Answer:
3Step-by-step explanation:
IF point E lies on the line segment DF, this means that all the points DEF are collinear and DE+EF = DF.
Given parameter
DE = 6
DF = 9
Required
EF
Substituting the given parameter into the expression above to get the required will be;
DE+EF = DF.
EF = DF-DE
EF = 9-6
EF = 3
Hence the length of EF is equivalent to 3
Help pleaseeeee. Tyyy
Answer:
Option B.
Step-by-step explanation:
The measure of cage is 90 feet by 40 feet.
Length of rope [tex]=40\sqrt{2}[/tex] foot
It is clear that, length of rope is greater than one side of cage and raw a line which divides the cage in two parts as shown in below figure.
We need to find the shaded area.
By Pythagoras theorem:
[tex]hypotenuse^2=base^2+perpendicular^2[/tex]
[tex](40\sqrt{2})^2=(40)^2+perpendicular^2[/tex]
[tex]3200=1600+perpendicular^2[/tex]
[tex]3200-1600=perpendicular^2[/tex]
[tex]1600=perpendicular^2[/tex]
[tex]40=perpendicular[/tex]
So, it is a square.
From the figure it is clear that the shaded area contains 1/8th part of circle are half part of square.
Area of circle is
[tex]A_1=\pi r^2[/tex]
[tex]A_1=\pi (40\sqrt{2})^2[/tex]
[tex]A_1=3200\pi[/tex]
Area of square is
[tex]A_2=a^2[/tex]
[tex]A_2=(40)^2[/tex]
[tex]A_2=1600[/tex]
Area of shaded portion is
[tex]A=\dfrac{A_1}{8}+\dfrac{A_2}{2}[/tex]
[tex]A=\dfrac{3200\pi}{8}+\dfrac{1600}{2}[/tex]
[tex]A=400\pi+800[/tex]
[tex]A=400(\pi+2)[/tex]
The required area is [tex]400(\pi+2)[/tex] sq. ft.
Therefore, the correct option is B.
A group of students is arranging squares into layers to create a project. The first layer has 4 squares. The second layer has 8 squares. Which formula represents an arithmetic explicit formula to determine the number of squares in each layer?
Answer:
answer is d
Step-by-step explanation:
Can you help me please.
Answer:
option 2.
Step-by-step explanation:
You use the y-intercept form: y=mx+b
mx=slope, and b=y-intercept.
Looking at this graph, you can see that the slope is -2/3 (rise over run), and the line is negative, so the slope becomes negative.
So now, we can see the only option having the slop -2/3x is option 2.
Shelly and Terrence earned points in a game by completing various tasks. Shelly completed x tasks and scored 90 points on each one. The expression below shows Terrence's total points in the game: 90x − 20 What does the constant term of the expression represent? (2 points)
Answer:
the constant term of the expression represents the difference between Shelly and Terrence points.
3x/4 - 5 = 10
I need help solving this equation someone please help
Answer:
x = 20
Step-by-step explanation:
Hello!
What we do to one side we have to do to the other
3x/4 - 5 = 10
Add 5 to both sides
3x/4 = 15
Multiply both sides by 4
3x = 60
Divide both sides by 3
x = 20
The answer is x = 20
Hope this helps!
Answer:
20
Step-by-step explanation:
3x/4 - 5 = 10
3x/4 = 10 + 5
3x/4 = 15
3x = 15 * 4
3x = 60
x = 60/3
x = 20
Solve (s)(-3st)(-1/3)
Answer:
Step-by-step explanation
What is the value of m in the equation 1/2m - 3/4n = 16, when n = 8?
Answer: m= 44
Step-by-step explanation:
1/2m - 3/4n = 16 when n is 8 put it into the equation and solve for m.
1/2m - 3/4(8) = 16
1/2m - 6 = 16
+6 +6
1/2m = 22
m = 44
Answer:
44
Step-by-step explanation:
● (1/2 )× m - (3/4) × n = 16
Replace n by 8 and the fraction by decimal numbers (1/2 = 0.4 and 3/4 =0.75)
● 0.5 × m - 0.75 × 8 = 16
● 0.5m - 6 = 16
Add 6 to both sides
● 0.5 m - 6 + 6 = 16+ 6
● 0.5 m = 22
Multiply both sides by 2
● 0.5m × 2 = 22 × 2
● m = 44
andy is making floor plans for a tree house using a scale 1in to 2ft he wants to make the floor of the tree house have a length of 8ft. how many inches should he show for this distance on his floor plan
Answer:
Andy should represent the 8 feet long floor on the floor plan with a dimension of 4 inches
Step-by-step explanation:
The scale of the tree house plan is given as 1 in. to 2 ft,
Therefore we have a scale of 1/2 in. of the floor plane is equivalent to 1 ft. in actual dimensions
Given that Andy wants the floor to make the tree house floor to have a length of 8 ft., let the dimension of the floor plan of the house floor be x, we have;
[tex]\dfrac{\frac{1}{2} \ inches \ plan }{1 \ feet \ actual} =\dfrac{x \ inches \ plan}{8 \ feet \ actual}[/tex]
[tex]x \ inches \ plan =\dfrac{\frac{1}{2} \ inches \ plan }{1 \ feet \ actual} \times 8 \ feet \ actual = 4 \ inches[/tex]
Therefore, Andy should represent the 8 feet long floor on the floor plan with a dimension of 4 inches.
write as an expression: a number that is equal to five less than b
Answer:
[tex]\huge\boxed{a = b-5}[/tex]
Step-by-step explanation:
Let the number be a
So, the given condition is:
a = b-5
Answer:
[tex]\Huge \boxed{a=b-5}[/tex]
Step-by-step explanation:
Let the number be [tex]a[/tex].
[tex]a[/tex] is equal to 5 less than [tex]b[/tex].
5 is subtracted from [tex]b[/tex].
Find the slope and Y-Intercept of the line. 6X plus 2Y equals -88
Answer:
That’s ez pz
Step-by-step explanation:
Answer:
The slope is -3 and the y intercept is -44
Step-by-step explanation:
6X+ 2Y= -88
The slope intercept form of a line is y= mx+b where m is the slope and b is the y intercept
Solve for y
6X-6x+ 2Y= -88-6x
2y = -6x-88
Divide by 2
y = -3x -44
The slope is -3 and the y intercept is -44
The winning times (in seconds) in a speed-skating event for men can be represented by the formula T = 46.97 - 0.099x, where x represents the year, with x = 0 corresponding to 1920. (For example in 1992, x would be 1992 - 1920 = 72.) According to the formula, what was the winning time in 1997? Round to the nearest hundredth. * 1 point 40.34 sec 39.35 sec 3609.07 sec 41.33 sec
Answer:
39.35 sec
Step-by-step explanation:
Given that:
The winning time is represented by the function:
T = 46.97 - 0.099x
Where x = year ; x = 0 corresponding to 1920
According to the formula, what was the winning time in 1997?
first find the value of x;
x = 1997 - 1920 = 77 years
Nowing plugging the value of x in the function :
T = 46.97 - 0.099(77)
T = 46.97 - 7.623
T = 39.347 seconds
T = 39.35 s
a red sea urchin grown its entire life, which can last 200 years. An urchin at age 30 has a diameter of 11.9 cm, while an urchin at age 110 has a diameter of 15.5 cm What is the average rate of change over this given period
A = (15.5 - 11.9) / (110 - 30) = 3.6 / 80 = 0.045
Average rate of change = 0.045 cm
The average rate of change of sea urchin's diameter with respect to its age is 0.0045 cm/yr.
What is Derivative in mathematics?
Derivative in mathematics represent the rate of change of a function with respect to a variable.
Given is a red sea urchin such that at age 30, the urchin has a diameter of 11.9 cm whereas urchin at age 110 has a diameter of 15.5 cm.
From the question we can write -
Initial age = A[1] = 30
Initial diameter = D[1] = 11.9 cm
Final Age = A[2] = 110
Final diameter = D[2] = 15.5 cm
Average rate [r] = D[2] - D[1] / A[2] - A[1]
r = D[2] - D[1] / A[2] - A[1]
r = 15.5 - 11.9/110 - 30
r = 3.6/80
r = 0.045
Therefore, the average rate of change of sea urchin's diameter with respect to its age is 0.0045 cm/yr.
To solve more questions on rate measurements, visit the link below-
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URGENT PLS HELP ASAP! THANK YOU :)
Answer:
box 1 and box2 are correct.
The surface area, A, of a cylinder of radius, r, and height, h, can be found with the equation above. Which of the following correctly shows the cylinder's height in terms of its radius and surface area?
Step-by-step explanation:
If r and h are the radius and height of the cylinder, then its surface area A is given by :
[tex]A=2\pi r^2+2\pi rh[/tex] ....(1)
We need to find the cylinder's height in terms of its radius and surface area. Subtracting [tex]2\pi rh[/tex] on both sides, we get :
[tex]A-2\pi r^2=2\pi rh+2\pi r^2-2\pi r^2\\\\A-2\pi r^2=2\pi rh[/tex]
Dividing both sides by [tex]2\pi r[/tex]. So,
[tex]\dfrac{A-2\pi r^2}{2\pi r}=\dfrac{2\pi rh}{2\pi r}\\\\h=\dfrac{A-2\pi r^2}{2\pi r}[/tex]
Hence, this is the required solution.
Find the values of θ in the range 0≤θ≤360° which satisfy: 2 sin^2 θ - sinθ -1= 0
Answer:
Step-by-step explanation:
Solving trig equations are just like solving "regular" equations. Let's get to it. First and foremost we are going to make a "u" substitution. You'll use that all the time in calculus, if you choose to go that route. Let
[tex]sin^2 \theta=u^2[/tex] and sinθ = u. Making the substitution, the equation becomes:
[tex]2u^2-u-1=0[/tex]
That looks like something that can be factored, right? If you throw it into the quadratic formula you get the factors:
(u - 1)(2u + 1) = 0
By the Zero Product Property, either u - 1 = 0 or 2u + 1 = 0, so we will solve those, but not until after we back-substitute!
Putting sinθ back in for u:
sinθ - 1 = 0 so
sinθ = 1 and in the other equation:
2sinθ + 1 = 0 so
2sinθ = -1 and
[tex]sin\theta=-\frac{1}{2}[/tex]
Get out the unit circle and look to where the sinθ has a value of 1. There's only one place in your interval, and it's at 90 degrees.
Now look to where the sinθ has a value of -1/2. There are 2 places within your interval, and those are at 210° and 330°. Now you're done!
Suppose
f
(
x
)
=
2
x
2
+
4
x
−
10
. Compute the following:
Answer:-80
Step-by-step explanation:f(x)=2*2+4*-10
Rejoice bought 600 oranges at 5 for GH¢3.00 to be sold at the market. On her arrival 5% of the oranges got rotten and she sold the rest at one for GH¢1.00...
I) How any oranges did she finally sell?
ii) Find her loss or profit percent.
Answer:
She finally sold 570 oranges
Profit %= 58.33%
Step-by-step explanation:
Quantity bought=600
Price=5 for GH¢3.00
Total cost price=600/5 * GH¢3.00
=120*GH¢3.00
=GH¢360.00
5% of 600 oranges got rotten
=5/100*600
=30 Oranges were rotten
I) How any oranges did she finally sell?
She finally sold
Sold oranges= Total oranges - Rotten oranges
=600-30
=570 oranges
Selling price=GH¢1.00 * 570 oranges
=GH¢570.00
ii) Find her loss or profit percent
Profit or loss percent= Selling price - cost price / cost price * 100
% profit or loss=S.P - C.P / C.P * 100
=GH¢570.00 - GH¢360.00 / GH¢360.00 * 100
=GH¢210.00/GH¢360.00 *100
=0.5833 * 100
=58.33% profit
plz help ASAP! thank u
Answer: Choice B)
The relation is a function because there are no vertical lines that can be drawn on the graph that pass through more than one point.
This graph passes the vertical line test. Any input (x) leads to one and only one output (y). An example of a graph failing the vertical line test would be a graph that is a sideways parabola.
i need help please :(
Answer:
-(1/3 · 1/3 · 1/3 · 1/3 )
Step-by-step explanation:
-(3)^-4= -1/3 ^4 = -1/81
-(1/3 · 1/3 · 1/3 · 1/3 )= -1/81
Answer:
Answer:
[tex] = - ( \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} )[/tex]
Step-by-step explanation:
[tex] - {(3)}^{ - 4} = \\ - ( { 3}^{ - 4} )= \\ - (\frac{1}{ {3}^{4} } )[/tex][tex] = - ( \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} )[/tex][tex] = - \frac{1}{81} [/tex]
The area of a trapezium is 105cm² and its height is 7 cm. If one of the parallel sides is longer than the other by 6cm, find the lengths of two parallel sides.
Answer:
Step-by-step explanation:
What is difference between internal and external trade
Answer:
Trade which takes place inside a country is known as internal trade. If trade takes place with other countries of the world, it is known as external trade.
Step-by-step explanation:
Answer:Internal refers to trade within the country itself while
External refers to trade with other countries whether foreign or bordering countries
Step-by-step explanation:
''Internal'' trade-Trade within the locals of the country itself
''External'' trade-refers to ;outside of the country...trade with other countries
In ΔABC, and m∠ABC = 90°. D and E are the midpoints of and , respectively. If the length of is 9 units, the length of is units and m∠CAB is °.
Applying the midsegment theorem and the definition of isosceles triangle:
DE = 4.5 units
m∠CAB = 45°
The image that shows ΔABC is attached below.
Since AB = BC, therefore, ΔABC is an isosceles triangle.
This implies that, the base angles will be equal.
Thus:
If m∠ABC = 90°, therefore,
m∠CAB = ½(180 - 90)
m∠CAB = 45°.
DE is the midsegment of the triangle, and is parallel to the third side, CA = 9 units.
Based on the midsegment theorem, we have the following equation:
DE = ½(9)
DE = 4.5 units.
Therefore, applying the midsegment theorem and the definition of isosceles triangle:
DE = 4.5 units
m∠CAB = 45°
Learn more about midsegment theorem on:
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Answer:
4.5
45
Step-by-step explanation:
line passing through points (-4,2) and (0,3)
Answer:
y-y1=m(x-x1)
or,y-2=1/4(x+4)
or,4y-8=x+4
or,x-4y+12=0 is the required equation.
Step-by-step explanation:
If it helps you, plz mark it as brainliest
Caculate the value of x on the figure below
Answer:
x = 58
Step-by-step explanation:
The angle at the centre is twice the angle at the circumference subtended by the same arc, thus
x + 62 = 2(x + 2)
x + 62 = 2x + 4 ( subtract x from both sides )
62 = x + 4 ( subtract 4 from both sides )
58 = x
i'm doing domain and range, and I'm kinda having a hard time with this... can someone help?
Answer:
Domain : any real number
Range : y ≥0
Step-by-step explanation:
The domain is the values that x can be
X can be any real number
The range is the values the y can be
Y can be zero or any positive value since y = x^2
Domain : any real number
Range : y ≥0
Answer:
[tex]\boxed{\sf Option \ A}[/tex]
Step-by-step explanation:
[tex]y=x^2[/tex]
[tex]\sf The \ domain \ of \ a \ function \ is \ all \ possible \ values \ for \ x.[/tex]
[tex]\sf There \ are \ no \ restrictions \ on \ the \ value \ of \ x.[/tex]
[tex]\sf The \ domain \ is \ all \ real \ numbers.[/tex]
[tex]\sf The \ range \ of \ a \ function \ is \ all \ possible \ values \ for \ y.[/tex]
[tex]\sf When \ a \ number \ is \ squared \ the \ result \ is \ always \ greater \ than \ or \ equal \ to \ 0.[/tex]
[tex]\sf The \ range \ is \ \{y:y\geq 0\}[/tex]
1. Find the slope of a line passing through points (0,0) and (4,5)
o 4/5
5/4
4/9
5/9
Option 5
Answer:
slope = [tex]\frac{5}{4}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (4, 5)
m = [tex]\frac{5-0}{4-0}[/tex] = [tex]\frac{5}{4}[/tex]
Answer:
The answer is 5/4Step-by-step explanation:
Slope of a line is given by
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]where
m is the slope and
( x1 , y1) and (x2 , y2) are the points of the line
Slope of the line between the points
(0,0) and (4,5) is
[tex]m = \frac{5 - 0}{4 - 0} = \frac{5}{4} [/tex]Hope this helps you
Find the length of the arc. A. 187π/12 ft B. 16π/3 ft C. 49π/6 ft D. 343π/12 ft
Answer:
[tex]\huge \boxed{\mathrm{Option \ C}}[/tex]
Step-by-step explanation:
Length of arc formula = θ/360 × 2[tex]\pi[/tex]r
The angle is 210 degrees.
The radius is 7 ft.
210/360 × 2[tex]\pi[/tex](7)
Simplify the expression.
210/360 × 14[tex]\pi[/tex]
2940/360[tex]\pi[/tex]
49/6[tex]\pi[/tex]
The length of the arc of circle having radius 7 feet is 49π/6 which is option C.
What is arc?An arc is a part of circumference of a circle which is formed from two radius of the circle. The length of arc is equal to Θr in which r is radius and Θ is angle in radian form.
How to find length of arc?We have been given the radius of the circle be 7 feet and angle be 210°.
The length of arc will be Θr in which r is the radius and Θ is the angle in radian form.
First we have to convert angle in radian form=210*π/180=7π/6.
Length of arc=7π/6*7
=49π/6
Hence the length of the arc of circle having radius 7 feet is 49π/6 which is option C.
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Find the GFC of 20 and 16
Find the slope and y-intercept of the line. y = x – 8
Answer:
y- intercept= -8
slope= 1
Step-by-step explanation:
Looking at the question, the y- intercept is always the number were the line on the graph passes over on the y- axis. The slope is always the number with x in front of it.
Answer:
Y-intercept = -8
Slope = 1
Step-by-step explanation:
The Y-intercept is the constant or the integer in the equation.
So, the y-intercept is "-8".
The slope is the number with which "x" is multiplied with.
So, the slope is 1, because 'x' and '1x' are similar; therefore the slope is 1.
The tee for the sixth hole on a golf course is 400 yards from the tee. On that hole, Marsha hooked her ball to the left, as sketched below. Find the distance between Marsha’s ball and the hole to the nearest tenth of a yard.
Answer:
181.8yd
Step-by-step explanation:
