Solve the problems below. Please answer with completely simplified exact value(s) or expression(s).
a)
In ΔABC, AC = BC, CD⊥AB with D∈AB, AB = 4 in, and CD = 3 in. Find AC.
b)
Given: ΔABC, AB = BC = AC = a. Find: The area of ΔABC
Answers
Answer:
a) AC = [tex]\sqrt{13}[/tex]
b) Area = [tex]\frac{\sqrt 3}{4}[/tex] × [tex]a^{2}[/tex]
Step-by-step explanation:
a) From question,
AC = BC, CD⊥AB
Now in ΔCAD and ΔCBD
AC=BC, ∠A = ∠B and AD=BD (because in isosceles triangle perpendicular bisects the side).
then, from SAS potulates
ΔCAD≅ΔCBD
So,
AD = [tex]\frac{AB}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2 in
From Pythagorean theorem in ΔADC
[tex]AC^{2}[/tex] = [tex]AD^{2}[/tex] + [tex]CD^{2}[/tex]
[tex]AC^{2}[/tex] = [tex]2^{2}[/tex] + [tex]3^{2}[/tex]
[tex]AC^{2}[/tex] = 4 + 9 = 13
AC = [tex]\sqrt{13}[/tex]
b) In given ΔABC,
AB = BC = AC = a, means ΔABC is a equilateral triangle.
So, area of equilateral triangle is
Area = [tex]\frac{\sqrt 3}{4}[/tex] × [tex]side^{2}[/tex]
side = a
then,
Area = [tex]\frac{\sqrt 3}{4}[/tex] × [tex]a^{2}[/tex]
Answer:
a) √7
Step-by-step explanation:
Related Questions
In a group of 25 students, 12 students play basketball, 11 students play football. Five students play both sports. A student is chosen randomly from this group.
What is the probability that the student plays both basketball or football?
Answers
Answer:
2/25 chance for both.
Step-by-step explanation:
There is a total of 25 students = 25 as my denominator.
11 + 12 = 23.
25 -23 = 2
Therefore my numerator is 2.
----> 2/25
what expression represents a number one fourth as great as 10-2
Answers
Answer:
The expression represents
[tex]a\geq\frac{1}{4}\times (10^{-2})[/tex] and solution is [tex]a \geq 0.0025[/tex]
Step-by-step explanation:
Given : Expression represents a number one fourth as great as [tex]10^{-2}[/tex]
To find : What is the expression?
Solution :
Let the number be 'a'.
According to question,
A number one fourth as great as [tex]10^{-2}[/tex]
i.e. [tex]a\geq \frac{1}{4}\times (10^{-2})[/tex]
Now, we solve the expression
[tex]a \geq \frac{1}{4}\times\frac{1}{100}[/tex]
[tex]a \geq\frac{1}{400}[/tex]
[tex]a \geq 0.0025[/tex]
Therefore, The expression represents
[tex]a\geq\frac{1}{4}\times (10^{-2})[/tex] and solution is [tex]a \geq 0.0025[/tex]
I will give a thanks and a 5star is you answer ASAP
Answers
Answer: -2,0,2,4,6
The solution of the inequality is x<1
Step-by-step explanation:
Answer:
x < 1
Step-by-step explanation:
2x < 2
Divide 2 on both sides
x < 1
------------------------------------------------------------------------
Table: (I think)
-2 , 0 , 2 , 4 , 6
Which inequality matches the graph?
A) x > -2
B) x < -2
C) x = -2
D) x ≤ -2
Answers
Answer:
D) x ≤ -2
Step-by-step explanation:
The dot is at -2 = -2
the dot is filled in = ≤ or ≥ because its means equal too
think of ≤ or ≥ like arrows = it points left.
so its x ≤ -2
Note on using the ≤ or ≥ like pointing arrows
this only works if its written:
variable < constant form,
which is the way they are usually seen, like x < 5
but it could be 5 > x which means the > points the opposite way
Hello! :)
Answer:
D. x≤-2
*The answer must have a negative sign and less than or equal to.*
Step-by-step explanation:
Lesson: It's about the graphing inequalities
An inequality is a statement that compares mathematical expressions that are not equal. The expressions are separated by an inequality symbol (<,>, ≤, ≥, or ≠).
The arrow points to the left. The circle is closed.
Hope this helps!
Have a nice day! :)
:D
-Charlie
Thanks!
if 4x+41=3x+45, what is the value for x
Answers
Answer:
x = 4
Step-by-step explanation:
4x+41=3x+45
Subtract 3x from both sides
x + 41 = 45
Subtract 41 from both sides
x = 4
On a trip, a family drove an average of 250 mi each day. If the family drove a total of 3,000 mi on their trip, how many days were they gone?
Answers
Answer: The answer is 12 days
Step-by-step explanation: miles total=miles per day times number of days
3000=250 times days
divide both sides by 250
12=days
at the amusement park each student is given $16 for food this covers the cost of two meals plus $4 for snacks how much money does the school expect the students to spend per meal. which equation could be used to represent this dituation
Answers
This would give you $6, so that is how much they expect you to spend per meal.
3/4( 1/6 x+16)= 3/7 (4 3/8 x−21)
Answers
Answer:
x=12
Step-by-step explanation:
Solve for x:
(3 (x/6 + 16))/4 = (3 ((4 + 3/8) x - 21))/7
Put 4 + 3/8 over the common denominator 8. 4 + 3/8 = (8×4)/8 + 3/8:
(3 (x/6 + 16))/4 = (3 ((8×4)/8 + 3/8 x - 21))/7
8×4 = 32:
(3 (x/6 + 16))/4 = (3 ((32/8 + 3/8) x - 21))/7
32/8 + 3/8 = (32 + 3)/8:
(3 (x/6 + 16))/4 = (3 ((32 + 3)/8 x - 21))/7
32 + 3 = 35:
(3 (x/6 + 16))/4 = (3 ((35 x)/8 - 21))/7
Put each term in x/6 + 16 over the common denominator 6: x/6 + 16 = x/6 + 96/6:
3/4 x/6 + 96/6 = (3 ((35 x)/8 - 21))/7
x/6 + 96/6 = (x + 96)/6:
3/4 (x + 96)/6 = (3 ((35 x)/8 - 21))/7
3/6 = 3/(3×2) = 1/2:
(x + 96)/(2×4) = (3 ((35 x)/8 - 21))/7
Put each term in (35 x)/8 - 21 over the common denominator 8: (35 x)/8 - 21 = (35 x)/8 - 168/8:
(x + 96)/(2×4) = 3/7 (35 x)/8 - 168/8
(35 x)/8 - 168/8 = (35 x - 168)/8:
(x + 96)/(2×4) = 3/7 (35 x - 168)/8
2×4 = 8:
(x + 96)/8 = (3 (35 x - 168))/(8×7)
8×7 = 56:
(x + 96)/8 = (3 (35 x - 168))/56
Multiply both sides by 56:
(56 (x + 96))/8 = (56×3 (35 x - 168))/56
56/8 = (8×7)/8 = 7:
7 (x + 96) = (56×3 (35 x - 168))/56
(56×3 (35 x - 168))/56 = 56/56×3 (35 x - 168) = 3 (35 x - 168):
7 (x + 96) = 3 (35 x - 168)
Expand out terms of the left hand side:
7 x + 672 = 3 (35 x - 168)
Expand out terms of the right hand side:
7 x + 672 = 105 x - 504
Subtract 105 x from both sides:
(7 x - 105 x) + 672 = (105 x - 105 x) - 504
7 x - 105 x = -98 x:
-98 x + 672 = (105 x - 105 x) - 504
105 x - 105 x = 0:
672 - 98 x = -504
Subtract 672 from both sides:
(672 - 672) - 98 x = -672 - 504
672 - 672 = 0:
-98 x = -672 - 504
-672 - 504 = -1176:
-98 x = -1176
Divide both sides of -98 x = -1176 by -98:
(-98 x)/(-98) = (-1176)/(-98)
(-98)/(-98) = 1:
x = (-1176)/(-98)
The gcd of -1176 and -98 is -98, so (-1176)/(-98) = (-98×12)/(-98×1) = (-98)/(-98)×12 = 12:
Answer: x = 12
0.7(3x−0.2)=0.3(0.8−2x)
URGENT
20 Points!
Please Help!!!
Answers
Answer:
x = .140741
Step-by-step explanation:
0.7(3x−0.2)=0.3(0.8−2x)
Distribute
.7 * 3x - .7*.2 = .3*.8 - .3 * 2x
2.1x - .14 = .24 - .6x
Add .6x to each side
2.1x +.6x -.14 = .24 -.6x+.6x
2.7x -.14 = .24
Add .14 to each side
2.7x -.14+.14 = .24+.14
2.7x = .38
Divide by 2.7 on each side
2.7x/2.7 = .38/2.7
x = .140741
PLEASE HURRY!
There is a geometric theorem that says "If twp lines in a plane are perpendicular to the same line, they are parallel to each other." Explain why this is true by writing and comparing equations for two different lines that are perpendicular to y= -1/3x.
Answers
Two lines perpendicular to a third line are parallel to each other because they both inherit the slope from their perpendicularity. The resulting lines only differ in their y-intercepts, indicating they run parallel.
Explanation:The theorem you're referring to essentially relates to the slope of the lines. If two lines are each perpendicular to the same line, this means the slope of all three lines are related. This occurs because the slope of any line perpendicular to y=-1/3x is 3, the negative reciprocal of -1/3. For example, if we have two lines L1: y = 3x + b1 and L2: y = 3x + b2 which are both perpendicular to y= -1/3x (and thus parallel to each other), their formulas would only differ by their y-intercepts (b1 and b2). Since the coefficient of x (the slope) remains the same (3), we can conclude that these two lines are indeed parallel to each other which confirms the mentioned geometric theorem.
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Which relation is a function?
Answers
Answer:
B
Step-by-step explanation:
For a relationship to be a function
Each value of x in the domain can only have 1 unique value of y in the range. That is, one-to-one correspondence.
The only relation which meets this criteria is B
Answer:
The answer is option B: {(1,3);(-1,5);(2,7);(-2,7);(3,5);(-3,3)}
Step-by-step explanation:
Each element is composed of a first and second point, or by an 'x' and 'y' coordinates, respectively. In this way, all x coordinate from the set of elements constitute the 'domain', and all y coordinates of the set of elements constitute the 'image'.
So, for a set of elements be a function, each point of the domain have to have one an only one image. In other words, two elements with the same image have to have a distinct x's coordinate.
If we take a look at the set of elements in the different options, we find different elements which repeat image:
1) The pairs (1,0) and (1,-1) in the set of point of option A
2) The pairs (-2,-1) and (-2,-2) in the set of point of option C
3) The pairs (1,3) and (1,3) in the set of point of option
In the set of elements of B option, all the elements with the same y coordinate have different x's coordinates.
Two boats sail away from a buoy making a 90 degree angle. The first boat is 165 meters away and is traveling at 25 m/s. The second boat has been traveling at 35 m/s for pi mINUTES. What is the rate of change in distance between the two boats?
Answers
Answer:
Step-by-step explanation:
lets say in the shown triangle x=165
so speed [tex]\frac{dx}{dt} =25[/tex]
and [tex]\frac{dy}{dt} =35[/tex]
Also since distance = speed* time
time = pi minutes = pi/60 seconds
y = [tex]\frac{35\pi \pi }{60}[/tex]
y = [tex]\frac{7\pi }{12}[/tex]
Now using the pythagorean :
[tex]x^2+y^2=z^2\\so \\165^2+(\frac{7\pi }{12} )^2 =z^2[/tex]
derivate the equation so we get :
[tex]x\frac{dx}{dt} +y\frac{dy}{dt} =z\frac{dz}{dt} \\[/tex][tex]165*25+35*\frac{7\pi }{12}=\sqrt{165^2+(\frac{7\pi }{12})^2} *\frac{dz}{dt}[/tex]
[tex]\frac{dz}{dt} =25.387[/tex] m/s
So Rate of change = 25.387 m/s
PLEASE HURRY
Use the frequency table. Find the probability that a person goes to the movies at least 2 times a month. Round to the nearest thousandth.
A 0.137 B 0.138 C 0.394 D 0.707
Answers
Answer:
0.707 to nearest thousandth
Step-by-step explanation:
People who go at least 2 times a month = 219 + 180 + 96
= 495
So the required probability = 495 / 700
= 0.707 14
leah has a collection of 36 baseball cards. She..
Answers
Answer:
She gave away 24 cards
Step-by-step explanation:
(36)*([tex]\frac{2}{3}[/tex])=24
Which equation correctly applies the distributive property?
a) −2.5⋅(4⋅3.67)=(−2.5⋅4)⋅3.67
b) (42⋅3.5)+(42⋅1.3)+(42⋅5.2)=42+(3.5+1.3+5.2)
c) −3⋅(6.48)=(−3⋅6)+(−3⋅0.4)+(−3⋅0.08)
d) 2.4⋅(−3.4)⋅(−1.25)=−3.4⋅2.4⋅(−1.25)
Answers
The distributive property: a(b + c) = ab + ac
Answer:c) -3 · (6.48) = -3 · (6 + 0.4 + 0.08) = (-3 · 6) + (-3 · 0.4) + (-3 · 0.08)Answer:
c) -3 · (6.48) = -3 · (6 + 0.4 + 0.08) = (-3 · 6) + (-3 · 0.4) + (-3 · 0.08)
Step-by-step explanation:
5|-6+r|=55
[tex]5 | - 6 + r| = 55[/tex]
Answers
Answer:
r= -5 , r= 17
Step-by-step explanation:
5|-6+r|=55
solve for 'r'
First we isolate absolute function
We divide both sides by 5
|-6+r| = 11
for absolute function we consider two cases, one with positive and one with negative. Now we make two equations
-6+r = 11 or -6+r = -11
Now solve both equations
-6 + r= 11
Add 6 on both sides
so , r= 17
-6 + r= -11
add 6 on both sides , so r= -5
9/10+7/100 WHAT DOES THE EQUAL
Answers
Answer:
97/100
Step-by-step explanation:
9/10 = 90/100
90/100 + 7/100 = 97/100
Please help please help
Answers
Answer:
D
Step-by-step explanation: 1/3 x 3 = 1/9 same with 2/3
Answer:
B is the one here as well
How do I show that x5-y5=(x-y)(x4+x3y+x2y2+xy3+y4)
Answers
The equation[tex]x^5 - y^5 = (x - y)(x^4 + x^3y + x^2y^2 + xy^3 + y^4)[/tex] is a representation of the Difference of Powers formula in algebra. This formula can be proven accurate by expanding the expression on the right hand side and simplifying.
Explanation:Your question essentially asks about the proof of a formula in algebra known as the Difference of Powers. This formula is applied when you have a difference of two terms, each raised to the same power.
Let us prove[tex]x^5 - y^5 = (x - y)(x^4 + x^3y + x^2y^2 + xy^3 + y^4):[/tex]
Expand the expression on the right-hand side: [tex](x - y)(x^4 + x^3y + x2y^2 + xy^3 + y^4).[/tex]You do this by distributing x to all the terms in the parenthesis and then y to all the terms in the parenthesis.When you simplify this expression, you will find that it equals to x5 - y5.
This demonstrates that the original formula you asked about is accurate.
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find the value of x in 2x+20=3x-8
Answers
Answer:
X=28
Step-by-step explanation:
3x-8=2x+20. So x=28
2x = 3x - 8 - 20 /subtract 3x from each side
2x - 3x = - 8 - 20 /combine like terms
-x = -28 /multiply by -1 to get rid of the minus
x = 28
a man pays 20% of his salary as tax and has 24,000$ left. How much did he pay as tax
Answers
Answer:
He paid $6,000 in taxes.
Step-by-step explanation:
His final amount after taxes is $24000. In order to obtain this number we had to tax 20% of the total (Note that 100%-20%=80%). In other words if he was taxed 20% he took home 80% of what he was paid. Therefore mathematically we have:
[tex]0.8A_{pre-tax}=A_{taxed}[/tex]
Since we know he was left with $24000 after taxes then:
[tex]0.8A_{pre-tax}=24000\\\\\frac{0.8A_{pre-tax}}{0.8}=\frac{24000}{0.8}\\\\A_{pre-tax}=\frac{24000}{0.8}\\\\A_{pre-tax}=30000[/tex]
So originally he had $30,000. So how much did he pay in taxes? We can calculate the difference of both pretax and after tax and we get:
$30,000 - $24,000= $6,000 taxed
A jacket costs $35 and has an 8 percent tax rate. Which expression will find the cost of the tax on the jacket
Answers
Answer:
Step-by-step explanation:
35 x .08 = $2.80
35 + 2.80 = 37.80
Answer:
T = 0.08 × 35
Step-by-step explanation:
The cost of a jacket = $35
The tax rate on the jacket = 8% = [tex]\frac{8}{100}[/tex]
= 0.08
The expression to find the cost of the tax on the jacket would be
T = 0.08 × 35
please help me with this question!!
Answers
Answer:
40
Step-by-step explanation:
5+1 3/8n=60
Subtract 5
1 3/8n=55
11/8n=55
8/11(55/1)
n=40
the expression 1.2p represents the total bill given to a pizza delivery man if he is given a tip of 20% and p represents the cost of the pizza. is this true expression?
Answers
Answer: The statement is false because 1.2 is calculating 120% of the cost of pizza. The expression should be .2p.
Step-by-step explanation:
The expression 1.2p correctly represents the total bill for a pizza including a 20% tip, with p representing the price of the pizza. To determine the total cost, you multiply the price by 1.20.
The expression 1.2p does indeed represent the total bill including a 20% tip for the delivery of a pizza where p is the cost of the pizza. When you give a tip of 20%, you are adding 20% of the cost of the pizza to the original price. This is calculated by multiplying the price by 1.20 (which is equivalent to 100% + 20%).
Example Calculation:
If the cost of the pizza is $10 (p = $10), then the total bill with a tip would be 1.2 × $10 = $12. The 20% tip on $10 is $2, so the total bill equals $10 + $2 = $12.
A college has a student to teacher ratio of 30 to 2. If there are 182 teachers at the college, how many students attend the college?
A.
3,822
B.
1,092
C.
2,184
D.
2,730
Answers
30/2 =15. So 182 times 15 is 2730, or D.
Can someone help please
Answers
I would say B. The mean is a good measure of central tendency.
I hope this helps!
Arithmetic, Geometric, or Neither Classify each sequence as arithmetic, geometric, or neither. (matching) 4/9, 4/3, 4, 12, 36. 0, 1, 2, 3, 4, 5, 6. -10, -6, -2, 2, 6, 10.
Answers
Answer:
The given sequence is neither arithmetic not geometric.
Step-by-step explanation:
A sequence is in arithmetic if it has a common difference.
i.e., a sequence a, b, c is in arithmetic if
b - a = c - b
Let's check if the given sequence is in arithmetic.
[tex]\frac{4}{3} -\frac{4}{9} =\frac{12}{9} -\frac{4}{9}[/tex]
[tex]= \frac{8}{9}[/tex]
[tex]4-\frac{4}{3} =\frac{12-4}{3}[/tex]
[tex]=\frac{8}{3}[/tex]
So, [tex]\frac{4}{3} -\frac{4}{9} \neq 4-\frac{4}{3}[/tex]
Hence, the given sequence is not arithmetic.
Let's check if the given sequence is in geometric.
A sequence is in geometric if it has a common ratio.
i.e., a sequence a, b, c is in geometric if
[tex]\frac{b}{a} =\frac{c}{b}[/tex]
[tex]\frac{4/3}{4/9} =\frac{4}{3} (\frac{9}{4} )[/tex]
= 3
[tex]\frac{4}{4/3} =4(\frac{3}{4} )[/tex]
= 3
Clearly, [tex]\frac{12}{4} =\frac{36}{12} =3[/tex]
But, [tex]\frac{0}{36} =0[/tex]
Therefore, the given sequence is not in geometric.
Hence, the given sequence is neither arithmetic not geometric.
I need help with this question show steps! Quickly please!
Answers
use both points to find the slope
[tex]\frac{y2-y1}{x2-x1}[/tex]
[tex]\frac{-13-3}{9-(-3)}[/tex]
[tex]\frac{-16}{12} =\frac{-4}{3} =slope[/tex]
Now, to find b, plug in one of the points in y=mx+b
3=[tex]\frac{-4}{3}[/tex](-3)+b
3=4+b
b= -1
therefore, your final equation should be,
y=[tex]\frac{-4}{3}[/tex]x-1
Need an educated answer fast
Answers
Answer:
y-2 = 2/3(x-8)
Step-by-step explanation:
We have the line 6x-9y = -7
Let's rewrite it in the form y=mx+b
6x-9y = -7
Subtract 6x from each side
6x-6x-9y = -7 -6x
-9y = -6x-7
Divide by -9
-9y/-9 = -6x/-9 -7/-9
y = 2/3 x + 7/9
The slope is 2/3
If the line is parallel, the slope will be the same so the slope will be 2/3
We have the slope and a point (8,2) on the new line, so we can use the point slope form of a line
y-y1 = m(x-x1)
y-2 = 2/3(x-8)
given: m = 1/2 and b=4
Answers
Answer:
y = [tex]\frac{1}{2}[/tex] x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y-intercept )
here m = [tex]\frac{1}{2}[/tex] and b = 4, hence
y = [tex]\frac{1}{2}[/tex] x + 4 ← equation of line
Answer:
where is the question?