Unless otherwise indicated, a line in geometry is understood to be _____. straight curved either
Which linear equation has a slope of 3 and a y-intercept of –2?
y = 3x + 2
y = 3x – 2
y = –2x + 3
y = –2x – 3
Answer: y = 3x - 2
Step-by-step explanation:
Equation of a straight line is
y=mx + c
m is the slope and c is the intercept
comparing it with the equation
y=3x - 2
m = slope =3
and c= intercept= -2
if x-2m=p make m the subject. answer must be written as fraction.
To make m the subject of the equation x-2m=p, add 2m to both sides, subtract p, and divide by 2. The result is m as the subject of the equation, represented as the fraction (x - p)/2.
Explanation:To solve the equation x-2m=p for m as the subject, we want to isolate m on one side of the equation. Here is the step-by-step process:
Start with the original equation: x - 2m = p.Add 2m to both sides to get x = p + 2m.Subtract p from both sides to get x - p = 2m.Divide both sides by 2 to isolate m: m = (x - p)/2.Now m is the subject of the equation, and it is represented as a fraction as requested.
Which expression represents the probability of rolling a 5 exactly three times in ten rolls of a number cube with six sides?
The probability of rolling a 5 exactly three times in ten rolls of a number cube with six sides is 0.034.
What is the probability?
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.
The probability of rolling a 5 exactly three times in ten rolls of a number cube with six sides is determined in the following steps given below.
[tex]\rm Probability=\dfrac{10}{3}\times \left (\dfrac{1}{3} \right ) ^3\times \left (\dfrac{5}{6} \right ) ^7\\\\Probability= \dfrac{10}{3}\times \dfrac{1}{27} \times \dfrac{78125}{279936}\\\\Probability=0.034[/tex]
Hence, the probability of rolling a 5 exactly three times in ten rolls of a number cube with six sides is 0.034.
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A pattern for 1 1 uniform uses 12 12 yards of material. Boleslaw wants to know how many yards are needed for 8 8 uniforms. Chantal wants to know how many yards she will need to make 15 15 uniforms.
To find the amount of material needed for a certain number of uniforms, we can use a proportion and multiply the amount of material needed for 1 uniform by the desired number of uniforms.
Explanation:To find out how many yards are needed for 8 uniforms, we can set up a proportional relationship between the number of uniforms and the amount of material needed. We can do this by dividing the amount of material needed for 1 uniform by the number of uniforms, and then multiplying by the desired number of uniforms. The formula for this is (Amount of material needed for 1 uniform / Number of uniforms) * Desired number of uniforms. Using this formula, we can determine that 8 uniforms would require (12 yards / 1 uniform) * 8 uniforms = 96 yards of material.
To find out how many yards are needed for 15 uniforms, we can use the same formula. (12 yards / 1 uniform) * 15 uniforms = 180 yards of material.
Therefore, 8 uniforms require 96 yards of material, and 15 uniforms require 180 yards of material.
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What is the area of a rectangle with vertices at (−6, 3) , (−3, 6) , (1, 2) , and (−2, −1) ?
Enter your answer in the box. Do not round any side lengths.
What is the area of a triangle with vertices at (0, −2) , (8, −2) , and (9, 1) ?
Enter your answer in the box.
What is the perimeter of a polygon with vertices at (−2, 1) , (−2, 4) , (2, 7) , (6, 4) , and (6, 1) ?
Enter your answer in the box. Do not round any side lengths.
What is the perimeter of the rectangle shown on the coordinate plane, to the nearest tenth of a unit?
15.3 units
20.4 units
30.6 units
52.0 units
(1) the area of a rectangle with vertices at (−6, 3) , (−3, 6) , (1, 2) , and (−2, −1)
To find area of rectangle we need to find the length and width
Length = distance between (−6, 3) and (−2, −1)
Distance = [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
= [tex]\sqrt{(-2-(-6))^2 + (-1-3)^2}[/tex]
= [tex]\sqrt{(4)^2 + (-4)^2}[/tex]=[tex]\sqrt{(16) + 16}[/tex] =[tex]\sqrt{32}[/tex]
width = Distance between (−6, 3) , (−3, 6)
Distance = [tex]\sqrt{(-3-(-6))^2 + (6-3)^2}[/tex]
=[tex]\sqrt{3^2+3^2}= \sqrt{18}[/tex]
Area = Length * width = [tex]\sqrt{32} *\sqrt{18} = \sqrt{576}= 24[/tex]
(2) the area of a triangle with vertices at (0, −2) , (8, −2) , and (9, 1)
Area of triangle = [tex]\frac{1}{2} * base * height[/tex]
base is the distance between (0,-2) and (8,-2)
Distance = [tex]\sqrt{(8-0)^2 + (-2-(-2))^2}[/tex] = 8
To find out height we take two vertices (8,-2) and (9,1)
Height is the change in y values = 1- (-2) = 3
base = 8 and height = 3
So area of triangle = [tex]\frac{1}{2} * 8 * 3 = 12[/tex]
(3) the perimeter of a polygon with vertices at (−2, 1) , (−2, 4) , (2, 7) , (6, 4) , and (6, 1)
To find perimeter we add the length of all the sides
Distance between (−2, 1) and (−2, 4) = [tex]\sqrt{(-2+2)^2 + (4-1)^2}[/tex]= 3
Distance between(−2, 4) and (2, 7) = [tex]\sqrt{(2+2)^2 + (7-4)^2}[/tex]= 5
Distance between (2, 7) and (6, 4) = [tex]\sqrt{(6 - 2)^2 + (4-7)^2}[/tex]= 5
Distance between (6, 4) and (6, 1) = [tex]\sqrt{(6 - 6)^2 + (1-4)^2}[/tex]= 3
Distance between (6, 1) and (−2, 1) = [tex]\sqrt{(-2-6)^2 + (1-1)^2}[/tex]= 8
Perimeter = 3 + 5 + 5 + 3 + 8 = 24
(4) four coordinates are (-7,-1) (-6,4) (3,-3) and (4,2)
Length = Distance between (3,-3) and (4,2) = [tex]\sqrt{(4-3)^2 + (2+3)^2}[/tex]= [tex]\sqrt{26}[/tex]
Width = Distance between (-6,4) and (4,2) = [tex]\sqrt{(4+6)^2 + (2-4)^2}[/tex]= [tex]\sqrt{104}[/tex]
Perimeter = 2(lenght + width) = 2*( [tex]\sqrt{26}[/tex]+[tex]\sqrt{104}[/tex] )
= 30.6 units
The area of the rectangle is [tex]24\;square\;units[/tex].
1. According to the question, the vertices of the rectagle are at [tex](-6, 3) ;(-3, 6) ;(1, 2)[/tex] , and [tex](-2, -1)[/tex].
The distance between two vertices on the coordinate plane is
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
So,
[tex]Length=D_1\\D_1=\sqrt{(6-3)^2+(-3+6)^2}\\D_1=\sqrt{9+9}\\D_1=3\sqrt 2 units[/tex]
Similarly,
[tex]Width=D_2\\D_2=\sqrt{(-2+6)^2+(-1-3)^2}\\D_2=\sqrt{16+16}\\D_2=16\sqrt 2\;units[/tex]
The area of the rectangle is equals to product of length and width of the rectabgle.
So,
[tex]Area=length\times width\\Area=3\sqrt{2}\times 4\sqrt{2}\\Area=24\;square\;units[/tex]
Hence, the area of the rectangle is [tex]24\;square\;units[/tex].
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Find the sum and express it in scientific notation. 0.00348 + (6.2 x 10^-2) A) 2.176 x 10^-4 B) 6.2348 x 10^-2 C) 6.2348 x 10^-1 D) 6.548 x 10^-2
23 POINTS PLZ HELP
The sum of the expression in scientific notation is given by option D) 6.548 × 10⁻².
Given expression is,
0.00348 + (6.2 x 10⁻²)
We have to first find the sum.
For that, rewrite the number in the scientific form in the normal form.
Since the exponent of 10 is -2, the decimal point is shifted 2 units to the left.
6.2 x 10⁻² = 0.062
0.00348 + (6.2 x 10⁻²) = 0.00348 + (0.062)
= 0.06548
Now, we have to write this in scientific notation as the power of 10.
After shifting the decimal point to the right up to 2 units, 0.06548 becomes = 6.548.
So, 0.06548 = 6.548 × 10⁻²
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Tom has been given 35 chores to complete today. This morning he finished 7 of them. How many chores does he now have left to do?
28 chores he now has left to do.
What is subtraction?An arithmetic intelligence operation minus simulates the process of deleting items from either a collection. To subtract is to take something or something from a particular group. The group's total number of items decreased and became lower when people eliminated it. The components of a subtraction issue are the issues dealing with, forces at play, and differences. The negative symbol, or, denotes subtraction.
35 tasks have been assigned to Tom for today.
He accomplished 7 of them this morning.
The remaining days are:
= 35-7
= 28 chores
The remaing chores are 28.
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Sine: the trigonometric function that is equal to the ratio of the side opposite a given angle (in a right triangle) to the hypotenuse.
What is the Sine of angle A?
3/4
4/3
3/5
4/5
Convert 30 feet per second to miles per minute.
5280 ft = 1 mi
Round to the nearest hundredth.
Answer:
0.34 miles per minute
Step-by-step explanation:
We have to convert 30 feet per second to miles per minute.
1 minute = 60 seconds
Therefore, in one minute = 60 × 30 = 1800 feet
5280 feet = 1 mile
180 feet = [tex]\frac{1800}{5280}[/tex]
= 0.3409 ≈ 0.34 mile
Therefore, 0.34 mile per minute.
The base angle of an isosceles triangle measures 54°. What is the measure of its vertex angle?
27°
36°
54°
72°
The measure of the vertex angle is 72 degrees
Isosceles triangleThe sum of the interior angle of a triangle is 180 degrees. Of the base angles are equal hence;
54 + 54 + x = 180
where
x is the vertex angles
Simplify
108 + x = 180
x = 180 - 108
x = 72 degrees
Hence the measure of the vertex angle is 72 degrees
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Ax + by = c find Y show steps
What is the remainder when 314^162 is divided by 7?
Final answer:
To find the remainder of 314162 divided by 7, we use modular arithmetic and find that the powers of 314 mod 7 repeat every 3 powers. Since 162 is a multiple of 3, 314162 mod 7 equals 1.
Explanation:
The question asks for the remainder when 314162 is divided by 7. To solve this problem, we can use a concept known as modular arithmetic, which deals with the remainder upon division. The key here is to find a pattern in the powers of 314 modulo 7, because large numbers can be cumbersome to work with directly. A helpful property is that (a×b) mod n = [(a mod n)×(b mod n)] mod n.
Let's consider the powers of 314 mod 7:
3141 mod 7 = 2
3142 mod 7 = (314 × 314) mod 7 = (2 × 2) mod 7 = 4
3143 mod 7 = (3142 × 314) mod 7 = (4 × 2) mod 7 = 1
Since we reached 1 again, the sequence will repeat every 3 powers. Now, 162 is divisible by 3 (162 = 3 × 54). Therefore, we can conclude that 314162 mod 7 will have the same remainder as 3143 mod 7, which is 1.
if the federal reserve decreases the reserve rate from 5% to 2.5% how does this affect the amount of money that would result because of fractional reserve banking from an initial deposit into a bank of $35000
It increases the amount by 700,000
What the opposite of 30 degrees North latitude
Petro had $15 dollars. He spent $9 dollars on a book. His friend had $12 how much money did pedro have left
Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t), is a(t) = 3t^2 + cos(t) and v(0) = 2.
v(t) = t^3 + sin(t) + 2
v(t) = t^3 - sin(t) + 3
v(t) = 6t - sin(t) + 2
v(t) = t^3 - sin(t) + 2
The velocity function of an object moving along the {x} - axis would be -
v{t} = sin(t) + t³ + 2.
What is instantaneous acceleration?The acceleration at any instant of time is called instantaneous acceleration. Mathematically -
a = dv/dt
dv = a dt
∫dv = ∫a dt
Given is the acceleration function as -
a(t) = 3t² + cos(t)
We know that -
a = dv/dt
dv = a dt
∫dv = ∫a dt
v{t} = ∫{3t² + cos(t)} dt
v(t) = sin(t) + t³ + C
Now -
v(0) = 2
sin(0) + 0 + C = 2
C = 2
So, we can write the velocity function as -
v{t} = sin(t) + t³ + 2
Therefore, the velocity function of an object moving along the {x} - axis would be -
v{t} = sin(t) + t³ + 2.
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Which phrase matches the algebraic expression below? (1 point)
2(x − 7) + 10
Two times the sum of x and seven plus ten
Two times the difference of x and seven plus ten
Two times x minus seven plus ten
Two times x minus the sum of seven and ten
Answer:
Two times the difference of x and seven plus ten
Step-by-step explanation:
A bakery packages 868 cupcakes into 31 boxes. The same number of cupcakes are pput into each box. How many cupcakes are in each box?
What is the graph of the equation 4x – 5y = 15?
A man’s age is two years more than four times his son’s age. His son is now 8. How old is the man?
A candy bar has 12 grams of fat. The company producing the candy bar also sells a reduced-fat version that has 25% less fat. How many grams of fat are in the reduced-fat candy bar? Do not include units in your answers
Answer:
it's 9 grams for apex
What’s the best answer
What is the quotient when (x+3) is divided into the polynomial 2x2+3x-9
A quotient is a quantity that is obtained by dividing two integers. The quotient of the division (2x²+3x-9) ÷ (x+3) is (2x - 3).
What is a quotient?A quotient is a quantity that is obtained by dividing two integers. The quotient is a term that is widely used in mathematics to refer to the integer component of a division, as well as a fraction or a ratio.
The quotient of the division (2x²+3x-9) ÷ (x+3) can be found as shown below,
[tex]\dfrac{2x^2+3x-9}{(x+3)}\\\\=\dfrac{2x^2+6x - 3x -9}{(x+3)}\\\\=\dfrac{2x(x+3)-3(x+3)}{(x+3)}\\\\=\dfrac{(2x-3)(x+3)}{(x+3)}\\\\[/tex]
= (2x - 3)
Hence, The quotient of the division (2x²+3x-9) ÷ (x+3) is (2x - 3).
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A line passes through the origin and has a slope of 4. What is the equation of the line that is parallel to the first line and passes through the point (1, –2)? A. y = 4x + 9 B. y = –4x + 2 C. y = 4x – 6 D. 2003-10-03-00-00_files/i0160000.jpg
Option C is correct, y=4x-6 is the equation of the line that is parallel to the first line and passes through the point (1, –2)
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
A line passes through the origin and has a slope of 4
y=4x is the equation of the line.
We have to find the equation of the line that is parallel to the first line and passes through the point (1, –2)
Slope is 4 as it is parallel.
We have to find the y intercept
-2=4(1)+b
b=-6
So equation is y=4x-6
Hence, Option C is correct, y=4x-6 is the equation of the line that is parallel to the first line and passes through the point (1, –2)
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the sum of two numbers is 8, and the sum of their squares is 34. what is the smaller number?
5 +3 = 8
3^2 = 9
5^2 = 25
25 +9 = 34
smaller number is 3
(4.5+7.6)-8*2.5 I really need help with this problem
Determine which of the following terms is a function: a. (1,2) (2,4) (3,5) c. (1,2) (2,4) (2,6) b. (1,2) (2,3) (1,5) d. (1,2) (3,5) (3,7)
Answer:
A is the mofluffin answer
Step-by-step explanation:
The temperature in degrees Celsius, c, can be converted to degrees Fahrenheit, f, using the equation mc026-1.jpg. Which statement best describes the relation (c, f)? It is a function because –40°C is paired with –40°F. It is a function because every Celsius temperature is associated with only one Fahrenheit temperature. It is not a function because 0°C is not paired with 0°F. It is not a function because some Celsius temperatures cannot be associated with a Fahrenheit temperature.
Answer:
B
Step-by-step explanation:
edge
what is the decimal equivalent to 15 1/4
The equivalent decimal number will be 15.25.
What is Decimal number?
A decimal number is a number that consists of a whole and a fractional part.
Given that;
The number is,
⇒ 15 1/4
⇒ 61 / 4
Now,
Solve the number in decimal form as;
The number is,
⇒ 15 1/4
⇒ 61 / 4
⇒ 61 ÷ 4
After divide we get;
⇒ 61 ÷ 4 = 15.25
Thus, The equivalent decimal number will be 15.25.
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