Answer:
Increasing x> 3
Decreasing x< 3
Step-by-step explanation:
If you imagine drawing a tangent line (a line which touches a curve or shape at one point) at some point on the graph, you can see if a curve is increasing or decreasing at that point; and on the whole interval.
Doing this I find that the curve is decreasing on x< 3 and increases on x> 3
Factorise : x^2-9x-70 Step by Step
Answer:
Step-by-step explanation:
x^2 - 9x - 70
we need to find two numbers whose sum is -9 and product id -17
The numbers are -14 and 5
By splitting the middle term,
x^2 - 14x + 5x - 70
= x ( x - 14 ) + 5 ( x - 14 )
( x + 5 ) ( x - 14 )
Hope this helps
Plz mark as brainliest!!!!!
Answer:
Step-by-step explanation:
Sum = -9
Product = -70
Factors = -14 , 5
x² - 9x - 70 = x² + 5x - 14x + (-14) * 5
=x(x + 5) - 14(x + 5)
= (x + 5)(x - 14)
Jack is building a square garden. Each side length measures 777 meters. Jack multiplies 7\times77×77, times, 7 to find the amount of space in his garden is equal to 494949 square meters. Which measurement does 494949 square meters represent?
Answer:
49 square meters represent area of the square garden
Step-by-step explanation:
Each side length=7 meters
He multiplied 7 × 7 times to find the amount of space
=49 square meters
Jack is trying to measure the area of his square garden
Area of the square garden = length^2
=Length × length
Recall,
Length=7 meters
Area of the square garden= 7 meters × 7 meters
=49 square meters
Axel has spent 25% of his money on a video game. If the price of the video game was $ 45, how much money did Axel have before the purchase?
Answer:
$180
Step-by-step explanation:
25% = 1/4
x/4 = 45
45*4 = 180
write an equation of the perpendicular bisector of the segment joining a(-2,3) and b(4,-5).
A) 3x+4y=7 B) 3x-4y=-7 C) 3x-4y=7 D) -3x-4y=7 E) 4x-3y=7
Answer:
C) 3x - 4y = 7
Step-by-step explanation:
The midpoint of AB is
M( (-2 + 4)/2, (-5 + 3)/2 ) = M(1, -1)
Line AB has slope:
(3 - (-5))/(-2 - 4) = 8/(-6) = -4/3
Slopes of perpendicular lines are negative reciprocals.
A perpendicular to line AB has slope 3/4.
The perpendicular to line AB that passes through the midpoint of segment AB is the line we want.
[tex] y - y_1 = m(x - x_1) [/tex]
[tex] y - (-1) = \dfrac{3}{4}(x - 1) [/tex]
[tex] y + 1 = \dfrac{3}{4}(x - 1) [/tex]
[tex] 4y + 4 = 3(x - 1) [/tex]
[tex]4y + 4 = 3x - 3[/tex]
[tex]3x - 4y = 7[/tex]
Answer:
C
Step-by-step explanation:
Segment joining a and b
m = 8/(-6) =-4/3
For that of the perpendicular bisector...
m = 3/4
Midpoint of Segment joining a and b
([-2+4]/2 , [3-5]/2)
=(1, -1)
y=mx+c
-1=(3/4)(1)+c
c= -7/4
y=3x/4 - 7/4
4y=3x - 7
3x-4y = 7
A coin is tossed. What is the theoretical probability of the coin NOT showing tails?
P(Not tails) =
Answer:
50%
Step-by-step explanation:
its 50% it will land on head and 50% it will land on tails since there is only two sides on a coin
Answer:
1/2 or .5
p(1/2)
Step-by-step explanation:
its simple, there are 2 sides to a coin, so there are 2 possible outcomes. and the question asks what is the probability of the coin landing on one or in other wrds, its asking what is te probilitity of one of the two heads to be up. SO the probility is 1/2
At the end of the day, a bakery gives everything that is unsold to food banks for the needy. If it has 12 apple pies left at the end of a given day, in how many different ways can it distribute these pies among 6 food banks for the needy?
Answer:
462 ways
Step-by-step explanation:
The formula to use in solving this problem is given as the Combination formula
The Combination formula is given as
C(n , r) = nCr = n!/r! (n - r)!
We are told that a food bakery has 12 pies unsold at the end of the day which they intend to share to 6 food banks
n = 12, r = 6
In order to ensure that at least 1 food bank gets 1 pie, we have:
n - 1 = 12 - 1 = 11
r - 1 = 6 - 1 = 5
Hence,
C(11, 5) = 11C5
= 11!/ 5! ×(11 - 5)!
= 11!/5! × 6!
= (11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1)/ (5 × 4 × 3 × 2 × 1) ×( 6 × 5 × 4 × 3 × 2 × 1)
= 462 ways
Simplify (1 − cos x)(1 + cos x).
Answer:
Sin^2 x
Step-by-step explanation:
● (1-cos x) (1 + cos x)
● 1^2 - cos^2 x
● 1 - cos^2 x
We khow that 1 = sin^2 x + cos^2 x
● [ sin^2 x + cos^2 x] - cos^2 x
● sin^2 x + cos^2 x - cos^2x
● sin^2 x
Sal washed 5 cars in 50 minutes. What is the unit rate?
Answer:
since Sal washed 5 cars in 50 minutes, we can express his time as follow:
[tex] \frac{5 \: cars}{50 \: minutes} [/tex]
simplifying it by diving by 5, we get:
[tex] \frac{1 \: car}{10 \: minutes} [/tex]
Thus the rate will be 10 minutes per car (10 min/car)
Answer:
10 mins / car
Step-by-step explanation:
50 / 5 = 10
If f(x)= 5x + 4
find
the inverse of f(x)
Answer:
f(x)=y
5x+4=y
5x=y-4
x=y-4/5
inverse of x=(x-4)/5
Write each fraction as a decimal and a percent. A) 7/8 B) 9/75 C/ 120/75
Answer:
A) 0.875, 87.5%
B) 0.12, 12%
C) 1.6, 160%
Step-by-step explanation:
Answer:
A) 0.875, 87.5%
B) 0.001, 0.1%
C) 1.6, 160%
Step-by-step explanation:
I honestly just used a calculator, but it could also be solved using the butterfly technique. For percentages just move the decimal to the left two places.
A company is making a new label for one of their containers. The container is a cylinder that is 9 inches tall and 5 inches in diameter. What is the area of the label that needs to be printed to go around the new container? Use π = 3.14.
Answer:
180.55 in².
Step-by-step explanation:
Data obtained from the question include the following:
Height (h) = 9 in.
Diameter (d) = 5 in
Pi (π) = 3.14
Area of the label =..?
Next, we shall determine the radius.
Diameter (d) = 5 in
Radius (r) =.. ?
Radius (r) = Diameter (d) /2
r = d/2
r = 5/2
r = 2.5 in.
Next, we shall determine the area of the label that needs to be printed to go around the new container by calculating the surface area of the cylinder.
This is illustrated below:
Height (h) = 9 in.
Pi (π) = 3.14
Radius (r) = 2.5 in.
Surface Area (SA) =.?
SA = 2πrh + 2πr²
SA = (2×3.14×2.5×9) + (2×3.14×2.5²)
SA = 141.3 + 39.25
SA = 180.55 in²
The surface area of the cylinder is 180.55 in².
Therefore, the area of the label that needs to be printed to go around the new container is 180.55 in².
Answer:
Step-by-step explanation:
i dont have the work but the answer is 182.6
The ratio of the measures of the three angles of a triangle is 2:2:5 . Find the measure of each angle
Answer:
Angle 1:Angle2: angle3: total
40 40 100 180
Step-by-step explanation:
The sum of the angles of a triangle is 180
Angle 1:Angle2: angle3: total
2 :2 :5 : 2+2+5 = 9
Divide 180 by 9
180/9 = 20
Multiply each by 20
Angle 1:Angle2: angle3: total
2*20 :2*20 :5*20 : 9*20
40 40 100 180
What is the explicit formula for this sequence?
-9, - 3, 3, 9, 15, ...
Answer:
-15+6d
Step-by-step explanation:
The common difference of the sequence is -3+9=6
The formula is an=a+(n-1)d, an=-9+(n-1)*6=-15+6d
please help! need the answers in order to move on:) will give brainliest to correct answer!
a rectangular garden is fenced on all sides with 128 feet of fencing. The garden is 4 feet longer than it is wide. Find the length and width of the garden
Answer:
Length = 34 feet
Breadth = 30 feet
Step-by-step explanation:
Perimeter= 128 ft
Let the breadth be = [tex]x[/tex]
Let the length be = [tex]x+4[/tex]
∴by the problem ,
2(length+breadth)= perimeter
[tex]2(x+4+x)=128\\2(2x+4)=128\\4x+8=128\\4x=128-8\\4x=120\\x=120/4\\x=30[/tex]
Therefore, length of the garden = 30+4= 34 feet
breadth of the garden = 30 feet
Will give brainliest. Find the length and measure of each arc. Show your work.
Problem 1
The circumference is the full perimeter around the circle. You can think of it as the combination of "circle" and "fence" to get "circumference", but there might be other tricks to remember the term.
Anyways, the formula to get the circumference of a circle is
C = 2*pi*r
In this case, r = 14 is our radius so,
C = 2*pi*r
C = 2*pi*14
C = 28pi .... exact circumference in terms of pi
We only want a portion of this circumference as shown by the piece of the circle darkened. The fractional portion we want is 135/360 of a circle. Divide the angle by 360 to get the fractional portion you want. If the angle was say 180 degrees, then 180/360 = 1/2 is the fractional portion.
So we take 135/360 and multiply it by the value of C found earlier
arc length = (fractional portion)*(circumference)
arc length = (135/360)*28pi
arc length = 10.5pi
That's the exact arc length in terms of pi. Use a calculator to find that
10.5pi = 32.9867228626929
Or you could use pi = 3.14 to say
10.5*pi = 10.5*3.14 = 32.97
Which is fairly close to what the calculator is saying
-----------------
Summary:Exact arc length = 28pi
Approximate arc length (using calculator) = 32.9867228626929
Approximate arc length (using 3.14 for pi) = 32.97
Units are in feet
When I write "using calculator", I mean using the calculator's stored version of pi, instead of pi = 3.14
======================================================
Problem 2
We could use the same idea as problem 1, or we could use the formula below. The formula is just a quick way of encapsulating what I discussed earlier.
L = arc length
x = central angle
L = (x/360)*2*pi*r
L = (150/360)*2pi*13
L = (65/6)pi .... exact arc length
L = 34.0339204138894 .... approx arc length (using calculator)
L = 34.0166666666667 .... approx arc length (using 3.14 for pi)
-----------------
Summary:Exact arc length = (65/6)pi
Approximate arc length (using calculator) = 34.0339204138894
Approximate arc length (using 3.14 for pi) = 34.0166666666667
Units are in meters
Is 8.888... a rational number?
=================================================
Explanation:
Since the decimal repeats itself infinitely (the 8s go on forever), this is one sign that we have a rational number.
Rational numbers always have some kind of infinitely repeating pattern when we convert them to decimal form.
---------------------
Extra info (optional section)
If you want to determine what this number is equal to, then let's say that
x = 8.8888...
Multiplying both sides by 10 gets us
10x = 88.888....
Now we'll subtract the two equations
The 10x-x becomes 9x while the 88.8888...-8.8888... turns into 80
We're left with 9x = 80 which solves to x = 80/9
Therefore, 80/9 = 8.8888.... showing that we have a rational number
Any rational number is basically a fraction of two whole numbers.
A dress shop bought material for £4.65 a metre and sold it for £6.90 a metre. How much
profit would be made on a roll of 30 metres?
Answer:
£67.50
Step-by-step explanation:
On each metre of material, the shop makes a profit of ...
£6.90 -4.65 = £2.25
So, for 30 metres, the profit will total ...
30 × £2.25 = £67.50
A profit of £67.50 would be made on a 30-metre roll of material.
HELP! answer if you can !!
Answer:
The formula for ABC Triangle
(AB×AC)/2
= (4.7×2.4)/
= 11,28/2
= 5,64 in²
solve for x? They are vertical angles
Answer:
Step-by-step explanation:
6x - 11 = 3x + 13
3x = 24
x = 8
x + y = 0
y = 2x + 6
8
Now graph y = 2x + 6 What are the graphing points (there needs to be 3 pairs)
Answer:
(-3,6) (1,8) (2,10) and so on.
The first four terms of a sequence are, 9,2,-5,-12.
State the pattern of the sequence using algebraic expressions.
Answer:
[tex]a_{n}[/tex] = 16 - 7n
Step-by-step explanation:
There is a common difference between consecutive terms , that is
2 - 9 = - 5 - 2 = - 12 - (- 5) = - 7
This indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 9 and d = - 7 , then
[tex]a_{n}[/tex] = 9 - 7(n - 1) = 9 - 7n + 7 = 16 - 7n
benifits of social media when reporting about gbv
Step-by-step explanation:
Coordinate referrals and advocate with partner organizations supporting GBV survivors to provide confidential services to clients, in accordance with their wishes, GBV guiding principles and informed consent.
help help help
From the top of a lighthouse was 60 m above sea level. A ship located 1200 m
from the shore could spot the lighthouse. What was the angle of depression from
the top of the lighthouse to the ship?
Answer:
I think 60 - 1200 but i am not conform
The angle of depression from the top of the lighthouse to the ship is 0.04998 radians.
Given that, the top of a lighthouse was 60 m above sea level. A ship located 1200 m from the shore could spot the lighthouse.
We need to find the angle of depression from the top of the lighthouse to the ship.
What is the angle of depression?The angle is formed by the line of sight and the horizontal plane for an object below the horizontal.
Now, sin b=60/1200
⇒sin b=1/20
⇒sin b=0.05
⇒b=0.04998 radians
Now, b=x=0.04998 radians
Therefore, the angle of depression from the top of the lighthouse to the ship is 0.04998 radians.
To learn more about the angle of depression visit:
https://brainly.com/question/13514202.
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How many of the positive integer factors of 15552 are perfect squares? (WILL MARK BRAINLIEST IF CORRECT)
15552|2
7776|2
3888|2
1944|2
972|2
486|2
243|3
81|3
27|3
9|3
3|3
1
[tex]15552=2^6\cdot 3^5=(2^3\cdot3^2)^2\cdot 3[/tex]
[tex](3+1)\cdot(2+1)=4\cdot 3=12[/tex]
It's 12
Finding Inverses
Find an equation for the inve
3.
y = 3x + 2
One of the legs of a right triangle measures 12 cm and its hypotenuse measures 20
cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer:
cm
Submit Answer
attempt 1 out of 2
PLS HELP
Answer:
16
Step-by-step explanation:
First use the Pythagorean theorem a^2+b^2=c^2.
12^2+b^2=20^2. Solve the exponents: 144+b^2=400. Then, subtract the 144 from 400. That would be 256. Therefore b^2=256. Then you find the square root of 256=16.
Step-by-step explanation:
using pythogoras theory
hyp^2=opp^2+adj^2
you have been given the hyp and the opp so lets make the unknown x
20^2=12^2+x^2
400 =144+x^2
make x the subject of the formula
400-144=x^2
266=x^2
x=the square root of 266
Chase took a taxi from his house to the airport. The taxi company charged a pick-up fee of $1.20 plus $4.75 per mile. The total fare was $48.70, not including the tip. Write and solve an equation which can be used to determine x, the number of miles in the taxi ride. write the equation
Pine Lane Middle School's student council has 10 seventh graders and 8 eighth graders serving as representatives. A subcommittee containing 3 seventh graders and 3 eighth graders is formed to organize a student dance. How many different subcommittees can be formed
Hey there! I'm happy to help!
When dealing with picking things and finding the number of possibilities, we can be dealing with two different types of things: permutations or combinations. We use permutations when order is important to the groups and we use combinations if order is not important.
It appears here that order is not important here as the subcommittee doesn't have to be in a specific order, so we will be using combinations.
So, we have ten seventh graders to choose from. Then we will have 9, and then 8. So, we multiply these numbers of choices.
10×9×8=720
Now, we need to divide by 6. This is to show that order doesn't matter. Why? Because there are 6 possible ways to organize 3 seats on the committee (3×2×1), and we want to divide out all of the different orders so it is just the specific group of people and not their different organizations that are counted.
720/6=120
Now, we need to find this with the eighth graders.
8×7×6=336
And we divide by the number of seats factorial (3 seats for the eighth graders, so 3×2×1=6 again)
336/6=56
Now, we multiply our numbers for seventh and eighth graders to find all off the possibilities.
120×56=6720
So, there are 6720 subcommittees possible.
Have a wonderful day and keep on learning! :D
Find the domain of the function y = 5∕3 tan(3∕4x).
A) All real numbers except odd integer multiples of 2π∕3
B) All real numbers except odd integer multiples of 4π∕3
C) All real numbers except 0 and odd integer multiples of 2π∕3
D) All real numbers except 0 and odd integer multiples of 4π∕3
Answer:
A
Step-by-step explanation:
tan(3x/4)=sin(3x/4)/cos(3x/4)
So the domain of tah(3x/4) is all real numbers except real numbers that make cos(3x/4)=0.
cos(pi/2 +n pi)=0
So we need to solve 3x/4=pi/2+n pi
Multiply both sides by 4/3: x=4/3(pi/2+n pi)
Distribute: x=2pi/3+4n pi/3
Or x=(2pi+4 n pi)/3
Or x=2 pi/3 ×(1+2n)
So odd integer multiples of 2pi/3 is the numbers to be excluded from the domain.
The required domain of the function y = 5/3 tan(3/4x) is (-∞, ∞) - {- 2/3 (2n + 1)π, 2/3 (2n + 1)π}.
What are trigonometric equations?These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operation.
y = 5/3 tan(3/4x)
Function tan defined at every x except x = nπ/2 where n = odd number. i.e x = (-∞,∞) - {(2n+1) * π/2, -(2n+1) * π/2}
3/4 * x = (2n + 1 ) * π/2
x = (2n + 1) * 4/3* π/2
x = 2/3 (2n + 1)π
So the required domain for the given function y = 5/36tan(3/4)x is given as,
Domain (x) = (-∞, ∞) - {- 2/3 (2n + 1)π, 2/3 (2n + 1)π}.
Thus, the required domain of the function y = 5/3 tan(3/4x) is (-∞, ∞) - {- 2/3 (2n + 1)π, 2/3 (2n + 1)π}.
Learn more about trigonometry equations here:
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