Answers
Answer:
a) 67.8m
b) 36.8m
(both answers rounded off to 3 s.f.)
Step-by-step explanation:
Please see the attached pictures for full solution.
*Instead of rewriting PF to QF +43 in part (a), you could also leave PF as it is and rewrite QF as PF -43 after the line I labelled as equation 2. The working would be about the same, just that you would not need to add 43 again in picture 3 because we would be working with PF. (PF would be factorised out instead)
Related Questions
What’s the distance between (6,4) , (-5,-1) round to the nearest ten
Answers
Answer:
The answer is
12.1 unitsStep-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(6,4) and (-5,-1)
The distance between them is
[tex]d = \sqrt{ ({6 + 5})^{2} + ( {4 + 1})^{2} } \\ = \sqrt{ {11}^{2} + {5}^{2} } \\ = \sqrt{121 + 25} \\ = \sqrt{146} \\ \: \: \: \: \: \: \: \: \: \: \: = 12.0830459[/tex]
We have the final answer as
12.1 units to the nearest tenthHope this helps
Can someone help me with this question? Thanks if you do!
Answers
2w – y = 7w – 2, solve for w
Answers
Answer:
-1/5y + 2/5
Step-by-step explanation:
add -7w to both sides
-5w-y=-2
Divide both sides by -5
w= -1/5y +2/5
please help very confused limited time!
Answers
slope-intercept form: y = mx + b
m = the slope and b = the y-intercept.
We know that the line passes through x-coordinate 1 and y-coordinate 1 and has a slope of 2
Let's plug our numbers into the slope-intercept form
1 = 2(1) + b
Simplify the right side
1 = 2 + b
Subtract 2 from both sides
-1 = b
The final answer: y = 2x - 1
substitute (1,1) in for y and x
1=2(1)+b
1=2+b
-1=b
solve 2x^2 = x^4 +1 to find the value of x
Answers
Answer:
x= -1
x=1
Step-by-step explanation:
Joyce’s teacher asks her to write the sequence formed by the number of red squares in each picture for the first five pictures. What sequence should Joyce write?
Answers
Answer:
Joyce should write [tex]1,8,64,512,4096[/tex]
Step-by-step explanation:
Let's analyze the procedure of how the pictures are formed.
Her teacher said the images were created by taking a red square, dividing it into 9 smaller squares, and removing the center square.
For the first two images we can see and count that there is 1 red square in the first picture and 8 red squares in the second picture.
For the third image, there are 8 squares formed by 8 red squares each one.
The number of red squares is 8 x 8 = 64
We can write the sequence as
1 , 8 , 64 ⇒ 1 , 8 , [tex]8^{2}[/tex]
For the fourth picture we can do the same reasoning and figure out that there are 8 x 8 x 8 = 512 red squares in the fourth image.
The sequence so far is
1 , 8 , 64 , 512 ⇒ 1 , 8 , [tex]8^{2}[/tex] , [tex]8^{3}[/tex]
We can generalize the sequence and write that the sequence is :
[tex]8^{n}[/tex] with [tex]n[/tex] ∈ IN ⇒ The first five numbers will be
[tex]8^{0},8^{1},8^{2},8^{3},8^{4}[/tex] = [tex]1,8,64,512,4096[/tex]
working together Alberto and Amanda can paint a fence in 4.12 hours. had she done it alone it would have taken Amanda 10 hours. find how long it would take Alberto to do it alone. A) 6.75 B) 5.02 c) 7.54 D)7.01
Answers
Answer:
D) 7.01
Step-by-step explanation:
The rates of doing work, in terms of jobs per hour, will add when the two painters are working together. If A represents Alberto's time to do the job alone, we have ...
1/4.12 = 1/10 + 1/A
(Jobs per hour is the inverse of hours per job.)
A = 1/(1/4.12 -1/10) ≈ 7.0068 ≈ 7.01
It takes Alberto 7.01 hours to do the job alone.
2p-3 = 3p+2.
answer please!!!!
Answers
Answer:
- 5
Step-by-step explanation:
Step 1:
2p - 3 = 3p + 2
Step 2:
2p = 3p + 2 + 3
Step 2:
2p = 3p + 5
Step 3:
- p = 5
Answer:
p = - 5
Hope This Helps :)
Answer:
-5
Step-by-step explanation:
2p - 3 = 3p + 2
combine the like terms
-3 -2 = 3p -2p
-5 = p
Copy and fill in the charts.
Answers
Answer:
15% = 3/20 = 0.15
1.25 =125% =5/4
12 3/8 = 12.375 = 1237.5%
Step-by-step explanation:
15% to fraction , then decimal ;
[tex]15\% = \frac{15}{100} \\Cross\:cancel\:common\:factor ; 5\\\\15\div 5 = 3\\100\div 5 = 20\\\\= \frac{3}{20}\\\\\frac{3}{20} = 0.15[/tex]
1.25 to fraction , then percentage
[tex]1.25 = \frac{1.25}{1} \times \frac{100}{100} \\\\1.25\times 100 =125\\1\times 100 = 100\\\\= \frac{125}{100} \\= \frac{5}{4} \\\\1.25\times 100\\= 125\%[/tex]
12 3/8 to decimal then percentage
[tex]12\frac{3}{8} =\frac{99}{8} = 12.375\\\\12.375\times 100\\\\= 1237.5\%[/tex]
i dont know can someone help me
Answers
Answer:
x = 11/4
Step-by-step explanation:
[tex]\frac{x+8}{4} = \frac{6x+5}{8}[/tex]
Step 1: Cross-multiply.
[tex](x+8)*(8)=(6x+5)*(4)[/tex]
[tex]8x+64=24x+20[/tex]
Step 2: Subtract 24x from both sides.
[tex]8x+64-24x=24x+20-4x[/tex]
[tex]-16x+64=20[/tex]
Step 3: Subtract 64 from both sides.
[tex]-16x+64-64=20-64[/tex]
[tex]-16x=-44[/tex]
Step 4: Divide both sides by -16.
[tex]\frac{-16x}{-16} = \frac{-44}{-16}[/tex]
[tex]x = \frac{11}{4}[/tex]
Find the slope and y−intercept. y − 8 = 2x + 6
Answers
which value of x satisfies the equation 7/3 (x + 9/28) = 20?
Answers
Answer:
x=8.25
Step-by-step explanation:
Divide both sides by 7/3
(x+9/28) = 8.57
Subtract 9/28 on both sides
x = 8.25
Midpoint (-10,9), (3,8)
Answers
Answer:
(-3.5 8.5)
Step-by-step explanation:
Midpoint Formula: ([tex]\frac{x2 + x1}{2}[/tex], [tex]\frac{y2 + y1}{2}[/tex])
What I did: -10 + 3 = 7, 7 / 2 = 3.5 x = 3.5 | 9 + 8 = 17, 17 / 2 = 8.5
Midpoint = (-3.5, 8.5)
If my function rule is y=x + 3, what is the OUTPUT if the input is 4?
Answers
Answer:
7
Step-by-step explanation:
The output is 'y'. The input would be 'x'.
[tex]y=x+3\\\\y=4+3\\\\y=7[/tex]
The output should be 7.
Hope this helps.
The output for the function y=x + 3 at input x = 4 will be y = 7.
What is a function?The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.
Given the function is y=x + 3. the value of the output at input x = 4 will be calculated as:-
y = x + 3
Put x = 4 in the function.
y = 4 + 3
y = 7
Therefore, the output for the function y=x + 3 at input x = 4 will be y = 7.
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Which of the following statements does not represent the same value as the others?
a) the distance between 0 and −9
b) the absolute value of negative 9
c) the opposite of 9the absolute value of 9
Answers
The statement that does not represent the same value as the others is 'the opposite of 9'
What is an absolute value of number?"It is the actual distance of the number from zero."
What is opposite of a number?"The opposite of number is a value which is an additive inverse of number.""The opposite of number 'a' is '-a'."For given question,
We need to find the statement which does not represent the same value as the others.
We find the value for each statement.
a) the distance between 0 and 9
The distance between 0 and 9 is 9.
b) the absolute value of negative 9
We know, |-9| = 9
So, the absolute value of -9 is 9
c) the opposite of 9
The opposite of 9 is -9.
d) the absolute value of 9
|9| = 9
So, the absolute value of 9 is 9.
Therefore, the statement that does not represent the same value as the others is 'the opposite of 9'
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14=7(2x-4)
I have to solve this equation using two different methods and I don’t know how
Answers
Answer:
14=7(2x-4)
0r, 14/7 = 2x-4
or, 2= 2x-4
0r,2x= 6
or x=3
14=7(2x-4)
14=14x -28
14x=42
x=42/14=3
Method 1
Divide both sides by 7 first to get
14 = 7(2x-4)
14/7 = 7(2x-4)/7
2 = 2x-4
Then add 4 to both sides
2+4 = 2x-4+4
6 = 2x
2x = 6
Finally, divide both sides by 2
2x/2 = 6/2
x = 3
which is the final answer
------------------------------------------------------------------------------------------------
Method 2
Distribute the 7 through to each term in the parenthesis
14 = 7(2x-4)
14 = 7*2x + 7*(-4)
14 = 14x - 28
Then we follow similar steps as done earlier. Add 28 to both sides
14+28 = 14x-28+28
42 = 14x
14x = 42
Then divide both sides by 14 to fully isolate x
14x/14 = 42/14
x = 3
Either way we get the same result. As to which method you pick (if you could only choose one), its up to you based on whichever you find easier.
The basic idea with either method is that we follow PEMDAS in reverse to undo everything happening to x. This way we fully isolate it.
----------------
Checking the answer:
Plug x = 3 into the original equation. Simplify to get
14 = 7(2x-4)
14 = 7(2*3-4)
14 = 7(6-4)
14 = 7*2
14 = 14
This confirms the answer. As you can see, if we know the value of x, we use PEMDAS to simplify both sides. But if we don't know x, and want to find it, then we follow PEMDAS in reverse.
401 km 101 m – 34 km 153 m
Answers
Given :
An expression D = 401 km 101 m – 34 km 153 m.
To Find :
Value of D.
Solution :
We know, 1 km = 1000 m.
So, 401 km 101 m =( 401000 + 101 ) m = 401101 m.
Also, 34 km 153 m = ( 34000 + 153 ) m = 34153 m.
Now, D is given by :
D = 401101 - 34153 m
D = 366948 m
Now, D = 366948 m = 366 km 948 m.
Therefore, the difference is 366 km 948 m.
Hence, this is the required solution.
A field in the shape of a square has an area of 8,100 square feet. How can you determine the length of one side of the field?
Answers
To determine the length of one side use the formula for the area of square. As a square is equal on all four sides, finding one length results in any of the four. Solve using the formula and you receive your answer of 90.
A = s²
8100 ft² = s² (set up formula)
√8100 ft² = s² ( get s alone by squaring both sides)
90 ft = s (answer)
We can conclude that the side of the given square with an area of 8100ft² is 90ft.
What is a square?A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles. It can alternatively be explained as a rectangle with two neighboring sides that are of equal length. A square is a two-dimensional plane object in geometry that has four equal sides and four equal but 90-degree angles.So, the area of the square is 8100ft².
Formula: s²So, we know that: 8100 = s²Now, calculate for s as follows:
s² = 8100s = √8100s = 90ftTherefore, we can conclude that the side of the given square with an area of 8100ft² is 90ft.
Know more about squares here:
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Help me solve the following
Answers
Answer:
C. c = 8
Step-by-step explanation:
Step 1: Write equation
7 - 3c = -17
Step 2: Subtract 7 on both sides
-3c = -24
Step 3: Divide both sides by -3
c = 8
Answer:
C)8
7-3c=-17
-3c= -24
c=8
Diego says the constant of proportionality is 550 Andrew say is the constant of proportionality is 9 1/6 do you agree with either of them explain your reason
Answers
Answer:
The question is incomplete. The complete question is :
A plane traveling at a constant speed flew over Pittsburgh, Saint Louis, Albuquerque, and Phoenix on its way from New York to San Diego.
Complete the table as you answer the questions. Be prepared to explain your reasoning.
segment time distance speed
Pittsburgh to Saint Louis 1 hour 550 miles
Saint Louis to Albuquerque 1 hour 42 minutes
Albuquerque to Phoenix 330 miles
Step-by-step explanation:
We can complete the table as :
segment time distance speed
Pittsburgh to Saint Louis 1 hour 550 miles 550 miles/hour
Saint Louis to Albuquerque 1 hour 42 minutes 93.5 miles 550 miles/hour
Albuquerque to Phoenix 3/5 hour 330 miles 550 miles/hour
Since it is given in the question that the plane is flying in a constant speed from one place top another place.
So, it is maintaining the same speed to cover different distances for different time.
Thus the constant of proportionality is 550.
Identify the geometric mean of 10 and 5/8.
Answers
24.08319
Step 1 : Find 1 / N
1 / N = 1 / 5 = 0.2
Step 2 : Find mean
GM = ( 1 * 3 * 5 * 7 * 10 ) 0.2
= ( 1050 ) 0.2
GM= 4.020
Ashley wants to pour 97.94 grams of salt into a container. So far, she has poured 39.1 grams. How much more salt should Ashley pour?
Answers
the dots above are
4
16
56
PLEASE HURRY
Answers
Answer:
Equation 1
hope this helps
You earn $15 an hour tutoring and $9 an hour working at the Sippy Drink. You can tutor a maximum of 10 hours a week. You have to put in at least 20 hours a week at the Sippy Drink to keep your job there. You can't work more than 40 hours a week. how many hours should you work at each job to earn the maximum amount of money a week?
Answers
Answer:
5hours
Step-by-step explanation:
1 week =7 days
10 hr +20hr = 30 hrs
If you work 4hrs a wee k you will achieve only 28hrs of work so you will have to work for 5hrs to achieve 35hrs of work which is still within the bracket of 40hrs of work
In each job you will work for 2hours 30
minute
Each day you will earn $60.00
At tutoring you get $37.50
At sippy drink you will get $22.50
In a week you will get a maximum of $420.00
A recipe for orange water says, “Mix 3 teaspoons yellow water with 1 teaspoon red water.” For this recipe, we might say: “The ratio of teaspoons of yellow water to teaspoons of red water is 3:1.”
Answers
Answer:6:2
Step-by-step explanation:
Answer:
how many batches you need to know? If 2 batches the answer is 6:2 and if 4 batches it is 12:4
PLEASE HELP MY BIRTHDAY WILL BE CANCELLED IF I DONT GET A GOOD GRADE ON THIS
Answers
Answer:
Option 4
Step-by-step explanation:
If the circle is filled in them it will be either ≤, ≥, ≈ .
One circle is open one is closed
What is the answer for this? Ugh I hate study island!!
Answers
Answer:
[tex]\frac{7x}{8}-\frac{1}{40}[/tex]
Step-by-step explanation:
[tex](\frac{3x}{4}-\frac{5}{8})+(\frac{x}{8}+\frac{3}{5})[/tex]
By combining the like terms,
= [tex](\frac{3x}{4}+\frac{x}{8})+(\frac{3}{5}-\frac{5}{8})[/tex]
= [tex](\frac{6x}{8}+\frac{x}{8})+(\frac{3}{5}\times \frac{8}{8}-\frac{5}{8}\times \frac{5}{5} )[/tex]
= [tex]\frac{7x}{8}+(\frac{24}{40}-\frac{25}{40})[/tex]
= [tex]\frac{7x}{8}-\frac{1}{40}[/tex]
Therefore, by solving the given expression we find the answer as [tex]\frac{7x}{8}-\frac{1}{40}[/tex].
helppp first to answerr will be marked as brainlist
Answers
Answer:
A
Step-by-step explanation:
in the end of the sentence it mentions "in the future" so you need to make that verb future tense as well
I think the correct answer is A.
Explanation: It just makes the most sense to me. I dont really know how to explain it any better! Im sorry! I hope this helped!! :)
is it greater than or less than 4.29__4.3
Answers
Step-by-step explanation:
Think of 4.29 and 4.3 as 429 and 430.
Now which is greater, 429 or 430?
430, right? Then we convert them back to decimals.
4.29<4.3
Hope it helps!
Solve the formula for m.
e = mc2
m =
Answers
Answer:
m = e/c^2
Step-by-step explanation:
Equation: e = mc^2
Isolate m: e/c^2 = mc^2/c^2
Cancel out: e/c^2 = m