Answer:
All you have to do is use the Triangle Inequality Theorem, which states that the sum of two side lengths of a triangle is always greater than the third side. If this is true for all three combinations of added side lengths, then you will have a triangle.
Step-by-step explanation:
3) The triangles shown are congruent using ASA, but they arb not marked completely. Mark the corresponding parts in this drawing that must be congruent in order to apply the ASA. Then write the congruence statement in the spaces provided. (2 pts) CAB FDE ____=____
Answer:
angle A = Angle E
ΔCAB ≅ΔFED
Step-by-step explanation:
ASA means Angle side Angle Where the side is between the two angles
We have an angle C= F and a side AC = EF
We need angle A = Angle E
ΔCAB ≅ΔFED
Find two numbers whose difference is 10 and whose product is a minimum.
Answer:
Answer: {-5, 5}. Product is -25, which is the minimum.
Step-by-step explanation:
let a, b denote the two numbers. We know that b-a=10.
We are looking for a minimum over the product a*b.
One can minimize this using derivatives. In case you have not yet had derivatives, you can also use the vertex of a parabola (since the above is a quadratic form):
The minimum is at the vertex a=-5 and so b=5
Their distance is 10, and their product attains the minimum value of all possiblities -25.
Answer:
Step-by-step explanation:
let the numbers be x and y,let y>x
y-x=10
y=x+10
product P=xy=x(x+10)=x²+10x
[tex]\frac{dP}{dx} =2x+10\\\frac{dP}{dx} =0,gives\\2x+10=0\\2x=-10\\x=-5\\\frac{d^2P}{dx^2} =2>0 ~at~x=-5\\[/tex]
∴P is minimum at x=-5
y=x+10=-5+10=5
numbers are -5,5
Mark is receiving a pay rise of 7%. He currently earns £15,000. How much will Mark earn after his pay rise?
Answer:
£16,050
Step-by-step explanation:
Mark's current pay is £15,000.
His pay raise is 0.07(£15,000), or £1,050
His new pay is the sum of these two results: £15,000 + £1,050 = £16,050
A ratio is equal to 3:8 if the antecedent is 21 find the consequent
Answer:
56
Step-by-step explanation:
To find the "consequent," write out and solve an equation of ratios:
3 x
------- = ------
8 21
Through cross-multiplication, this yields 8x = 63, so that x must be x = 63/8.
Alternatively, solve this modified version of the original equation for x:
3 21
------- = ------
8 x
Then 3x = 8(21), or x = 8(7), or x = 56.
Note that 21 and 56 are in the ratio 3:8
SOMEONE PLEASE HELP ME WITH THIS QUESTION. A circle has a circumference of 36.
What is the area of the circle? Take the pi to be 3.142. State the answer to the nearest whole
number.
Answer:
The correct answer is - 103.13
Step-by-step explanation:
Given:
Circumference (C) = 36
Area =?
Formula:
Formula of area
A=πr2
formula of circumference
C=2πr
Solution:
C= 36 given so
36 = 2*3.142*r (r is radius)
r = 36/6.284
= 5.729
Putting the value of r in the formula of Solving for Area
A = 3.142*(5.729)^2
= 3.142*32,821
= 103.1124 or 102.3
What is the definition of exponential growth?
Any help out there
Answer:
Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change of a quantity with respect to time is proportional to the quantity itself.
Answer:
The answer is probably B. If not it might be C.
Step-by-step explanation:
Exponential growth is growth that becomes more and more rapid. I hope this helps :).
Suppose that the 100 people in society C all know the same 10 facts, while the 10 people in society D specialize, with each person knowing 5 unique facts as well as 5 facts also known by the other 9 members of the society. If the standard of living is roughly equivalent to the average number of social facts known per person, how many times better is the standard of living in society D
Answer:
29 times
Step-by-step explanation:
Given :
Society C ;
Population = 100
Number of facts known = 10
Average fact known per person = known fact / population = 10 / 100 = 0.1
Society D:
Population = 19
Common fact = 5
Specialized fact = 5 * 10 = 50
Total facts = 55
Average fact known per person = 55 / 19 = 2.8947368 fact per person
Number of times society D is better :
2.8947368 / 0.1 = 28.947 times
Approximately 29 times
Suppose your mother can clean your kitchen in 30 minutes. You can clean the kitchen in 45 minutes. How long will it take you and your mother to clean the kitchen working together? (write equation and show work to solve)
Answer:
it will take 18 min
Step-by-step explanation:
1/45+1/30=2/90+4/90=5/90=90 divided by 5 is 18
Simplify cot x - cos to the power 3 x csc x
Complete the table for the given rule. Rule: y = x + 3
Answer:
Step-by-step explanation:
since there is no table included with the question I'm concluding that you need to find values of y using values of x, simply substitute the x values in the equation and you'll get the y value like this
if x = 1 y = 4
Answer:
x - 0 1 2 3 4 5
y - 3 4 5 6 7 8
It is very simple, all you have to do is add three to x every time, for example if x is 153, y will be 156. 3 should be the beginning, the y intercept in graphs, and the beginning means x should be 0.
In a city, the distance between the library and the police station is 3 miles less than twice the distance between the police station and the fire station. The distance between the library and the police station is 5 miles. How far apart are the police station and the fire station?
Answer:
4 miles apart. the answer this question.
a+b+c=68
a-b=5
b:c=3
-------------------
a,b,c=?
-------------------
Answer:
a = 32
b= 27
c = 9
Step-by-step explanation:
a= 5+ b from the second equation
c= b/3 from the third equation
substitute the above equations to the first equation then solve for b your answer will be 27
substitute the value of b in the second equation you will solve for a
perform the same substitution to the third equation you will get the answer for c
Step-by-step explanation:
a-b=5<=>a=5+b (1)
b:c=3<=>b=3c (2)
a+b+c=68<=>5+b+3c+c=68<=>5+3c+3c+c=68
<=>7c=63<=>c=9
Fill in (2), we have b=3c=3.9=27
and in (1), we have a=5+b=5+27=32
So, a=32, b=27, c=9
Hhhheeeelllllpppppppp
Answer:
35square meters
Step-by-step explanation:
5×7=35
What is the answer to this
umm I don't know hehe oops
Answer:
Length of old board = 68.2cm
Step-by-step explanation:
Let old board length be x
Given new board is 120 % longer than old board = x + 120% of x
Length of new board = 150cm
Therefore,
x + 120% of x = 150
[tex]x + \frac{120}{100} x = 150\\\\x + 1.20x = 150\\\\2.2x = 150 \\\\x = 68.18 = 68.2cm[/tex]
Find the sum of the first seven prime numbers that have a units digit of 7.
Answer:
7, 17, 37, 47, 73, 79, 97
Step-by-step explanation:
they have 7's as one of their digits
If a computer prints 225 lines in 3 seconds how many lines can it print per minute
Answer:
225 lines * 60 seconds = 13500 lines = 4500 lines
3 Seconds 1 minute 3 minutes 1 minute
Step-by-step explanation:
Please help!!!!!!!!!!!!
What must be a factor of the polynomial function f(x) graphed on the coordinate plane below?
==========================================================
Explanation:
The x intercepts (aka roots) are where the graph crosses or touches the x axis. These locations directly correspond to help set up the factors.
The root x = -6 shows that x+6 is a factor.
Effectively, we add 6 to both sides so that we go from x = -6 to x+6 = 0.
There were 24 1/4 crates of tomatoes in the barn but 7 3/5 crates of tomatoes were rotten and had to be thrown out. Joe sold 8 1/3 crates and canned 7 5/6 crates of tomatoes. How many crates of tomatoes were left?
Answer:
29/60 of the crates are left behind.
Step-by-step explanation:
Total number of crates = 24 1/4= 97/4
Rotten tomatoes crates = 7 3/5= 38/5
Joe sold crates = 8 1/3= 25/8
Canned crates of tomatoes =7 5/6= 47/6
Therefore
24 1/4 - 7 3/5 - 8 1/3 - 7 5/6
= 97/4-38/5-25/3-47/6
= (97*5-38*4)/20 - (25*2+47)/6
= 485-152/20 - 97/6
= 333/20-97/6
= 333*3-97*10/60
=999-970/60
=29/60
29/60 of the crates are left behind.
This question is solved in 2 steps.
First the LCM of fraction 1 and 2 is taken separately from the LCM of fraction 3 and 4 for simplification purposes.
Then again the LCM is taken for the answers obtained from fraction 1&2 and fraction 3& 4.
Can some please help me? ~ASAP~
Answer:
B 12 ^ 1/2 x^ 3/2
Step-by-step explanation:
sqrt( 12x^3)
Rewriting the square root as a fractional power
12 ^ 1/2 x^3^1/2
We know that a^b^c = a^ (b*c)
12 ^ 1/2 x^ 3/2
Answer:
B. 12^1/2 x^3/2
Step-by-step explanation:
For example, x^3/2 is equivalent to √x³. The numerator of the exponent represents that number's exponent and the denominator represents the number root.
what is the corrct answer
help please!!!!!!!!!!!!!!!
Answer:
C
Step-by-step explanation:
.........................
reverse percentage problem
answer: you're missing the problem
helppppopoop help help help
Answer:
160
Step-by-step explanation:
Hope this helps
Answer:
Step-by-step explanation:
VOLUME...
1) π*r^2*h
π*(2.5)^2 *h
(π)*(2.5)^2* 6
= 117.8
2) π*r^2*h + 1/2 *[(4/3) · π · r3]
(π)*(3)^2* 3 + 1/2 *[(4/3) · π · 3^3]
84.8+ 56.5 = 141.41
3) (1/3) π*r^2*h
(1/3) π*3^2*h
3^2 + h^2 = 36
h = sqrt(27) = 5.1
(1/3) π*3^2*5.1
= 48.06
Answer please thanks. Brainliest
Answer:
its the 3rd answer
Step-by-step explanation:
Answer:
t-h=negative
Step-by-step explanation:
Use the Pythagorean Theorem (a? + b2 = (?) to find the missing side length. Round to the nearest tenth.
Answer: 3.9 (choice A)
==============================================
Work Shown:
a = 1b = unknownc = 4Apply the pythagorean theorem to get
a^2+b^2 = c^2
1^2+b^2 = 4^2
1+b^2 = 16
b^2 = 16-1
b^2 = 15
b = sqrt(15)
b = 3.87298
b = 3.9
Select the correct answer. Which expression is equivalent to 8x^2^3 sqrt 375x + 2^3 sqrt 3x^7, if x=0?
Answer:
[tex](8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7} =28x^3\sqrt{3x}[/tex]
Step-by-step explanation:
The question is poorly formatted. The original question is:
[tex](8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7[/tex]
We have:
[tex](8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7[/tex]
Open bracket
[tex](8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7} =(8^ \frac{2}{3} *x^{3* \frac{2}{3}}) \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}[/tex]
[tex](8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7} =(8^ \frac{2}{3} *x^2) \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}[/tex]
Express 8 as 2^3
[tex](8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7} =(2^{3* \frac{2}{3}} *x^2) \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}[/tex]
[tex](8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7} =(2^2 *x^2) \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}[/tex]
[tex](8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7} =4x^2 \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}[/tex]
Express 2^3 as 8
[tex](8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}=4x^2 \sqrt{75x^3} + 8\sqrt{ 3x^7}[/tex]
Expand each exponent
[tex](8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}=4x^2 \sqrt{25x^2 *3x} + 8\sqrt{ 3x * x^6}[/tex]
Split
[tex](8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}=4x^2 \sqrt{25x^2} *\sqrt{3x} + 8\sqrt{3x} * \sqrt{x^6}[/tex]
[tex](8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7} =4x^2 *5x *\sqrt{3x} + 8\sqrt{3x} * x^3[/tex]
[tex](8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7} =20x^3\sqrt{3x} + 8x^3\sqrt{3x}[/tex]
Factorize
[tex](8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7} =28x^3\sqrt{3x}[/tex]
Answer:
42x^2 ^3 square root 3x
Step-by-step explanation:
i got it right
PLEASE HELP its urgent! If answer is right I'll mark as brainliest:)
The force, F (Newtons), between two objects is inversely proportional to the square of the distance, d (metres), between them.
The force is 0.006 Newtons when the distance between the objects is 3 metres.
Work out d (rounded to 2 DP) when F=0.035 Newtons.
Answer:
1.24 m
Step-by-step explanation:
F ∝ 1/d²
F = k/d²
Use values given to solve for k
0.006 = k/3²
k = 0.054 (I multiplied both sides by 3² in the equation above)
New equation is F= 0.054/d²
Plug in your numbers so 0.035 = 0.054/d²
0.054/0.035 = d²
You can simplify if you want so d² = 54/35
Square root both sides to solve for d
√54/35 = 1.24 m
Question 2 of 10
If you apply the changes below to the quadratic parent function, f(x) = x2,
what is the equation of the new function?
• Shift 1 unit left.
• Vertically stretch by a factor of 3.
• Reflect over the x-axis.
A. g(x) = -3(x-1)2
B. g(x) = -3(x + 1)2
C. g(x) = (-3x+1)
D. g(x) = -3x2 - 1
Given:
The parent function is:
[tex]f(x)=x^2[/tex]
This function shift 1 unit left, vertically stretch by a factor of 3 and reflected over the x-axis.
To find:
The function after the given transformations.
Step-by-step explanation:
The transformation is defined as
[tex]g(x)=kf(x+a)+b[/tex] ... (i)
Where, k is stretch factor, a is horizontal shift and b is vertical shift.
If k<0, then the graph of f(x) is reflected over the x-axis.
If 0<|k|<1, then the graph compressed vertically by factor |k| and if |k|>1, then the graph stretch vertically by factor |k|.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
It is given that the graph of f(x) shifts 1 unit left, so a=1.
The graph of f(x) vertically stretch by a factor of 3, so |k|=3.
The graph of f(x) reflected over the x-axis, so k=-3.
There is no vertical shift, so b=0.
Putting [tex]a=1,k=-3,b=0[/tex] in (i), we get
[tex]g(x)=-3f(x+1)+0[/tex]
[tex]g(x)=-3f(x+1)[/tex]
[tex]g(x)=-3(x+1)^2[/tex] [tex][\because f(x)=x^2][/tex]
Therefore, the correct option is B.
Which represents the solution(s) of the system of equations, y = x2 – 2x – 15 and y = 8x - 40? Determine the solution set algebraically. O (-5, -80) (5,0) O (5,0) and (-5, -80) O no solutions
Answer:
(5, 0)
Step-by-step explanation:
Se the equations equal
x² - 2x - 15 = 8x - 40
Subtract 8x from both sides
x² - 10x - 15 = -40
add 40 to both sides
x² - 10x + 25 = 0
Factor
(x - 5)(x - 5) = 0
x = 5
---------------
plug in x = 5 into
y = 8x - 40
y = 8(5)- 40
y = 0
-----------------
Solution
(5, 0)