Answer:
Uncertain if the second term is 30 and not 3o. IF 30, then the coefficients are
-1, 30 and 6.
Step-by-step explanation:
Coefficients are numbers ahead of the variables (letters).
The number 4 is called a constant. A constant is not a coefficient.
The coefficient (number ahead of the letters) of -xyz is -1.
Hope this helps.
2. ABCD is a square and P, Q are the midpoints of BC,CD respectively. If AP = a
and AQ = b. find in terms of a and b the directed line segments (i) AB (ii) AD
(iii) BD and (iv) AC.
Answer:
The answer is below
Step-by-step explanation:
A square is a quadrilateral (four sides and angles). All the sides and angles of a square are equal. Each angle of a square is 90° and the diagonals are equal.
In square ABCD:
AB = BC = CD = AC (all the sides of a square are equal)
Given that P is the midpoint of BC and Q is the midpoint of CD. AP = a and AQ = b.
a) Triangle APB is a right angled triangle:
BC = AB (all sides of a triangle are equal)
PB = 1/2 (BC) = 1/2(AB) = 0.5AB
Using Pythagoras theorem:
AB² + PB² = AP²
substituting:
AB² + (0.5AB)² = a²
AB² + 0.25AB² = a²
1.25AB² = a²
AB² = 0.8a²
AB = a√0.8
b) Triangle AQD is a right angled triangle:
AD = DC (all sides of a triangle are equal)
DQ = 1/2 (DC) = 1/2(AD) = 0.5AD
Using Pythagoras theorem:
AD² + DQ² = AQ²
substituting:
AD² + (0.5AD)² = b²
AD² + 0.25AD² = b²
1.25AD² = b²
AD² = 0.8b²
AD = b√0.8
c) In right triangle ADB, Using Pythagoras theorem:
AB² + AD² = BD²
But AB = AD
Substituting:
0.8a² + 0.8b² = BD²
BD = √(0.8a² + 0.8b²)
But AD = AB, hence 0.8a² = 0.8b²
BD = √(1.6a²)
BD = a√1.6
D) AC = AD (diagonals of a square are equal)
AC = √(0.8a² + 0.8b²)
AC = √(1.6b²) = b√1.6
mark and heather starr are celebrating their 25th anniversary by having a reception at local reception hall. they have budget 4500 for their reception. if the reception hall charges 50 cleanup fee plus 30 per person find the greatest number of people they may invite
Answer:
Step-by-step explanation:
The $50 cleanup fee is a "fixed cost."
The "$30 per-person fee is a "variable cost." That is, it varies with the number of people.
"within" means "less than or equal to"
Cost = $50 + $30x [where x = number of people]
Cost ≤ $4500 ["stay within their budget"]
$50 + $30x ≤ $4500 [substitute for cost]
$30x ≤ $4450 [subtract $50 from both sides retains sense of inequality]
x ≤ 148.3333 [divide by +$30 retains sense of inequality]
Mark and Heather may invite up to 148 guests.
[note: to be "≤," always truncate, never round up]
Check:
148 people for $30 each + $50 is $4440+$50 = $4490.
One more person makes it $4520 -- that is too much.
There we go, my bad
Answer:
Step-by-step explanation:
First we need a linear equation for the situation. 50 cleanup fee applies regardless of how many people they have. Even if NOBODY shows up, they will be charged $50, so $50 is our y-intercept. If they are charged $30 per person, and we are looking for the number of people they can invite, x will represent the number of people and y will represent the cost of everything. The linear equation is
y = 30x + 50. If they have 4500 to spend, then
4500 = 30x + 50, and now solve it for x:
4450 = 30x and now divide by 30 to get
148 1/3 = x. Now, you can't invite a third of a person, so it would be safe to invite 148 people and you won't go over your budget.
POINTS PLZ HELP!!!!!
Drag the terms to the correct locations in the expression. Not all terms will be used.
What is the complete factorization of 2x2 − 11x − 21?
x
2x
3x
1
3
7
they can be used more than once.
place them here
(__+__)(__-__)
Answer:
(2x+3)(x-7)
Step-by-step explanation:
2x^2+3x-14x-21
2x(x-7)+3(x-7)
The factors of the expression are (2x+3)(x-7).
What is factorization?Factorization is the breaking or decomposition of an entity (a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together give the original number. Factorize an expression involves take out the greatest common factor (GCF) of all the terms.
For the given situation,
The expression is [tex]2x^{2} -11x-21[/tex]
The complete factorization of the expression is as,
⇒ [tex]2x^{2} -11x-21=0[/tex]
⇒ [tex]2x^{2} -14x+3x-21=0[/tex]
⇒ [tex]2x(x-7)+3(x-7)=0[/tex]
⇒ [tex](2x+3)(x-7)=0[/tex]
The value of x can be found as
⇒ [tex]2x+3 = 0[/tex] or [tex]x-7 = 0[/tex]
⇒ [tex]x=\frac{-3}{2}[/tex] or [tex]x=7[/tex]
Then -3/2 and 7 are the zeroes of the expression.
Hence we can conclude that the complete factorization of the expression are (2x+3)(x-7).
Learn more about factorization here
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ABCD∼EFGH
The value of x is
Answer
didn't know there was an image
If you subtract 14 from twice a number, the result is 6. What is the number?
The equation for this statement:
2x – 14 = 6
=> 2x = 6 + 14
=> 2x = 20
=> x = 20/2
=> x = 10
sum of two numbers is 35 and the difference is 15
Answer
IM not too sure
Step-by-step explanation:
Not too sure sorry kid
Answer:
25 and 10 are the numbers
Step-by-step explanation:
x - 6
———
x + 8
=
9
—
3
Step 1 of 2: State any restriction(s) on the variable, if they exist.
need help asap!!
yes those are fractions ^^
Answer:
dont know....mmm sorry
an eight foot ladder leans against a building. if the ladder makes an angle of 60° with the ground, how far up the wall does the ladder reach?
Answer:
The ladder reaches (4)(√3) ft up the wall (6.93 ft)
Step-by-step explanation:
Think of a triangle with a 60 degree angle in the lower left corner. The lower right corner is a right triangle, and 8 ft is the length of the hypotenuse. The other angle is 30 degrees.
We know the angle 60 degrees, plus the length of the hypotenuse, but need the length of the vertical side opposite the 60 degree angle. Use the sine function here because it involves these knowns:
opposite side
sin 60 degrees = ------------------------ = x/(8 ft) = (√3)/2
Cross-multiplying, we get:
2x = (8 ft)(√3), or through reduction, x = (4)(√3)
The ladder reaches (4)(√3) ft up the wall (6.93 ft)
With the ground, [tex]6.92 ft[/tex] the wall does the ladder reach.
What is right angled triangle?A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any one angle is a right angle. Therefore, this triangle is also called the right triangle or 90-degree triangle.
According to the question
An eight foot ladder leans against a building. if the ladder makes an angle of 60° with the ground.
From the right angle triangle,
[tex]sin 60^{0} =\frac{h}{8}[/tex]
[tex]\frac{\sqrt{3} }{2}[/tex] = [tex]\frac{h}{8}[/tex]
[tex]8\sqrt{3} =2h[/tex]
[tex]h = 4\sqrt{3}[/tex]
[tex]h = 6.92 ft[/tex]
Hence, With the ground, [tex]6.92 ft[/tex] the wall does the ladder reach.
Find out more information about right angle triangle here
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There are some red counters and some yellow counters in a bag in the ratio 1 : 5
There are 20 yellow counters in the bag.
Janet puts some more red counters into the bag.
The ratio of the number of red counters to the number of yellow counters is now 1 : 2
How many red counters does Janet put into the bag?
Answer:
Janet put 6 red counters into the bag
Step-by-step explanation:
There are 5 yellow counters for every 1 red counter. If there are 20 yellow counters in the bag then there are 4 red counters. (20/5). If the ratio becomes 1:2 this means there are 2 yellow counters for every 1 red counter. There are 20 yellow counters so there must be 10 red counters in the bag. (20/2). 10 - 4 = 6. Janet put 6 red counters into the bag. (Brainliest would be appreciated!)
12+22+32+...+102 =?
Answer:
750 is the answer. Hope it helps!
Simplify 7-(3x+5y)+6(2x-3y)+8y
Answer:
Step-by-step explanation:
First get rid of the parentheses. Distribute the - sign and the +6 to each one.
[tex]7-3x-5y+12x-18y+8y\\7+9x-5y-18y+8y\\7+9x-15y[/tex]
Look at pic plz help
Answer:
tree C was planted first
Step-by-step explanation:
Since Tree c was 10 inches tall when it was first grown and Tree A was 5 at first and Tree B was 3 inches tall. 10>5 10>3
2x²+2 (2x) +5=0
solve indices
Step-by-step explanation:
2x²+4x+5=0
.....
solve it by using the factorisation method or completing the square method
don't mind the hand writing
am I correct btw
A field is a rectangle with a perimeter of 1240 feet. The length is 400 feet more than the width. Find the width and length of the rectangular field.
The width
Answer: The length is 510 and the width is 110.
Step-by-step explanation:
To find the area of a rectangle, you will have to add the 2 times the length plus 2 times the width because a rectangle have 4 sides. Two widths and two lengths.
You can now use the formula P= 2l + 2w
were P is the perimeter , l is the length, and w is the width.
the length is 400 more than the width, so we can represent that by the equation, l = w + 400
And now we know that the width is w.
So now we will input the perimeter, length, and into the formula to solve for w.
1240 = 2(w + 400) + 2w
1240 = 2w + 800 + 2w
1240 = 4w + 800
-800 -800
440 = 4w
w = 110
L= 110 + 400
L = 510
Check :
1240 = 2(510) + 2(110)
1240 = 1020 + 220
1240 = 1240
Can someone please help and explain I will mark brainliest
Answer:
I really don't know I am sorry.
Step-by-step explanation:
Answer:
i = integers greater than n
n < i
n = smallest integer
a = 2nd largest integer
b = 3rd largest integer
c = largest integer
d = sum of all the integers
n + a + b + c = 2174
Step-by-step explanation:
2
8.
14
Y
2
10
50 250
Is the relationship linear, exponential, or neither?
Answer:
Exponential relationshipStep-by-step explanation:
Looking at the y-values, it seems a geometric progression with the common ratio of 5. Therefore it can be exponential relationship.
By trying the values in the table we get the equation:
y = 2×[tex]5^{(x+4)/6}[/tex]8/9 ÷ 4/9 = ????????
Answer:
2
Step-by-step explanation:
Please help me!!!!!!!!!!
Lisa has $150 at most to spend on clothes. She wants to buy a pair of jeans for $58 and will spend the rest on t-shirts that cost $14 each.
Then on the way to the register, Lisa notices a cool pair of shoes that cost $39. If she wants those shoes and the jeans, how many t-shirts will she be able to purchase? Create an inequality to represent the number of t-shirts that Lisa can purchase?
Answer:
To determine the number of shirts that Lisa can buy, knowing that each one is worth $ 14, that she can spend a maximum of $ 150 and that she will also buy a pair of jeans for $ 58 and a pair of shoes for $ 39, the following calculation must be performed:
(150 - 58 - 39) / 14 = X
53/14 = X
3.78 = X
53 - (14 x 3) = X
11 = X
Therefore, Lisa can buy 3 T-shirts, and she will have 11 dollars left over.
4)
Write an equation to model the
scenario:
You buy a house for $215,000. The
value of the house increases 3%
Each year
What is 9.52 rounded to the nearest tenth?
o 9.0
9.5
o 9.6
O 10.0
I need this fast
Answer:
9.5
Step-by-step explanation:
When rounding to the nearest tenth, check to see what the hundredths place value is.
If it is 0.05 or greater, we will round the tenths place up one.
If not, the tenths place will remain the same.
Since 9.52 has a hundredths place value of 0.02, we will keep the same tenths place value.
So, the correct answer is 9.5
An arithmetic sequence has the following properties:
The sum of its 18 term and 4th term is 29
1) The sum of its oth and 8th terms is 74
Find a formula for the nth term T of this sequence.
Answer:
Easy peasy
Step-by-step explanation:
7+(n-1)5
SPEED, DISTANCE AND TIME
please please !!!!!!!!!!!!!!!!!!!!!!!!!!!!!! emergency will give thanks
1) A cyclist travels a distance of 90 miles in 5 hours. What
was her average speed?
2) How far along a motorway would you travel if you drove at
70 mph for 4 hours?
3) I drive to Bude in Cornwall from Sheffield in about 6
hours. The distance from Sheffield to Bude is 315 miles.
What is my average speed?
4) The distance from Leeds to London is 210 miles. The train
travels at an average speed of 90 mph. If I catch the 9.30 am
train in London, at what time should I expect to arrive in
Leeds?
5) How long will an athlete take to run 2000 m at an average
speed of 4 metres per second?
6) The distance between Sheffield and Land’s End is 420
miles.
a) What is the average speed of a journey from Sheffield to
Land’s End that takes 8 hours 45 minutes?
b) If Sam covered the distance at an average speed of 63
mph, how long would it take him?
Answer:
1 --- The cyclist's average speed was 18 miles per hour.
2 --- I would travel 280 miles far.
3 --- Your average speed was 52.5 miles per hour.
4 --- You should expect to arrive in Leeds at 11:50 AM.
5 --- The athlete will run 2000 m in 8 minutes and 20 seconds.
6A --- The average speed of the journey is 48 miles per hour.
6B --- It will take him 6 hours and 40 minutes.
Step-by-step explanation:
1) 90 / 5 = 18
2) 70 x 4 = 280
3) 315 / 6 = 52.5
4) 210 / 90 = 2.3333
0.333 = 0:20
9:30 + 2:20 = 11:50
5) 2000 / 4 = 500
500 / 60 = 8.3333
0.3333 = 0:20
8.3333 = 8:20
6A) 0:45 = 0.75
420 / 8.75 = 48
6B) 420 / 63 = 6.666
6.6666 = 6:40
Find each missing side, then the perimeter
Answer:
A 10
B10
C10
in total is 106
A 10.0 mL sample of copper has a mass of 89.6 g. What is the density of copper?
Answer:
8.96 g/cm3
Step-by-step explanation:
89.6 divided by 10 is 8.96
find the value of x
Answer:
the us 113, hope this helps you out
help me solve this please.
A package of 3 pairs of insulated gloves costs $16.77. What is the unit price of the pairs of gloves?
Answer:
5.59
Step-by-step explanation:
Your cellphone plan is by the minute. Each minute of use costs $0.10. Create a relation that represents the amount spent, A, per minute, m, of call time.
Answer:
A = 0.10m
Step-by-step explanation:
A = total amount spent
0.10 = cost per minute
m = how many minutes
Please help me, I think this is easy but I just don't get it...
Answer:
the last one?
Step-by-step explanation:
i dont know, but that one seems like it would
Answer:
answer is A if only one can be chosen. if more than one can be, b might be an answer as well, but not c and d.
Step-by-step explanation:
think of a 3 4 5 triangle for answer a.
just remembered this method, do Pythagorean theorem for each answer. that will tell you which equals a triangle. answer a foe sure is one cmbecuase of a 3 4 5 triangle.