Answer:
p = (7 - 6)/5Step-by-step explanation:
Given the expression 5 p + 6 = 7, to know the value of variable p. we need to make p the subject of the formula as shown;
Given 5 p + 6 = 7
Step 1: Subtract 6 from both sides
5p+6-6 = 7-6
5p = 7-6
Step 2: We will then divide both sides by the coefficient of p i.e 5 to have;
5p/5 = (7 - 6)/5
p = (7 - 6)/5
Hence, the correct expression of variable p is p = (7 - 6)/5
Solve for x and draw a number line. 3x−91>−87 AND 17x−16>18
Answer:
I hope this will help!
Step-by-step explanation:
Astrid is in charge of building a new fleet of ships. Each ship requires 404040 tons of wood, and accommodates 300300300 sailors. She receives a delivery of 444 tons of wood each day. The deliveries can continue for 100100100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 210021002100 sailors.
To build the fleet of ships, Astrid must consider each of the given rates (i.e. the daily tons of wood, the sailors per ship, etc.). The available deliveries are enough to build ships that can accommodate at least 2100 sailors.
Given that:
Required quantities
[tex]Wood = 40\ tons[/tex]
[tex]Sailors = 300[/tex] per ship
Available quantities
[tex]Wood = 4\ tons[/tex] daily
[tex]Days = 100[/tex] at most
First, we calculate the total tons of woods Astrid can receive.
[tex]Total = Days \times Wood\ Available[/tex]
[tex]Total = 100 \times 4[/tex]
[tex]Total = 400\ tons[/tex] ---- in 100 days
Next, we calculate the number of ships that can be made from the 400 tons.
[tex]Ships = \frac{Total\ tons}{Wood\ Required}[/tex]
So, we have:
[tex]Ships = \frac{400}{40}[/tex]
[tex]Ships = 10[/tex]
This means that Astrid can build up to 10 ships
The number of sailors the ship can accommodate is:
[tex]Sailors = Ships \times Sailors\ per\ ship[/tex]
So, we have:
[tex]Sailors = 10 \times 300[/tex]
[tex]Sailors = 3000[/tex]
It means the 10 ships can accommodate 3000 sailors.
3000 sailors is greater than 2100 sailors.
So, we can conclude that she can build enough ship for the 2100 sailors.
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Answer:
280 tons
Step-by-step explanation:
:)
For a ,a relationship to be a function, which values cannot repeat: the x-
values or the y-values? *
Answer:
The x - valuesThe y-values repeat in various functions (for example: quadratic function: y=x²; y=4 for x=2 and for x=-2)
help me asap you guys i need help
Hi there! :)
Answer:
[tex]\huge\boxed{C}[/tex]
To simplify the process, convert each given weight into standard notation:
Lion:
[tex]1 * 10^{5} = 1 * 100000 = 100,000 g[/tex]
Ant:
[tex]2 * 10^{-3} = 2* 0.001 = 0.002[/tex]
Divide the ant's weight from the lion's weight:
[tex]100000 / 0.002 = 50,000,000[/tex]
Convert to scientific notation: (use # of zeros to determine exponent)
[tex]50,000,000 = 5 * 10^{7}[/tex]
Therefore, the correct answer is C.
Evaluate |3 - 5 + 7|. -5 5 -15 15
Answer:
5
Step-by-step explanation:
|3 - 5 + 7|
= |-2 + 7|
= |5| = 5
Answer:
The correct answer would be 5.
Step-by-step explanation:
A company makes nylon and canvas backpacks. The profit on a nylon backpack is $3 and the profit on a canvas backpack is $10. How many backpacks must the company sell to make a profit of more than $250? Write a linear inequality that describes the situation.
Answer:
3x +10y is greater than or equal to 250.
Step-by-step explanation:
The question asks us to write an inequality which shows that both nylon and canvas added should be greater than or equal to 250.
Since we don't know the number of nylon backpacks and canvas backpacks the company makes, we used the variables "x" and "y" to represent the number of backpacks they made from each style.
Answer:
3n + 10c > 250
Step-by-step explanation:
I confirmed it in grandpoint
Th sum of a number and two is equal to eight
The equation?
Answer:
2+n = 8
Step-by-step explanation:
2+ something must equal 8.
8 minus 2 = 6
n=6
Answer:
Let the number be n.
According to question,
2+ n =8
=) n = 8-2
=) n =6
hope you understand.
In 2002, the population of a district was 22,800. With a continuous annual growth rate of approximately 5% what will the population be in 2012 according to the exponential growth function?
Answer:
37,139
Step-by-step explanation:
Given the following :
Population in 2002 = Initial population (P0) = 22,800
Growth rate (r) = 5% = 0.05
Growth in 2012 using the exponential growth function?
Time or period (t) = 2012 - 2002 = 10years
Exponential growth function:
P(t) = P0 * (1 + r) ^t
Where P(t) = population in t years
P(10) = 22800 * (1 + 0.05)^10
P(10) = 22800 * (1.05)^10
P(10) = 22800 * 1.62889
P(10) = 37138.797
P(10) = 37,139 ( to the nearest whole number)
Pick out the set of numbers that is not Pythagorean triple
9 40 46
16 30 34
10 24 26
50 120 130
Answer:
[tex]\huge\boxed{9,40,46}[/tex]
Step-by-step explanation:
Let's check it using Pythagorean Theorem:
[tex]c^2 = a^2 + b^2[/tex]
Where c is the longest sides, a and b are rest of the 2 sides
1) 9 , 40 , 46
=> [tex]c^2 = a^2 + b^2[/tex]
=> [tex]46^2 = 9^2 + 40^2[/tex]
=> 2116 = 81 + 1600
=> 2116 ≠ 1681
So, this is not a Pythagorean Triplet
2) 16, 30 and 34
=> [tex]c^2 = a^2 + b^2[/tex]
=> [tex]34^2 = 16^2 + 30^2[/tex]
=> 1156 = 256 + 900
=> 1156 = 1156
No need to check more as we've found the one which is not a Pythagorean Triplet.
Answer:
[tex] \boxed{ \huge{ \boxed{ \sf{ \blue{9 , \: 40 \:, 46 \: }}}}}[/tex]Option A is the correct option.
Step-by-step explanation:
1. Let h , p and b are the hypotenuse , perpendicular and base of a right - angled triangle respectively.
From Pythagoras theorem,
[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]
Here, we know that the hypotenuse is always greater than perpendicular and base,
h = 46 , p = 40 , b = 9
⇒[tex] \sf{ {46}^{2} = {40}^{2} + {9}^{2} }[/tex]
⇒[tex]2116 = 1600 + 81[/tex]
⇒[tex] \sf{2116 ≠ 1681}[/tex]
Thus , the relation [tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex] is not satisfied by h = 46 , p = 40 , b = 9
So, The set of numbers 9 , 40 , 46 is not Pythagorean triple.
------------------------------------------------------
2. 16 , 30 , 34
h = 34 , p = 30 , b = 16
[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]
⇒[tex] \sf{ {34}^{2} = {30}^{2} + {16}^{2} }[/tex]
⇒[tex] \sf{1156 = 900 + 256}[/tex]
⇒[tex] \sf{1156 = 1156}[/tex]
The relation [tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex] is satisfied by the particular values of h , p and b i.e h = 34 , p = 30 , b = 16
So, the set of numbers 16 , 30 , 34 is a Pythagorean triple.
------------------------------------------------------
3. 10, 24 , 26
h = 26 , p = 24 , b = 10
[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]
⇒[tex] \sf{ {26}^{2} = {24}^{2} + {10}^{2} }[/tex]
⇒[tex] \sf{676 = 576 + 100}[/tex]
⇒[tex] \sf{676 = 676}[/tex]
The relation [tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex] is satisfied by the particular values of h , p and h i.e h = 26 , p = 24 , b = 10
So, the set of numbers 10, 24 , 26 is the Pythagorean triple.
-----------------------------------------------------
4. 50 , 120 , 130
h = 130 , p = 120 , b = 50
[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]
⇒[tex] \sf{ {130}^{2} = {120}^{2} + {50}^{2} }[/tex]
⇒[tex] \sf{16900 = 14400 + 2500}[/tex]
⇒[tex] \sf{16900 = 16900}[/tex]
The relation [tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex] is satisfied by the particular values of h , p and b i.e h = 130 , p = 120 , b = 50
So, the set of numbers 50, 120 , 130 is the Pythagorean triple.
-----------------------------------------------------
In this way, to satisfy the Pythagoras Theorem , the hypotenuse ( h ) , perpendicular ( p ) and the base ( b ) of a right - angles triangle should have the particular values in order. These values of h , p and b are called Pythagorean triple.
Hope I helped!
Best regards!!
Use the difference of squares identity to write this polynomial expression in factored form : 9x^2-49
Answer:
The expression in factored form is (3x - 7)(3x + 7)
Step-by-step explanation:
Here in this question, we are interested in using the difference of two squares to factor the given expression.
Mathematically, supposed we have two squares a^2 and b^2, and we are told to factorize a^2-b^2.
By using the difference of two squares;
a^2-b^2 can thus be written as;
(a-b)(a + b)
Now, we can apply same approach to the problem at hand.
9x^2 - 49
kindly note that 9x^2 can be written as ((3x)^2 and 49 can be written as 7^2
So applying what we have said earlier about difference of two squares;
9x^2 - 49 will be ;
(3x-7)(3x + 7)
Answer:
The answer is (3x - 7) (3x +7)
Step-by-step explanation:
Find the volume of a pyramid with a square base, where the side length of the base is 17 in 17 in and the height of the pyramid is 9 in 9 in. Round your answer to the nearest tenth of a cubic inch.
Answer:
The volume of the pyramid is 867 inch^3
Step-by-step explanation:
Here in this question, we are interested in calculating the volume of a square based pyramid.
Mathematically, we can use the formula below to calculate the volume V of a square based pyramid.
V = a^2h/3
where a represents the length of the side of the square and h is the height of the pyramid
From the question, the length of the side of the square is 17 in while the height is 9 in
Plugging these values, we have ;
V = (17^2 * 9)/3 = 17^2 * 3 = 867 cubic inch
the volume of a solid come is 616cm^3. Find it's height if the base radius is 7cm
Answer:
height = 4cm
Step-by-step explanation:
volume = п r² h
п = 3.14 (aprox.)
r = radius
h = height
volume = 616cm³
then:
616 = 3.14 * 7² * h
616 = 3.14*49*h
616 = 153,86 * h
h = 616 / 153.86
h = 4
height = 4cm
Answer:
Your answer is
Step-by-step explanation:
If u multiply 616cm^3 multipied by 7 cm gives you the correct answer because volume multiplied by radius=height of that particular object.Hope this helps....
Have a nice day!!!!
Please help with this question!!!!!
===================================
Explanation:
Start with the parent function [tex]y = |x|[/tex]
Replacing x with x-1 shifts the graph 1 unit to the right
Tack a -1 at the end to get [tex]y = |x-1|-1[/tex] which will shift everything down 1 unit.
The vertex started at (0,0) and moved to (1,-1)
What is the equation for the line of symmetry in this figure?
Answer:
x = -1
Step-by-step explanation:
the line of the simetry is x = -1
Answer:
Its x = -1 because it splits the diamond shape perfectly at x -1
Step-by-step explanation:
Which equations have one solution and which have infinitely many solutions?
Answer:
Step-by-step explanation:
1). [tex]\frac{1}{2}g-4=2g-\frac{1}{2}g+4[/tex]
[tex]\frac{1}{2}g-4=\frac{3}{2}g+4[/tex]
Since left side of the given equation is not equal to the right side, there will be one solution to the given equation.
2). -2.1b + 5.3 = b - 3.1b + 5.3
-2.1b + 5.3 = -2.1b + 5.3
Since left side of the equation is exactly same as right side of the equation.
Equation will have infinitely many solutions.
3). [tex]\frac{3}{4}w+\frac{5}{4}=\frac{10}{4}-\frac{3}{4}w[/tex]
[tex]\frac{3}{4}w+\frac{5}{4}=\frac{5}{2}-\frac{3}{4}w[/tex]
Since left side of the given equation is not equal to the right side, there will be one solution to the given equation.
4). 5.7c - 1.5 + 3.2c = 7.8c - 1.5 + 1.1c
8.9c - 1.5 = 8.9c - 1.5
Left side of the equation is same as right side of the equation.
Therefore, there will be infinitely many solutions of the equation.
Answer:
C and f
Step-by-step explanation:
Hope this helps
PLEASE ANSWER QUICKLY ASAP
COMPLETE QUESTION B
Answer:
Sector
Step-by-step explanation:
A sector of a circle is the portion of circle enclosed by two radii and arc
Please help quickly!!
A truck is driving up a hill with a 24% grade, so it climbs 24 feet vertically for every 100 feet horizontally.
What is the slope of the hill?
Answer:
6/25
Step-by-step explanation:
rise / run
24/100 = 6/25
Answer:
[tex]\frac{6}{25}[/tex]
Step-by-step explanation:
The slope of any relationship is always rise over run. This means the vertical distance traveled over the horizontal distance traveled will get us our slope.
We travels 24 feet vertically for every 100 feet horizontally, so:
[tex]\frac{24}{100}[/tex].
We can simplify this fraction to find the slope in fraction form.
[tex]\frac{24\div4}{100\div4} = \frac{6}{25}[/tex]
So the slope of this equation is [tex]\frac{6}{25}[/tex].
Hope this helped!
Sandy’s older sister was given $2,400 and was told to keep the balance of the money after sharing with her siblings. Give Sandy exactly $350. Write Sandy’s portion
Sandy got 350 out of 2400.
Her portion is 350/2400 which can be reduced to:
35/240 = 7/48
The portion is 7/48
How to solve this maths equation??? pls help me, its urgent!!! asap
Answer:
x = [tex]\frac{3wyz}{4wz+wy-2yz}[/tex]
Step-by-step explanation:
Given
[tex]\frac{2}{w}[/tex] + [tex]\frac{3}{x}[/tex] - [tex]\frac{4}{y}[/tex] = [tex]\frac{1}{z}[/tex]
Multiply through by wxyz to clear the fractions
2xyz + 3wyz - 4wxz = wxy ( subtract wxy from both sides )
2xyz + 3wyz - 4wxz - wxy = 0 ( subtract 3wyz from both sides )
2xyz - 4wxz - wxy = - 3wyz ( factor out x from each term on the left side )
x(2yz - 4wz - wy) = - 3wyz ( divide both sides by (2yz - 4wz - wy )
x = [tex]\frac{-3wyz}{2yz-4wz-wy}[/tex] ( multiply numerator/ denominator by - 1 )
x = [tex]\frac{3wyz}{4wz+wy-2yz}[/tex]
show that the point p(-6,2), Q(1,7) and R(6,3) are the vertices of scalene triangle
Answer:
the sides are different lengths as shown in the diagram
Step-by-step explanation:
Plotting the three points, you can see by "inspection" that the middle length side (PQ) is longer than the shortest side (QR) and shorter than the longest side (PR). You could use the distance formula to show this, or you can use a scale to measure the drawing.
A triangle with three unequal sides is a scalene triangle. ∆PQR is scalene.
The Acme Company lost 650 hours due to accidents on the job in the first quarter of the year. The average hourly wage of the employees who contributed to the lost hours was $15.00. The company benefits add 25% to the wages. Using the cost-of-lost-hours formula (employee hours lost X average loaded labour rate = cost), calculate the direct cost of the lost work hours. Discuss the approach you would use to estimate the hidden costs that would also be associated with the lost hours.
Your answer must be at least 200 words in length.
Answer:
Step-by-step explanation:
Given that ;
The Acme Company lost 650 hours due to accidents on the job in the first quarter of the year
The average hourly wage of the employees who contributed to the lost hours was $15.00 . i.e the direct labor cost = $15.00
The company benefits add 25% to the wages. = 0.25
The loaded labor cost = $15.00/hr × 0.25 = $3.75/hour
If we add the additional cost of benefit, then we have the loaded labor cost to be = $15.00/hour + $3.75/hour
= $18.75 / hour
However, the direct labor costs that the workers continued to receive without working. for the first quarter of the year by using the cost-of-lost-hours formula is :
= 650 hours × $15.00 / hours
= $9750
The hidden costs can be estimated from the Acme company's contributions to the employee. Given that the company benefits add 25% to the wage of the employee, therefore, this wage must be incorporated in order to find out the total wage cost for the lost work hours in the Acme company.
As a result of the company benefits, the fully loaded labor cost is 650 hours × $18.75 /hour which gives $12187.5.
Consequently, it is pertinent to determine the cost for additional benefits that the workers are receiving even though they are not working, this is achieved by the difference in the $9750 direct cost paid to labor and the benefits amount of $12187.5
i.e
the cost for additional benefits that the workers are receiving even though they are not working = $12187.5 - $9750 = $2437.5
Other ways the hidden cost can be estimated is by take note of the amount paid to the employee on the day the employee had an emergency, amount paid to the rescue team involved. etc
john always wears a shirt, pants, socks, and shoes. he owns 12 pairs of socks, 3 pairs of shoes, 5 pairs of pants, and 5 shirts. how many different outfits can john make? PLEASE ANSWER
Answer:
900 outfits
Step-by-step explanation:
You just have to multiply them all together :)
n urn contains 3 red balls, 9 green, 2 yellow, 2 orange, and 4 purple balls. Two balls aredrawn, one at a time with replacement. Find the probability of drawing a green ball and an orangeball.
Answer:
[tex]\frac{9}{100}[/tex]
Step-by-step explanation:
Given:
Number of red balls, n(R) = 3
Number of green balls, n(G) = 9
Number of yellow balls, n(Y) = 2
Number of orange balls, n(O) = 2
Number of purple balls, n(P) = 4
Two balls are drawn one at a time with replacement.
To find:
Probability of drawing a green ball and an orange ball ?
Solution:
Total number of balls, n(Total) = 3 + 9 + 2 + 2 + 4 = 20
Formula for probability of an event E is given as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Probability that a green ball is drawn at first:
[tex]P(Green) = \dfrac{\text{Number of Green balls}}{\text {Total number of Balls}}[/tex]
[tex]P(Green) = \dfrac{9}{20}[/tex]
Now, the ball is replaced , so total number of balls remain the same i.e. 20.[tex]P(Orange) = \dfrac{\text{Number of Orange balls}}{\text {Total number of Balls}}[/tex]
[tex]P(Orange) = \dfrac{2}{20} = \dfrac{1}{10}[/tex]
[tex]P(Green\ then\ orange) = P(Green) \times P(Orange)\\\Rightarrow P(Green\ then\ orange) = \dfrac{9}{10} \times \dfrac{1}{10}\\\Rightarrow P(Green\ then\ orange) = \bold{ \dfrac{9}{100} }[/tex]
A train travels 250 km with a average speed of 75 km/hr and 350 km with 70km/hr and 200 km with average speed of 30km/hr. What will the average speed of whole journey of the train?
Answer:
53 1/3 km/h
Step-by-step explanation:
average speed = (total distance)/(total time)
average speed = distance/time
time * average speed = distance
time = distance/(average speed)
250 km at 75 km/h
distance = 250 km
time = (250 km)/(75 km/h) = 3.33333... hours
350 km at 70 km/h
distance = 350 km
time = (350 km)/(70 km/h) = 5 hours
200 km at 30 km/h
distance = 200 km
time = (200 km)/(30 km/h) = 6.6666... hour
total distance = 250 km + 350 km + 200 km = 800 km
total time = 3.33333... hours + 5 hours + 6.66666... hours = 15 hours
average speed = (total distance)/(total time)
average speed = (800 km)/(15 hours)
average speed = 53 1/3 km/h
The average speed of whole journey of the train is 45 km/hr
Average speed is the ratio of total distance travelled to total time taken. It is given by:
Average speed = total distance / total time
Given that a train travels 250 km with a average speed of 75 km/hr, hence:
75 = 250/time
time = 3.33 hours
It the travel 200 km with average speed of 30km/hr, hence:
30 = 200/time
time = 6.67 hours
The total distance = 200 km + 250 km = 450 km
The total time = 3.33 hr + 6.67 hr = 10 hours
Average speed = total distance/total time = 450 km/10 hours = 45 km/hr
The average speed of whole journey of the train is 45 km/hr
Find out more at: https://brainly.com/question/12322912
9(p−4)=−18 p= I am not great at math, please explain just a little bit
Answer:
[tex]\large \boxed{{p=2}}[/tex]
Step-by-step explanation:
9(p-4) = -18
Expand brackets.
9p -36 = -18
Add 36 on both sides.
9p -36 + 36 = -18 + 36
9p = 18
Divide both sides by 9.
(9p)/9 = 18/9
p = 2
Answer:
p = 2
Step-by-step explanation:
9(p - 4) = -18
You are solving for the variable, p. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operation, and =
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
~
First, divide 9 from both sides:
(9(p - 4))/9 = (-18)/9
(p - 4) = -18/9
p - 4 = -2
Isolate the variable, p. Add 4 to both sides:
p - 4 (+4) = -2 (+4)
p = -2 + 4
p = 4 - 2
p = 2
Check. Plug in 2 for p in the equation:
9(p - 4) = -18
9(2 - 4) = -18
9(-2) = - 18
-18 = -18.
~
52 divided by 5424
198 div by 8549 but need to see how to get the correct answer . Don’t want to use a calculator
Answer:
52 / 5424 = 0.00958..
198 / 8549 = 0.0231 ..
Step-by-step explanation:
52 / 5424
First of all, you need to add 0 plus a coma → 0.
52 becomes 520, but this value is smaller than 5424, so we need to add another 0
5200 → another 0 → 52000
So now, we have 52000 / 5424.
We start, 5424 . 10 = 54240, we are higher than 52000, so let's try 9
5424 . 9 = 48816, great!
52000 - 48816 = 3184
This is smaller than 5424, so we need a zero, again. But we do not add 0 to the result, because we are in the decimal side
31840 → 31840 / 5424. We would try 6,
5424 . 6 = 32544. It's bigger!, We use 5
5424 . 5 = 27120!
31840 - 27120 = 4720. We get another 0
47200, and we try 8.
5424 . 8 = 43392
47200 - 43392 = 3808.
So we are going to add 0, until we have four digits that can be divided by 5424 and decimals are infinte.
52 / 5424 = 0.00958..
198 / 8549 → Need to add, the first 0 to convert 198 to 1980
1980 = 0. → Another zero
19800 = 0.0 → 19800 / 8549
We try 2 → 8549 . 2 = 17098
19800 - 17098 = 2702 → we add 0
27020 / 8549 → We try 3
8549 . 3 = 25647 → 27020 - 25647 = 1373 → we add 0
13730 / 8549 → We use 1 → 13730 - 8549 = 5181
As decimal are infinite, we can express the result as:
198 / 8549 = 0.0231 ..
Translate the following phrase into an algebraic expression using the variable m. Do not simplify,
the cost of renting a car for one day and driving m miles if the rate is $39 per day plus 45 cents per mile
Answer:
y = 0.45X + 39
Find the midpoint of NP⎯⎯⎯⎯⎯ given N(2a, 2b) and P(2a, 0).
Answer:
(2a, b )
Step-by-step explanation:
Given the endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
[ [tex]\frac{1}{2}[/tex](x₁ + x₂ ), [tex]\frac{1}{2}[/tex](y₁ + y₂ ) ]
Here (x₁, y₁ ) = N(2a, 2b) and (x₂, y₂ ) = P(2a, 0), thus
midpoint = [ [tex]\frac{1}{2}[/tex](2a + 2a), [tex]\frac{1}{2}[/tex](2b + 0 ) ] = (2a, b )
I will give brainliest to the right answer!! Find the vertex and the length of the latus rectum. x= 1/2 (y - 5)² + 7
Answer:
(7, 5)2Step-by-step explanation:
When the quadratic is written in vertex form:
x = a(y -k)^2 +h
the vertex is (x, y) = (h, k), and the length of the latus rectum is 1/a.
For your given equation, ...
x = (1/2)(y -5)^2 +7
you have a=1/2, k = 5, h = 7, so ...
the vertex is (7, 5)
the length of the latus rectum is 1/(1/2) = 2
Which of the following is the first step when copying a line segment to construct a new line segment?
a. draw a line segment
b. use a straight edge to connect the point not on the line segment to a point in the arc
c. plot a point not on the original line segment
d. draw an arc
Answer:
The correct option is;
c. Plot a point not on the original line segment
Step-by-step explanation:
The steps to copy a line segment are;
1) Plot a point that will be an endpoint of the new line segment
2) With the compass pin at the beginning of the original line segment, open the compass width to the end of the original line segment
3) With the adjusted compass width from the above step place the compass pin at the plotted point of the new line segment and draw an arc in the region the new line segment is to be located
4) Select a point on the arc where the other end of the new line will be
5) From the selected point from the above step, draw a line to the point plotted as the beginning of the new line segment
6) The length of the line drawn above is the same as the length of the original line segment.
