Answer:
(4x2 +5)⋅(4x2 −5)
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:
https://brainly.com/question/7423948
Answer:
4.5
45
Step-by-step explanation:
AB = 3.2 cm
BC= 8.4 cm
The area of triangle ABC is 10 cm²
Calculate the perimeter of triangle ABC.
Give your answer correct to three significant figures.
Answer:
Therefore, perimeter of the given triangle is 18.300 cm.
Step-by-step explanation:
Area of the triangle ABC = [tex]\frac{1}{2}(\text{AB})(\text{BC})(\text{SinB})[/tex]
10 = [tex]\frac{1}{2}(3.2)(8.4)(\text{SinB})[/tex]
Sin(B) = [tex]\frac{10}{3.2\times 4.2}[/tex]
B = [tex]\text{Sin}^{-1}(0.74405)[/tex]
B = 48.08°
By applying Cosine rule in the given triangle,
(AC)² = (AB)² + (BC)²-2(AB)(BC)CosB
(AC)² = (3.2)² + (8.4)² - 2(3.2)(8.4)Cos(48.08)°
(AC)² = 10.24 + 70.56 - 35.9166
(AC)² = 44.88
AC = [tex]\sqrt{44.8833}[/tex]
AC = 6.6995 cm
Perimeter of the ΔABC = m(AB) + m(BC) + m(AC)
= 3.200 + 8.400 + 6.6995
= 18.2995
≈ 18.300 cm
Therefore, perimeter of the given triangle is 18.300 cm
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.
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:
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
what is the range and domian of y=(x-4)
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
If 3sinA+4cosA=5 then find the value of cosA
Answer:
Cos A =1.4
Step-by-step explanation:
3sinA=5-4cosA; square both sides: 9sin^2(A)=25-40cosA+16cos^2(A);
9-9cos^2(A)=25-40cosA+16cos^2(A); 25cos^2(A)-40cosA+16=0=(5cosA-4)^2.
cosA=4/5 so sinA=3/5 (√(1-16/25) and sinA+cosA=7/5=1.4.
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
Can someone tell me if this is correct? I said neither is correct.
Answer:
Neither is correct
Answer:
You are right.
Step-by-step explanation:
Neither transformation gives the triangle FGE.
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
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:
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 finite geometric series is the sum of a sequence of numbers. Take the sequence 1, 2, 4, 8, … , for example. Notice that each number is twice the value of the previous number. So, a number in the sequence can be represented by the function f(n) = 2n–1. One way to write the sum of the sequence through the 5th number in the sequence is ∑5n-12n-1. This equation can also be written as S5 = 20 + 21 + 22 + 23 + 24. If we multiply this equation by 2, the equation becomes 2(S5) = 21 + 22 + 23 + 24 + 25. What happens if you subtract the two equations and solve for S5? Can you use this information to come up with a way to find any geometric series Sn in the form ∑an-1bn-1?
hope this helps you alot
Solve (s)(-3st)(-1/3)
Answer:
Step-by-step explanation
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]
Find the GFC of 20 and 16
Determine the slope of a line which contains the points (2, 4) and (-6, 9). Write your answer in simplest form.
Answer:
-5/8
Step-by-step explanation:
(2,4) (-6.9)
m= y2-y1/x2-x1
= 9-4/-6-2
=5/-8
=-5/8
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.
URGENT PLS HELP ASAP! THANK YOU :)
Answer:
box 1 and box2 are correct.
Which ppint is the center of the circle?
O point w
O point X
O point Y
O point z
Answer:
??????????????????????????????????????????????????????????????
Step-by-step explanation:
Answer:
where is Point or picture
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
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].
Solve for a. Worth 10 pts!
[tex] \frac{1}{5} a - 5 = 20[/tex]
Answer:
Step-by-step explanation:
1/5 a-5=20 addition properties
1/5 a -5+5=20+5
1/5=25 multiply both sides by 5
5/5 a=25*5
a=125
check the answer:
125/5 -5=20
25-5=20
20=20 correct
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.
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
Please answer answer question
Answer:
The correct answer is
Step-by-step explanation:
11 square centimeters.
Hope this helps....
Have a nice day!!!!
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-
https://brainly.com/question/11965077
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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:
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