In two column proof the right column states your reasons is true statement.
In a two-column proof, the right column typically contains the statements of reasons or justifications for each step taken in the left column.
The left column contains a sequence of statements that represent the logical progression of the proof, while the right column provides the reasoning or logical basis for each step to show that it follows from the previous statements.
This format is commonly used in geometry to provide a clear and organized presentation of the proof's logical structure.
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Fill in the correct justification for each step in solving the EQUATION below 36-27x=-16x+58
Which function represents the number if seats in a theater with n rows?
What is the equation of the axis of symmetry of the graph of y + 3x – 6 = –3(x – 2)2 + 4?
A. x=3/2
B. x=-1/6
C. x=-1/2
D. x=-3/2
Option: A is the correct answer.
The axis of symmetry is:
A. x=3/2
Step-by-step explanation:We are given a graph as:
[tex]y+3x-6=-3(x-2)^2+4[/tex]
and
[tex]y=-3(x-2)^2+4+6-3x[/tex]
and
[tex]y=-3[(x-2)^2+x]+10\\\\i.e.\\\\y=-3[x^2+4-4x+x]+10\\\\i.e.\\\\y=-3[x^2-3x+4]+10[/tex]
This equation could also be written in the form:
[tex]y=-3[x^2-3x+4-\dfrac{9}{4}+\dfrac{9}{4}]+10\\\\i.e.\\\\y=-3[(x-\dfrac{3}{2})^2+4-\dfrac{9}{4}]+10\\\\i.e.\\\\y=-3[(x-\dfrac{3}{2})^2+\dfrac{7}{4}]+10\\\\i.e.\\\\y=-3(x-\dfrac{3}{2})^2-3\times \dfrac{7}{4}+10\\\\i.e.\\\\y=-3(x-\dfrac{3}{2})^2+\dfrac{19}{4}[/tex]
Now, we know that for any general equation of the type:
[tex]y=a(x-h)^2+k[/tex]
The axis of symmetry of the graph of the equation is:
[tex]x=h[/tex]
Here we have:
[tex]h=\dfrac{3}{2}[/tex]
Hence, the answer is: Option: A
julia knows 19 latin words. Each day, she learns 6 new words. How many days until she knows 145 words?
Number of days Julia took to learn 145 word is 21 days.
Given that, Julia knows 19 latin words. Each day, she learns 6 new words.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number of days be x.
Here, 145-19=126
Number of days = 126/6
= 21
Therefore, number of days Julia took to learn 145 word is 21 days.
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Lisa has $7.80 to spend on some tomatoes and a loaf of bread. Tomatoes cost $1.20 per pound, and a loaf of bread costs $1.80. The inequality 1.20x + 1.80 ≤ 7.80 models this situation, where x is the number of pounds of tomatoes. Solve the inequality. How many pounds of tomatoes can Lisa buy? A. x ≤ 8; Lisa can buy 8 pounds or less of tomatoes. B. x ≥ 5; Lisa can buy 5 pounds or more of tomatoes. C. x ≤ 5; Lisa can buy 5 pounds or less of tomatoes. D. x ≥ 8; Lisa can buy 8 pounds or more of tomatoes.
Answer:
C. [tex]x\leq 5[/tex]; Lisa can buy 5 pounds or less of tomatoes.
Step-by-step explanation:
We have been given an inequality [tex]1.20x+1.80\leq 7.80[/tex], where x is the number of pounds of tomatoes. The inequality represents amount spend by Lisa on tomatoes and loaf. We are asked to find number of pounds that Lisa can buy.
First of all, we will subtract 1.80 from both sides of our inequality.
[tex]1.20x+1.80-1.80\leq 7.80-1.80[/tex]
[tex]1.20x\leq 6.00[/tex]
Now, we will divide both sides of our inequality by 1.20.
[tex]\frac{1.20x}{1.20}\leq \frac{6.00}{1.20}[/tex]
[tex]x\leq 5[/tex]
Therefore, Lisa can buy 5 pounds or less of tomatoes and option C is the correct choice.
Simplify negative 15.5 divided by 5..
-3.1
3.1
-3.3
3.3
this was correct on my test, hope it helps! ;)
(Brainliest would help a lot btw)
What are not irrational out of square root of 15,16,17, and 18?
If a=2b, then a-c=2b-c
I am four times as old as my brother and in two years time i will be just three times as old. in how many years will i be twice as old as my brother?
To solve the problem, set up and solve an algebraic equation. Find the value of x, then use it to determine the number of years it will take for you to be twice as old as your brother.
Explanation:To solve this problem, we can use algebraic equations. Let's assume the age of your brother is x. Since you are four times as old as your brother, your age would be 4x. In two years, your age would be 4x + 2, and your brother's age would be x + 2. According to the problem, 4x + 2 = 3(x + 2). We can solve this equation to find x, and then determine the number of years it will take for you to be twice as old as your brother.
By simplifying the equation, we get 4x + 2 = 3x + 6. Subtracted 3x from both sides, we get x + 2 = 6. Subtracting 2 from both sides, we get x = 4.
So, your brother's age is currently 4 and your age is currently 16. To determine the number of years it will take for you to be twice as old as your brother, we need to find the value of y that satisfies the equation 2(4 + y) = 16 + y. By solving this equation, we'll find that it will take 8 years for you to be twice as old as your brother.
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Solve the equation for y
-x+y=0
Which statement best describes the excluded values of a rational expression?
A.The number of excluded values of a rational expression cannot exceed the degree of the numerator.
B.The number of excluded values of a rational expression cannot exceed the degree of the denominator.
C.The number of excluded values of a rational expression cannot exceed the sum of the degrees of the numerator and denominator.
D.The number of excluded values of a rational expression cannot exceed the difference in the degrees of the numerator and denominator.
Option: B is the correct answer.
B. The number of excluded values of a rational expression cannot exceed the degree of the denominator.
Step-by-step explanation:We know that a rational expression is a expression of the form:
[tex]\dfrac{p(x)}{q(x)}[/tex]
where p(x) and q(x) are polynomials.
Excluded value--
The excluded value of a rational expression are the values where the denominator of the expression is zero.
Also, the number of zeros of a polynomial is always less than or equal to degree of the polynomial.
Hence, the number of excluded values of a rational expression cannot exceed the degree of the denominator.
The answer is:
Option: B
The interior angles of a regular polygon each measure 165 degrees. how many sides does the polygon have
If a regular polygon has interior angles each measuring 165 degrees, the polygon has 24 sides. This is calculated by using the formula to find the number of sides in a regular polygon, given the angle size.
Explanation:To find out how many sides a regular polygon has, based on the size of its interior angles, you can use the formula to calculate the sum of the interior angles of a polygon:
n
= 180(
n
- 2), where
n
is the number of sides.
However, this formula gives the sum of the interior angles as a whole. Since, in a regular polygon, all angles are equal, you can then divide this sum by the known size of each angle.
So the specific formula to calculate the number of sides of a regular polygon, given the angle size, is:
n
= 360 / (180 -
angle size
).
In this case, you can substitute the angle size of 165 degrees into this formula:
n
= 360 / (180 - 165) = 360 / 15 = 24.
So a regular polygon with interior angles each measuring 165 degrees has 24 sides.
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A sofa regularly sells for 590 the sale price is 477.90 find the percent decrease of the sale price form the regular price
what is the value of the digit 6 in 31.26?
50 points
What are the steps for using a compass and straightedge to construct a square?
Put them in order!
Answer:
1. Using your straightedge, draw a reference line, if one is not provided.
2. Copy the side of the square onto the reference line, starting at a point labeled A'.
3. Construct a perpendicular at point B' to the line through ab2.
4. Place your compass point at B', and copy the side of the square onto the perpendicular b'g. Label the end of the segment copy as point C.
5. With your compass still set at a span representing AB, place the compass point at C and swing an arc to the left.
6. Holding this same span, place the compass point at A' and swing an arc intersecting with the previous arc. Label the point of intersection as D.
7. Connect points A' to D, D to C, and C to B' to form a square.
Step-by-step explanation:
Jackson purchased some power tools totaling $1,543 using a six month deferred payment plan with an interest rate of 23.76%. He did not make any payments during the deferment period. What will the total cost of the power tools set be if he must pay off the power tools within two years after the deferment period?
$1,543.00
$1,735.63
$2,197.44
$2,746.80
The total cost of the power tools set if Jackson must pay off the tools within two years after the deferment period is $2,644.82.
To find the total cost of the power tools set after the deferred payment period, we need to consider both the initial cost of the tools and the interest accrued during the deferment period and the subsequent payment period.
First, let's calculate the interest accrued during the deferment period:
Interest = Principal × Rate × Time
Interest = $1,543 × 23.76% × (6/12) (since the deferment period is 6 months)
Interest = $1,543 × 0.2376 × 0.5
Interest = $183.78
Now, add this interest to the initial cost of the power tools:
Total cost after deferment = Initial cost + Interest
Total cost after deferment = $1,543 + $183.78
Total cost after deferment = $1,726.78
Next, we need to calculate the total amount Jackson must pay off within two years after the deferment period. This includes the principal amount and the interest accrued during the payment period. We'll use the formula for calculating the total payment for a loan with compound interest:
[tex]\[A = P(1 + r/n)^{nt}\][/tex]
Where:
A = Total amount to be paid
P = Principal amount (initial cost after deferment)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Time in years
In this case, we'll compound interest annually, so (n = 1), and (t = 2) years.
[tex]\[A = $1,726.78(1 + 0.2376/1)^{1*2}\][/tex]
[tex]\[A = $1,726.78(1 + 0.2376)^2\][/tex]
[tex]\[A = $1,726.78(1.2376)^2\][/tex]
[tex]\[A = $2,644.82\][/tex]
So, the total cost of the power tools set if Jackson must pay off the tools within two years after the deferment period is $2,644.82.
Solve the equation.
–3x + 1 + 10x = x + 4
x = 1/2
x = 5/6
x = 12
x = 18
Answer:
x = 1/2
Step-by-step explanation:
-3x +1 +10x = x + 4
7x + 1 = x + 4
6x + 1 =4
6x = 3
x = 3/6
x = 1/2
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The value of x in the equation -3x + 1 + 10x = x + 4 is 1/2.
x = 1/2
Option A is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 6 is an equation.
3x + 4 = 6 is an equation.
x + 5 is an equation.
3x + 4x + 5 is an equation.
We have,
The equation:
-3x + 1 + 10x = x + 4
We will solve for x.
Add 3x on both sides.
1 + 10x = x + 4 + 3x
1 + 10x = 4x + 4
Subtract 4x on both sides.
1 + 10x - 4x = 4
1 + 6x = 4
Subtract 1 on both sides.
6x = 4 - 1
6x = 3
Divide 6 on both sides.
x = 3/6
x = 1/2
Thus,
The value of x in the equation -3x + 1 + 10x = x + 4 is 1/2.
x = 1/2
Option A is the correct answer.
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Which graph represents f(x)=−2x4 ?
abcdefghijklmnopqrstuvwxyz
The graph of y = x⁴ is also a parabola that opens upward and it is an even function.
The blue graph represents a quadratic function and the red graph represents a biquadratic function.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
We also know that graph of a quadratic function y = x² is a parabola,
Now, the graph of y = x⁴ will also be a parabola,
and it is more steeper or has a greater slope than the graph y = x² as the independent variable has a larger exponent value it is also an even function that is symmetric about the y-axis.
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Find the 30th term in the sequence: 18,15,12
Coffee with sugar and milk added to it can contain up to calories.
The posted speed limit in many parts in europe is 100 km/hr.what is the equivalent speed limit in miles per hour
Answer:
62.1371 miles/hr
Step-by-step explanation:
The posted speed limit in many parts in Europe = 100 kilometers per hour
We have to convert the speed limit into miles per hour.
As we know, 1 kilometer = 0.621371 miles
Therefore, 100 kilometers = 100 × 0.621371
= 62.1371 miles
The equivalent speed of 100 km/hr is 62.1371 miles/hr.
the angle measure for m
I will mark the correct answer as brainliest! A piece of fabric 180 inches long is cut in 2 pieces such that 3 times the larger piece is greater than 4 times the smaller piece. How large are the 2 pieces. Also please give details if possible
The length of the larger piece lies in the interval [102.85 , 180) and the length of the smaller piece lies in the interval [0 , 77.15]
What is an interval?In mathematics, a (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0, 1, and all numbers in between.
Given here, that 3 times the larger piece is greater than 4 times the smaller piece. let the length of the larger piece be x and length of the smaller piece be 180-x, then we get the following inequality-
3x > 4(180-x)
3x>720-4x
7x>720
x>102.85
therefore 102.85≤ x <180
Hence, the larger piece lies in the interval [102.85 , 180) and the length of the smaller piece lies in the interval [0 , 77.15]
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the total amount of money (in cents) in x nickels, (x+2) quarters, and 3x dimes. total amount is? please help!!!!
To find the total amount of money in nickels, quarters, and dimes, we need to add the value of each coin together. In this case, the total amount of money is represented by the expression 60x + 50 cents.
Explanation:To find the total amount of money, we need to determine the value of each coin in cents. A nickel is worth 5 cents, a quarter is worth 25 cents, and a dime is worth 10 cents.
The total amount of money in x nickels is 5x cents. The total amount of money in (x+2) quarters is 25(x+2) cents. The total amount of money in 3x dimes is 30x cents.
Adding these values together, we can find the total amount of money:
Total amount of money = 5x + 25(x+2) + 30x cents Now, simplify the expression:
Total amount of money = 5x + 25x + 50 + 30x cents
Total amount of money = 60x + 50 cents
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1. The graph of the function B is shown below. Find B(1).
A. -1
B. 1
C. 2
It is NOT B... it's either A or C!
Answer:ANSWER
The correct answer is C
EXPLANATION
is just the y-value of the point where
That is, the image of 1.
If we were given the function
,we would have plug in 1 to find
Since the function is not given, we were given the graph so that we trace
from it.
So we read from the grid to find that y-value .
Each grid is one unit. So moving one unit on the x-axis and two units on the y-axis will give us the point
This means that,
ANSWER The correct answer is C EXPLANATION [tex]B(1)[/tex] is just - 1
Step-by-step explanation:
What is the area of a rectangle with vertices at (−3, −1) , (1, 3) , (3, 1) , and (−1, −3) ?
Enter your answer in the box. Do not round any side lengths.
The area of a rectangular rug is given by the trinomial r squared minus 4 r minus 77r2−4r−77. What are the possible dimensions of the rug? Use factoring.
Answer:
[tex]r>\frac{4 +\sqrt{23732} }{154} \approx1.03\\[/tex]
Step-by-step explanation:
The area of the rectangular rug is given by this equation:
[tex]77r^2-4r-77[/tex]
The area must be a number greater than 0 since a negative area, or an area equal to 0 wouldn't have much sense. So:
[tex]77r^2-4r-77>0[/tex]
Let's find the roots of this equation using the quadratic formula:
[tex]r=\frac{-b\pm \sqrt{b^2-4ac} }{2a} =\frac{-(-4)\pm\sqrt{(-4)^2-(4)(77)(-77)} }{2(77)} \\\\r=\frac{4 \pm \sqrt{23732} }{154} \\\\r_1=\frac{4 +\sqrt{23732} }{154} \approx1.03\\\\r_2=\frac{4 - \sqrt{23732} }{154} \approx-0.97[/tex]
Now, let's evaluate the area for [tex]r>r_1[/tex] for example r=1.05:
[tex]A=77(1.05)^2-4(1.05)-77=3.6925>0[/tex]
The result is greater than zero, so for [tex]r>r_1[/tex] the values make sense.
Now let's evaluate the area for [tex]r_2<r<r_1[/tex] for example r=0.5 and r=-0.7:
[tex]A=77(0.5)^2-4(0.5)-77=-59.75<0\\\\A=77(-0.7)^2-4(-0.7)-77=-36.47<0[/tex]
The result is less than zero, so for [tex]r_2<r<r_1[/tex] the values don't make sense.
Now, let's evaluate the area for [tex]r<r_2[/tex] for example r=-1:
[tex]A=77(-1)^2-4(-1)-77=4>0[/tex]
The result is greater than zero, so for [tex]r<r_2[/tex] the values make sense
However, since negative values of r wouldn't make much sense (I never heard about of -8 inches for example) the possible dimensions of the rug are just:
[tex]r>\frac{4 +\sqrt{23732} }{154} \approx1.03\\[/tex]
The side lengths of triangle ABC are written in terms of the variable p, where p ≥ 3.
Which is correct regarding the angles of the triangle?
mA > mC > mBAnswer: C) mC > mA > mB is correct regarding the angles of the triangle ABC.
Step-by-step explanation:
Given: In Δ ABC, the side lengths of triangle ABC are written in terms of the variable p, where p ≥ 3.
AB=4p-1 , AC=p+4 , BC=3p
where p+4 < 3p [as p≥3]
3p < 4p-1 [as p≥3]
⇒ 4p-1> 3p > p+4
⇒AB>BC>AC
Angle opposite to AB ,BC and AC is m∠C ,m∠A and m∠B.
Therefore mC > mB > mA [∵Angle opposite to greater side is greater]
Thus , mC > mA > mB is correct regarding the angles of the triangle ABC.
Answer:
C
Step-by-step explanation:
A fish swims at a speed of 12 miles per hour. A boy swims at a speed of 4.4 feet per second.
3ft= 1yd
5280ft= 1mi
How much faster does the fish swim than the boy in yards per minutes?
The fish swims 264 yards per minute faster than the boy.
Explanation:To find out how much faster the fish swims than the boy in yards per minute, we first need to convert both speeds to yards per minute. Since 3 feet is equal to 1 yard, we can convert the fish's speed of 4.4 feet per second to yards per minute by multiplying it by (3 feet/1 yard) × (60 seconds/1 minute) = 4.4 × 3 × 60 yards per minute = 792 yards per minute. Similarly, the boy's speed of 12 miles per hour can be converted to yards per minute by multiplying it by (5280 feet/1 mile) × (1 yard/3 feet) × (1 hour/60 minutes) = 12 × 5280/3/60 yards per minute = 1056 yards per minute.
To find out how much faster the fish swims than the boy, we subtract the boy's speed from the fish's speed: 792 - 1056 = -264 yards per minute. Therefore, the fish swims 264 yards per minute faster than the boy.
The 26-oz jar of chocolate fudge costs $3.12. The 16-oz jar costs $2.40. How much can you save on each ounce by choosing the better buy?