) = -80
x-intercepts are 10, and -8.
y-intercept is: -80.
The zeros are: x = 10 and x = -8
Find f(2):
f(2) = (2²) - 2(2) - 80,
f(2) = 4 - 4 - 80
f(2) = -80
Find x when f(x) = -65:
-65 = x² - 2x - 80
-65 + 80 = x² - 2x
15 = x² - 2x
x² - 2x - 15 = 0
Factorize
(x - 5)(x + 3) = 0
x = 5; x = -3
Therefore, f(x) = -65 when x = 5 or -3.
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The carter family spent a total of $25.50 at the movies. they bought 3 popcorns and 3 drinks each popcorn cost $2.50 more than a drink. write and solve an equation to find the cost of each drink
The equation to represent the cost of each drink is 3(x + 2.5) + 3x = 25.50. The cost of each drink will be $3.
In the given question, it is stated that the family spent a total of $25.50 and they bought 3 Popcorn and 3 Drinks. Each popcorn costs $2.5 more than the drink. Now, suppose the cost of one drink is 'x' then we get:
Cost of 3 Drinks = 3x
Cost of 3 Popcorn = 3(x + 2.5)
The equation to represent this will be:
=> 3(x + 2.5) + 3x = 25.50
=> 3x + 7.5 + 3x = 25.50
=> 6x = 18
=> x = 3
We get x = 3, Cost of one drink will be $3
Hence, equation representing it will be 3(x + 2.5) + 3x = 25.50, and the cost of each drink will be $3
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if 9^(2-x)=3,find the value of x
9^(2-x) = 3 -> 2-x = 1/2
into details about why it is 1/2 (ill call 2-x as y for easier demonstration)
9^y = 3
(3^2)^y = 3
And we have : (x^m)^n = x^mn
-> (3^2)^y = 3^2y = 3
-> 2y = 1
y = 1/2, therefore 2-x = 1/2.
So, x = 2 - 1/2 = 3/2.
A force of 85 N is applied to an area of 530 cm2. Calculate the pressure in N/m2. Give your answer to the nearest integer
A force of 85 N is applied over an area of 530 cm2. Then the pressure on it is equal to 1603.8 [tex]\frac{N}{m^{2} }[/tex].
Force(F) = 85 N
Area(A) = 530 [tex]cm^{2}[/tex]
Pressure(P) = ?
Calculating as per the above amount
Area = 530/100 × 100
= 0.053 [tex]m^{2}[/tex]
The definition of pressure is "force applied per unit area." The equation P = FA, where F is the force acting perpendicular to surface area A, provides the answer. The pascal (Pa), or one newton per square meter, is the accepted unit of pressure [tex]\frac{N}{m^{2} }[/tex].
Pressure is the physical amount of force exerted on a particular area. The definition of pressure is "force per unit of area." The pressure being applied to a body can be calculated by taking the amount of force being applied and dividing it by the area of contact.
Pressure = force/area
= 85/0.053
= 1603.8 [tex]\frac{N}{m^{2} }[/tex]
Pressure on the body is 1603.8 [tex]\frac{N}{m^{2} }[/tex]
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if you know the names of the remaining three students in the spelling bee, what is the probability of randomly selecting an order and getting the order that is used in the spelling bee?
The probability of randomly selecting an order and getting the order that is used in the spelling bee is 1/6
Here we have 6 possible arrangements:
3!=3*2*1
3!= 6
Hence, the probability of selecting an order and getting the order = 1/6.
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Lizzie wants to shelve her books with the same number of books on each shelf. if she uses five shelves, she has two books left over. if she uses six shelves, three books are left over. if she uses seven shelves, four books are left over. if lizzie has fewer than $314$ books, how many books does she have?
Take 1 cm of 5th, 6th and 7th shelves, it comes out to be = 210
Now,
5 - 2 = 3 book in the shelves
6 - 3 = 3 book in the shelves
7 - 4 = 3 book in the shelves
3 books are in common, so, 210 - 3 = 207 book Lizzie have.
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Given that all sides are equal for this
triangle, if its height if the triangle is 16
in, and the length of the prims is 33 in.
Solve for the surface area of the
equilateral prism(4 Points)
Type answer in the space provided and attach »
15 in
20 in.
33 M
Enter your maths answer
The equilateral triangular prism has a surface area of 1997.321 square inches
How to determine the surface area of the equilateral triangular prism?From the question, the given parameters are
Side length of the triangle, a = 20 inchesHeight of the equilateral triangular prism, h = 33 inchesThe total surface area of an equilateral triangular prism is calculated using the following formula
Surface area = a(√3/2) + 3(a × h);
Substitute the known values in the above equation
So, we have the following equation
Surface area = 20 * (√3/2) + 3(20 × 33);
Evaluate the product
So, we have the following equation
Surface area = 1997.321
Hence, the surface area of the equilateral triangular prism is 1997.321 square inches
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Under her cell phone plan, Sydney pays a flat cost of $35.50 per month and $5 per gigabyte. She wants to keep her bill under $50 per month. Write and solve an inequality which can be used to determine x x, the number of gigabytes Sydney can use while staying within her budget.
The number of gigabytes that Sydney can use while staying within her budget is less than 2.9 gigabytes.
How to illustrate the information?From the information, Sydney pays a flat cost of $35.50 per month and $5 per gigabyte. She wants to keep her bill under $50 per month.
The inequality that can be used to determine x x, the number of gigabytes Sydney can use while staying within her budget will be:
35.50 + 5x < 50
Collect like terms
5x < 50 - 35.50
5x < 14.50
x < 14.50 / 5
x < 2.9
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I need help with this. I honestly forgot how to do algebra 1 and I know that’s embarrassing for me but yea I need help on this whole thing I think I did 1-3 wrong too
The required equation of slope intercept the line parallel to the given line and passing through (4,5) is y = -1/4x + 6.
What exactly does slope intercept mean?
A method of expressing a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form. The point where the line is drawn the y-axis is known as the y-intercept, and the slope refers to how steep the line is.
1) 5x + y = 3
y = - 5x + 3
compare equation y = mx + c
m = -5
2) 7x - 5y = 20
5y = 7x - 20
y = 7/5x - 4
compare equation y = mx + c
m = 7/5
3) y = -1/3x - 4
compare equation y = mx + c
m = -1/3
4) points ( 4,5) parallel to y = 1/4x - 4
m₁ = m₂
compare equation y = mx + c
m₁ = 1/4 c = -4
now lets put the value
1/4 = m₂
So the equation of the line parallel to the given line assuming that its y-intercept is b will be
y = 1/4x + b
the equation of the parallel line which passes through
(4,5, it should satisfy these points.
So let's substitute these points
5 = -4/4 + b
5 = -1 + b
b = 6
Hence the required equation of the line parallel to the given line and passing through (4,5) is
y = -1/4x + 6
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The ski team needs new uniforms. The students plan to sell plush toy hawks (the school mascot) for $5 each. The students find three companies on-line that sell stuffed mascots. Company A sells 15 hawk for $41.10. Company B sells 18 hawks or $48.96. Company C charges $35.92 for 12 hawks.1 Which company has the best buy?
Answer:Company b
Step-by-step explanation: 41.10/15=2.74
48.96/18=2.72
35.92/12=2.99
A series circuit has two resistors having the values of R1= 200 and R2= 300, with a source of 300 V. Compute for the following.
Answer: R1=0
Step-by-step explanation:
R1 = 200 divide R1 = 200 by 2 = R1 = 0
i dont understand can you right it in order on the table
Answer:
oh k
Step-by-step explanation:
sure, I will!
Pls help willing to give 15 points and brainliest for 2 graph questions.
1. The slope of the line on the graph is: 6
2. The graph of the line with a slope of 4/3 is shown in the image below.
What is the Slope of a Line?Slope of a line = change in y / change in x = rise/run.
How to Graph an Equation?The equation that can be used to represent a linear graph can be written in slope-intercept form as y = mx + b, where the value of b is the y-intercept of the line and the value of m is the slope of the line.
1. Using two points on the line, (0, -1) and (1, 5):
Slope of the line = change in y / change in x = (-1 - 5)/(0 - 1)
Slope of the line = -6/-1
Slope of the line = 6
2. Slope (m) = 4/3
A point on the line is given as (1, 3)
Write the equation of the line by substituting (a, b) = (1, 3) and m = 4/3 into y - b = m(x - a):
y - 3 = 4/3(x - 1)
y - 3 = 4/3x - 4/3
y = 4/3x - 4/3 + 3
y = 4/3x + 5/3
The graph of y = 4/3x + 5/3 is shown in the image below.
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The sat exams are scaled so that scores should roughly follow the normal distribution with mean 500 and standard deviation 100.how high must a student score on the sat mathematics exam to fall in the top 25% of all scores?
Answer:
568
Step-by-step explanation:
Using a z-score table, we see the minimum z-score is about 0.68.
Using the formula for the z-score,
[tex]\frac{x-500}{100}=0.68 \\ \\ x-500=68 \\ \\ x=568[/tex]
Determine if the conjecture is true or false. If false, give a counterexample.
Given : x is a non-negative number
Conjecture : -x is a negative number
Answer:
Step-by-step explanation:
TRUE
5 is a non-negative number
Conjecture : - 5 is a negative number
Which is NOT a method that can be used to prove that lines i and k are parallel?
Responses
A Show congruence of a pair of alternate interior angles.Show congruence of a pair of alternate interior angles.
B Show that both lines are perpendicular to a third line.Show that both lines are perpendicular to a third line.
C Show that a pair of interior angles on opposite sides are supplementary.Show that a pair of interior angles on opposite sides are supplementary.
D Show congruence of a pair of corresponding angles.Show congruence of a pair of corresponding angles.
Question 2
Lines l and k intersect forming two pairs of vertical angle. If one of these angles measure 120°, what are the measures of the other three angles?
Responses
A 60°, 60°, 60°60°, 60°, 60°
B 120°, 120°, 120°120°, 120°, 120°
C 60°, 90°, 90°60°, 90°, 90°
D 60°, 60°, 120°60°, 60°, 120°
The method that can not be used to prove that lines i and k are parallel is the statement "shows that both lines are perpendicular to a third line".
and the measures of the other three angles are 60°, 60°, and 120°
What are Interior Angles?Interior angles are defined as the pair of angles created on the inner side of the parallel lines and on the opposite sides of the transversal when two parallel lines are intersected by a transversal are referred to as alternate internal angles
The method that can not be used to prove that lines i and k are parallel is the statement "shows that both lines are perpendicular to a third line".
Lines l and k intersect forming two pairs of vertical angles. If one of these angles measures 120°,
As per the given question,
Let angle ∠1 is 120°
here angles ∠1 and ∠2 are supplementary
So ∠2 = 180° - 120° = 60°
However, if a transversal intersects two parallel lines, then each pair of alternate interior angles is equal.
∠2 = ∠4 = 60°
∠1 = ∠3 = 120°
Therefore, the measures of the other three angles are 60°, 60°, and 120°.
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Which fraction is closest to zero?
8/12 , 5/8 , 6/10 , 2/3
Answer:
6/10
Step-by-step explanation:
first, use your calculator to convert them to decimals
8/12 = 0.66
6/10 = 0.60
5/8 = 0.625
2/3 = 0.66
then see which one is the smallest
6/10 =0.60
done!!!! your answer