y=2x-3 is the equation of line that includes the point (6, 3) has a slope of 2
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
We need to find the equation of line that includes the point (6, 3) has a slope of 2.
y minus y one equal to m time of x minus x one.
(y-y₁)=m(x-x₁)
x₁=6,y₁=3 and m is 2
y-3=2(x-3)
Apply distributive property on right hand side.
y-3=2x-6
Shift -3 to the RHS side
y=2x-6+3
y=2x-3
Hence y=2x-3 is the equation of line that includes the point (6, 3) has a slope of 2
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What is the product of all positive divisors of $100$?
The product of all positive divisors of the number 100 is 1,000,000, using the property that the product of an integer's positive divisors is equal to the integer raised to the power of half its total number of divisors.
Explanation:The product of all positive divisors of 100 can be found using a special property. This property states that for any positive integer n, the product of all its positive divisors will be equal to n raised to the power of half its total number of divisors. Now, factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. So, there are 9 divisors, and the product of all positive divisors will be 100^((9/2)). The answer is 1,000,000.
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What is the equation of the line in standard form? (-1,-4) (2,2)
94 POINTS
Ricardo draws three right triangles. In each figure, he measures a pair of angles.
What is a reasonable conjecture for Ricardo to make by recognizing a pattern and using inductive reasoning?
A.) In a right triangle, all of the angles are right angles.
B.) In a right triangle, all of the angles are acute.
C.) In a right triangle, the acute angles are complementary.
D.) In a right triangle, the acute angles are congruent.
Answer:its c
Step-by-step explanation:
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A magazine has a special offer of 18 issues for $28.44. How much does each issue cost?
Answer:
A magazine has a special offer of 18 issues for $28.44. Each issue costs $1.58. Solution: 28.44 / 18 = 1.58.
Simplify (5ab4c)(-abc2). 4b3c -5a2b5c3 -5ab4c2
it will be simplified as [tex]\( -5a^2b^5c^3 \).[/tex]
Sure, let's simplify the expression step by step:
Given expression: [tex]\( (5ab^4c)(-abc^2) \)[/tex]
Step 1: Multiply the coefficients (numbers) together:[tex]\( 5 \times -1 = -5 \)[/tex]
Step 2: Multiply the variables with the same base together and add their exponents. Start with 'a': [tex]\( a \times a = a^{1+1} = a^2 \)[/tex]
Step 3: For 'b', multiply[tex]\( b^4 \) with \( b^1 \) which gives \( b^{4+1} = b^5 \).[/tex]
Step 4: For 'c', multiply[tex]\( c^1 \) with \( c^2 \) which gives \( c^{1+2} = c^3 \).[/tex]
Combine all these results together:[tex]\( -5a^2b^5c^3 \)[/tex]
So, the simplified expression is [tex]\( -5a^2b^5c^3 \).[/tex]
1. Start by multiplying the coefficients (numbers) together. In this case,[tex]\( 5 \times -1 = -5 \).[/tex]
2. Next, multiply the variables with the same base together and add their exponents. For 'a',[tex]\( a^1 \) times \( a^1 \) gives \( a^{1+1} = a^2 \). Similarly, for 'b', \( b^4 \) times \( b^1 \) gives \( b^{4+1} = b^5 \), and for 'c', \( c^1 \) times \( c^2 \) gives \( c^{1+2} = c^3 \).[/tex]
3. Combine all these results together to get [tex]\( -5a^2b^5c^3 \).[/tex]
This process ensures that each term in the expression is simplified according to the rules of exponents and multiplication of coefficients.
complete question
Simplify (5ab4c)(-abc2). 4b3c -5a2b5c3 -5ab4c2
In the diagram below, what is the approximate length of the minor Arc de? "if you can, explain please"
Answer:
D) 23.6 cm
Step-by-step explanation:
We first find the circumference of the circle. Circumference is given by the formula
C = 2πr, where π = 3.14 and r is the radius. The radius of our circle is 15 cm; this gives us
C = 2(3.14)(15) = 94.2.
Next we find the portion of the circumference associated with the given arc. The measure (in degrees) of the arc is 90°; this makes it 90/360 of the circle. 90/360 simplifies to 1/4; this means this arc is 1/4 of the circumference:
1/4(94.2) = 23.55
This rounds to 23.6.
At 2:00 p.m. two cars start toward each other from towns 240 miles apart. If the rate of one car is 10 mph faster than the other, how fast does each car go if they meet at 5:00 p.m.? If 3x represents the distance that the slower car traveled, then which expression represents the distance the faster car traveled?
To find the speed of each car, we set up and solve an equation based on the given information. The slower car's speed is 35 mph and the faster car's speed is 45 mph.
Explanation:To solve this problem, we need to set up an equation based on the given information. Let's assume that the slower car's speed is x mph, so the faster car's speed would be (x + 10) mph. Since they meet at 5:00 p.m. and start at 2:00 p.m., they have been traveling for 3 hours.
Using the formula: speed = distance/time, we can write the equation:
x * 3 + (x + 10) * 3 = 240
Simplifying the equation, we get:
3x + 3(x + 10) = 240
6x + 30 = 240
6x = 210
x = 35
So, the slower car's speed is 35 mph and the faster car's speed is (35 + 10) = 45 mph.
You need to buy fertilizer for a circular flower bed with a diameter of 13 feet. If one bag will fertilize 10 square feet, how many bags do you need to buy?
The area of the flower bed is approximately 132.73 square feet. Each bag of fertilizer covers 10 square feet, so we'd need 13.27 bags. Rounding up, we'll need to buy 14 bags.
Explanation:The question involves the calculation of the area of a circular flower bed and determining the amount of fertilizer needed for that area. The area of a circle can be calculated using the formula πr², where 'r' (radius) is half of the diameter. In this case, the diameter of the flower bed is 13 feet, so the radius is 13/2 = 6.5 feet. We then square the radius (6.5²) which gives us 42.25 and multiply by π (approximately 3.14), resulting in an area of approximately 132.73 square feet. Given that each bag of fertilizer covers 10 square feet, we would need 13.27 bags of fertilizer. Since we cannot buy a fraction of a bag, we would need to buy 14 bags to fully cover the flower bed.
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Need help ASAP quick
what system of linear inequalities is represented by the graph?
Answer:
y > 2x - 4 and y ≤ [tex]\frac{x}{2}-1[/tex]
Step-by-step explanation:
In this question we will find the equations of the lines first then decide the inequality sign.
Dotted line in the graph passes through two points (2, 0) and (0, -4)
Let the equation of the line is y = mx + c
Where m = slope and c = y-intercept
Slope (m) of the line will be = [tex]\frac{y-y'}{x-x'}[/tex]
m = [tex]\frac{0+4}{2-0}[/tex]
m = 2
y-intercept of the line = (-4)
So, equation of the line will be y = 2x - 4
Now we see the shaded area is above the dotted line so inequality will be
y > 2x - 4
Now for the bold line
Let the equation of this line is y = m'x + c'
This line passes through points (2, 0) and (0, -1)
then slope of the line m' = [tex]\frac{y-y'}{x-x'}[/tex]
m = [tex]\frac{0+1}{2-0}[/tex] = [tex]\frac{1}{2}[/tex]
y-intercept = c = -1
Then equation of the line will be
y = [tex]\frac{x}{2}-1[/tex]
Since shaded area is below the bold line therefore, inequality sign will be "less than equal to"
Inequality of the bold line will be y ≤ [tex]\frac{x}{2}-1[/tex]
System of the linear inequalities will be
y > 2x - 4 and y ≤ [tex]\frac{x}{2}-1[/tex]
The measure of DCG is 145°. What is mDCE? 90° 100° 180° 190°
The measure of ∠DCE is 100° so option (B) will be correct.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.
In another word, the angle is the measurement of the angular distance for example for linear motion we have a meter inch but for angular rotation, we don't have the measurement so the angle is useful to measure the angular rotation.
Given the angle,
∠DCG = ∠DCE + 20 + 25
145° = ∠DCE + 20 + 25
∠DCE = 100°
Hence "The measure of ∠DCE is 100°
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A single fair die is rolled twice. determine the number of points in the sample space
There are a total of 36 outcomes if you rolled a fair single die twice.
The sample space for this event would be: (check in the attached file)
To which graph does the point (−1, 4) belong?
y ≤ −x + 4
y ≤ −x − 2
y ≤ 2x − 3
y ≤ 4x + 1
Answer: First one
Step-by-step explanation:
Due to slope form which is y=mx + b.
-1 = x and y = 4.
It does not show the one because it would be equal to X, but it does show the negative
Wen takes a job with a starting salary of $100,000 for the first year. She earns a 3% increase each year. What does S5 represent?
Final answer:
S5 represents Wen's salary in the fifth year after receiving a 3% annual raise from a starting salary of $100,000. Fifth year salary is $112,550.
Explanation:
The student is asking about an arithmetic sequence or a geometric sequence involving a salary increase. In this case, S5 represents the salary Wen will earn in the fifth year of her employment, assuming a 3% annual salary increase from a starting salary of $100,000. To calculate S5, we use the formula for the sum of a geometric sequence because a constant percentage change implies exponential growth. The first term (a) is her starting salary, the common ratio (r) is 1.03 (reflecting the 3% increase), and the term we want to calculate is the fifth term (n=5).
The formula for the nth term of a geometric sequence is Tn = a × r^(n-1), where Tn is the nth term, a is the first term, and r is the common ratio. Applying the formula:
First Term (a): $100,000Common Ratio (r): 1.03Fifth Term (S5): $100,000 × (1.03)^(5-1)S5 = $100,000 * (1.03)^4 = $100,000 * 1.1255 = $112,550.Therefore, S5 calculates the salary Wen will earn in year five after receiving a 3% raise each year from the starting salary of $100,000 to $112,550.
Evaluate 3/2y - 3 + 5/3z when y = 6 and z = 3
To solve the expression, you should substitute the provided values for y and z then simplify the resulting expression. The solution is 11.
Explanation:To evaluate the expression 3/2y - 3 + 5/3z when y = 6 and z = 3, first, we should substitute the values of y and z into the expression.
So, the expression becomes 3/2*6 - 3 + 5/3*3. Multiply to reduce fractions: 9 - 3 + 5. This simplifies to 11.
So the value of the given expression when y = 6 and z = 3 is 11.
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What is the value of x in the equation 1/5x – 2/3y = 30, when y = 15? 4 8 80 200
Simplify. 1/3(−32.48−14.02) Enter your answer, as a decimal to tenths, in the box.
Answer: After doing the order of operations and round the decimal to tenths the result is - 15.5
Solution:
1/3(-32.48-14.02)
1. Operations inside the parentheses: Add numbers with the same sign:
1/3(-46.50)
2. Multiplication:
1/3(-46.50/1)=[(1)(-46.50)] / [(3)(1)]=(-46.50)/(3)
3. Dividing:
(-46.50)/(3) = - 15.50
4. Rounding decimal to tenths:
- 15.50 = - 15.5
5. In “The Pigman & Me,” John announces that he is going to exact revenge on Paul. What does
he mean by exact?
(1 poin
in a precise way
sign into law
take by force
separate one object from another
A stadium has 46,000 seats. Seats sell for $30 in Section A, $24 in Section B, and $18 in Section C. The number of seats in Section A equals the total number of seats in Sections B and C. Suppose the stadium takes in $1,193,400 from each sold-out event. How many seats does each section hold?
You are returning from a trip to England with €100 euro. The exchange rate is USD/EUR 1.3847 . How much in US dollars should you receive
Using the exchange rate of USD/EUR 1.3847, you need to multiply your €100 by 1.3847 to determine the amount in US dollars, which is USD 138.47. Therefore, you will receive USD 138.47 for your €100.
You are returning from a trip to England with €100 euro, and the exchange rate is USD/EUR 1.3847. To calculate how much in US dollars you should receive, you use the exchange rate to convert euros to USD.
Start with the amount in euros: €100.Multiply by the exchange rate: 100 × 1.3847 = 138.47.Therefore, you should receive USD 138.47.
Which statements are true about the ordered pair (−3, 1) and the system of equations?
{x−4y=6
3x+y=−8
Select each correct answer.
The ordered pair (−3, 1) is a solution to the first equation because it makes the first equation true.
The ordered pair (−3, 1) is a solution to the second equation because it makes the second equation true.
The ordered pair (−3, 1) is not a solution to the system because it makes at least one of the equations false.
The ordered pair (−3, 1) is a solution to the system because it makes both equations true.
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Does 1/1 count as 1 in fractions
Simplify the expression 2.1(4.5x)
Mike is 11 years old. jim is twice as old as mike. when jim is 50 years old, how old will mike be? 28
A car averages 27 miles per gallon. If gas costs $4.04 per gallon, which of the following is closest to how much the gas would cost for this car to travel 2,727 typical miles? Individual Question $44.44 $109.08 $118.80 $408.04 $444.40
There are 50 cards numbered from 1 to 50. two different cards are chosen at random. what is the probability that one number is twice the other number?
The probability that one number is twice the other number when two different cards are chosen at random is 1/49.
Explanation:To find the probability that one number is twice the other number when two different cards are chosen at random from a set of 50 cards numbered from 1 to 50, we need to determine the number of favorable outcomes and the total number of possible outcomes.
The favorable outcomes occur when one card is twice the value of the other card. Let's consider the smaller number as 'x'. In that case, the larger number would be '2x'. We can see that 'x' can take any value from 1 to 25, since the larger number '2x' should be less than or equal to 50.
So, the number of favorable outcomes is 25. The total number of possible outcomes is the number of ways to choose 2 cards out of 50, which is given by the combination formula: C(50, 2) = 50! / (2! * (50-2)!), which simplifies to 50 * 49 / 2 = 1225.
Therefore, the probability is given by the ratio of the favorable outcomes to the total number of possible outcomes: 25/1225 = 1/49.
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The height of a right circular cone is multiplied by 3, but its radius remains fixed. By what factor will the volume of the cone be multiplied?
The volume of the cone will be multiplied by a factor of [tex]\(3^1 = 3\).[/tex]
The volume of a right circular cone is given by the formula:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
where [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height of the cone.
Given that the height of the cone is multiplied by 3, the new height [tex](\( h' \))[/tex] becomes 3 times the original height [tex](\( h \))[/tex]:
[tex]\[ h' = 3h \][/tex]
Now, let's find the volume of the new cone with the updated height:
[tex]\[ V' = \frac{1}{3} \pi r^2 (3h) \][/tex]
[tex]\[ V' = \pi r^2 (h) \times 3 \][/tex]
So, the volume of the new cone is three times the original volume.
Now, let's dive into the explanation:
When the height of a cone is multiplied by a factor, the volume of the cone is directly proportional to the cube of that factor. This is because the volume formula contains the height term raised to the power of 3. So, if the height is tripled, the volume will be multiplied by[tex]\(3^3 = 27\).[/tex]
Alternatively, we can calculate it directly:
Original Volume: [tex]\(V = \frac{1}{3} \pi r^2 h\)[/tex]
New Volume:[tex]\(V' = \frac{1}{3} \pi r^2 (3h) = \pi r^2 h \times 3\)[/tex]
Therefore, the volume of the cone will be multiplied by a factor of [tex]\(3^1 = 3\).[/tex]
Complete question:
The height of a right circular cone is multiplied by 3, but its radius remains fixed. By what factor will the volume of the cone be multiplied?
Prove that the sum of three consecutive positive integers is divisible by 3
[tex]n+n+1+n+2=3n+3=3(n+1)[/tex]
The angles with measures x and 4x are complementary angles. which is the value of x?
Answer:
x=18 degrees
Step-by-step explanation:
Hello
by definition, two angles are called complementary angles, if the sum of their degree measures is 90. Each angle is called complement of the other.
A = angle 1=x
B=angle 2 =4x
A and B are complementary angles,hence
A+B=90
replacing
[tex]x+4x=90\\\\5x =90\\x=\frac{90}{5} \\x=18\ degrees[/tex]
A=18 degrees
B=4*x
B=72 degrees
x=18 degrees
If m FDG = 50°, what is m FEG?
75°
50°
100°
25°
Thank you!