Answer:
Given: Two Isosceles triangle ABC and Δ PBC having same base BC. AD is the median of Δ ABC and PD is the median of Δ PBC.
To prove: Point A,D,P are collinear.
Proof:
→Case 1. When vertices A and P are opposite side of Base BC.
In Δ ABD and Δ ACD
AB= AC [Given]
AD is common.
BD=DC [median of a triangle divides the side in two equal parts]
Δ ABD ≅Δ ACD [SSS]
∠1=∠2 [CPCT].........................(1)
Similarly, Δ PBD ≅ Δ PCD [By SSS]
∠ 3 = ∠4 [CPCT].................(2)
But, ∠1+∠2+ ∠ 3 + ∠4 =360° [At a point angle formed is 360°]
2 ∠2 + 2∠ 4=360° [using (1) and (2)]
∠2 + ∠ 4=180°
But ,∠2 and ∠ 4 forms a linear pair i.e Point D is common point of intersection of median AD and PD of ΔABC and ΔPBC respectively.
So, point A, D, P lies on a line.
CASE 2.
When ΔABC and ΔPBC lie on same side of Base BC.
In ΔPBD and ΔPCD
PB=PC[given]
PD is common.
BD =DC [Median of a triangle divides the side in two equal parts]
ΔPBD ≅ ΔPCD [SSS]
∠PDB=∠PDC [CPCT]
Similarly, By proving ΔADB≅ΔADC we will get, ∠ADB=∠ADC[CPCT]
As PD and AD are medians to same base BC of ΔPBC and ΔABC.
∴ P,A,D lie on a line i.e they are collinear.
Write the equation of the line that goes through (-2/3, 7/8) and is PARALLEL to 3x + 4y = 7
Answer:
6x+8y = 3
Step-by-step explanation:
we have 3x + 4y = 7
4y = -3x + 7
y = -3/4 x + 7/4
so slope is -3/4
2 parallel lines always have same slope
so the slope of our new line is -3/4
so y = -3/4 x + C
for c,
we have (x,y) = (-2/3,7/8)
7/8 = -3/4 * -2/3 + C
C = 3/8
so equation is
y = -3/4 x + 3/8
simplyfyig,
8y = -6x + 3
or, 6x+8y = 3
help me please, i’ll give brainliest
Answer:
Step-by-step explanation:
THE BEST ANSWER IS C>>>>>>>>>>>>
Which two ratios are equivalent to 10 : 12?
11 : 13 and 20 : 24
10 : 12 and 11 : 13
5 : 6 and 20 : 24
5 : 6 and 11 : 13
Answer:
10 : 12 is equivalent to 5 : 6 and 20 : 24.
Step-by-step explanation:
You can divide and multiply the ratio by 2 to get an equivalent ratio.
The ratio which is equivalent to 10: 12 are 5: 6 and 20: 24 Therefore, option (C) will be correct.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
As per the given ratio, 10:12.
Divide numerator and denominator by 2
(10/2):(12/2) = 5:6.
Multiply the numerator and denominator by 2
(10×2);(12×2) = 20:24
Hence "The ratio which is equivalent to 10: 12 are 5: 6 and 20: 24".
For more information about ratios and proportions,
brainly.com/question/26974513
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A basketball team played six games. In those games, the team won by 7 points, lost by 20, won by 8, won by 11, lost by 3, and won by 9. What is the mean amount by which the team won or lost over the six games?
Answer:
the mean of which the team won is 8.75
The mean of which the team lost is 11.5
Step-by-step explanation:
add all the numbers of which the team won by then divide the sum by the number of numbers there are
example:
7+8+11+9=35/4=8.75
Y’all please help I have so many missing assignments and it would help if you even did one question for my homework
Answer:
Step-by-step explanation:
3a + 10 − 4q + 7a − 4q − 6.
Answer:
Step-by-step explanation:
3a+10-4q+7a-4q-6 combine terms
10a-8q+4
Answer:
10a - 8q + 4
General Formulas and Concepts:
Alg I
Combining like termsStep-by-step explanation:
Step 1: Define expression
3a + 10 - 4q + 7a - 4q - 6
Step 2: Simplify
Combine like terms (a): 10a + 10 - 4q - 4q - 6Combine like terms (q): 10a - 8q + 10 - 6Combine like terms: 10a - 8q + 4HELP PLEASE ILL GIVE BRAINLIEST!!!!!!!!!
Answer:
the first questions answer is yes the seconds is no
HAVE A NICE DAY!!!
10 + 2 - 3 = 3(2 + 2)
Answer:
My answer is = 9 cannot equal 12. There are no variables present in this equation, so what are you solving for?
Step-by-step explanation:
On the right you would use distributive property and on the left you would just simply add and subtract.
However, you cannot equal it to zero either because there are no variables nor exponents.
Tim throws a stick straight up in the air from the ground. The function h = -16t^2+ 48t models the height, h, in feet, of
the stick above the ground after t seconds. Which inequality can be used to find the interval of time in which the stick
reaches a height of more than 8 feet?
Answer:
[tex]-2t^2+ 6t -1 > 0[/tex]
Step-by-step explanation:
Function Modeling
The height h in feet of the stick threw by Tim is modeled by the function:
[tex]h = -16t^2+ 48t[/tex]
where t is the time in seconds.
It's required to write an inequality that can be used to find the interval of time in which the stick reaches a height of more than 8 feet, i.e. h > 8.
Using the given model, we write the inequality:
[tex]-16t^2+ 48t > 8[/tex]
Dividing by 8
[tex]-2t^2+ 6t > 1[/tex]
Subtracting 1, we get the required inequality:
[tex]\mathbf{-2t^2+ 6t -1 > 0}[/tex]
Answer:
you want more than 8 feet so the answer would be -16t^2+48t>8
Step-by-step explanation:
h=-16t^2+48t
-16t62+48t>8
-16t^2+48t=8
divide both sides of the equal sighn by 8
-2t^2+6t=1
put the symbol back in
-2t^2+6t>1
substitute a random mumber for t
-2(5)^2+6(5)>1
-10^2+30>1
subtract 30 from both sides
100>-29
state is true so -16t62+48t>8 is the correct answer
Please Find 23% of 40
Answer:
9.2
Step-by-step explanation:
THE POWER OF MULTIPLICATION
To paint a house, a painting company charges a flat rate of $500 for supplies, plus $50 for each hour of labor. a. How much would the painting company charge to paint a house that needs 20 hours of labor?
Answer:
For 20 hours it would be $1,500.
Step-by-step explanation:
The equation for this problem would be Y = 50x + 500.
Y is the total charge and x is the number of hours.
Hope this helps! Sorry if it was not what you were looking for!
Answer: 1500
Step-by-step explanation: 50x20=1,000 plus the addition price of the supplies 1,000+500= $1500
Gloria’s washing machine is broken. Since her machine is pretty old, she doesn’t want to spend more than $100 for repairs. A service call will cost $35 and the labor will be an additional $20 per hour. There are no other charges. What is the maximum number of hours that the repair person can work without the total cost exceeding $100?
Answer:
The actual answer is 3.25
Step-by-step explanation:
I just took the test
the maximum number of hours that the repair person can work is 3.5 hours
Given :
Gloria doesn’t want to spend more than $100.
A service call will cost $35 and the labor will be an additional $20 per hour
Let 'h' be the maximum number of hours the repair can take.
Lets find out the total cost for 'h' hours
35+ additional 20 per hour
[tex]35+20h[/tex]
The total cost should not exceed 100
[tex]35+20h \leq 100\\20h \leq 100-35\\20h\leq 65\\Divide \; by \; 20\\h\leq 3.5[/tex]
So , the maximum number of hours that the repair person can work is 3.5 hours
Learn more : brainly.com/question/19042935
is y=-2/5x inverse or direct variation
Answer:
direct
Step-by-step explanation:
The standard form of an equation representing direct variation is
y = kx ← k is the constant of variation
The standard form of an equation representing inverse variation is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
y = - [tex]\frac{2}{5}[/tex] x ← represents direct variation with k = - [tex]\frac{2}{5}[/tex]
negative 3 times x equals?
Answer:
-3x
Step-by-step explanation:
Answer:
Step-by-step explanation:
If we multiply any negative number in this case -3 times a POSITIVE we will always get a negative. So the positive we can put as x and multiply -3 times x = -3x.
Hope this helps :D
PLEASE SOMEONE HELP ME. I WILL BRAINLIEST YOU AND GIVE YOU POINTS.
Answer:
ok it has to be c baceau it loooks like it
Step-by-step explanation:
Factorise: (a) 3x2 + 27y2 + z2 - 18xy + 6 √3yz -2 √3zx (b) 27 x3 + 125y3 (c) (2a – 3b + c )2
(d) 1 a3 + b3 + 125 c3 - 15 a b c (e) [x – 1/x y]3 (f) x4 y4 – x y
64^4
(g) 8x3 – (2x – y)3 (h) a6 _ b6
Answer please
Answer:
(a) [tex]3x^2 + 27y^2 + z^2 - 18xy + 6 \sqrt{3} yz -2 \sqrt{3} zx[/tex]
this can be written as
[tex](-x\sqrt{3})^2 + (y3\sqrt{3})^2 + (z)^2 +2 ( -x\sqrt{3} )( y3\sqrt{3}) + 2( y3\sqrt{3})(z) + 2(z)( -x\sqrt{3})[/tex]
which is equivalent to
[tex]a^2+ b^2 + c^2 + 2ab + 2bc + 2ac = (a+b+c)^2[/tex]
[tex](-x\sqrt{3} + y3\sqrt{3} + z)^2 = (-x\sqrt{3} + y3\sqrt{3} + z)(-x\sqrt{3} + y3\sqrt{3} + z)[/tex]
(b)[tex]27 x^3 + 125y^3[/tex] = [tex](3x)^3 + (5y)^3[/tex]
which is same as [tex]a^3 + b^3 = (a+b)(a^2 +b^2 -ab)[/tex]
= [tex](3x + 5y)(9x^2 + 25y^2 -15xy)[/tex]
(c) [tex](2a - 3b + c )^2[/tex] = (2a -3b +c)(2a -3b+c)
(d) [tex]a^3 + b^3 + 125 c^3 - 15 a b c[/tex]
this is same as
[tex]a^3 + b^3 +c^3 - 3abc[/tex] = [tex](a+b+c)( a^2+b^2+c^2 -ab-bc-ac)[/tex]
= [tex](a + b + 5c)(a^2+b^2 +25c^2 -ab -5bc -5ac)[/tex]
(e) [tex](x - 1/x y)^3[/tex] = [tex](x - 1/xy)(x - 1/xy)(x - 1/xy)[/tex]
(f) [tex]x^4 y^4 - x y64^4 = xy( x^3y^3 - 64^4) = xy( x^3y^3 - (256)^3) \\ = xy( xy - 256 )(x^2y^2 + 65536 + 256xy)[/tex]
(using the property of [tex]a^3 -b^3 = (a-b)(a^2+b^2 +ab)[/tex] )
(g) [tex]8x^3 - (2x - y)^3 = (2x)^3 - (2x-y)^3 \\ = (2x - 2x + y)(4x^2 + (2x-y)^2 + 2x(2x-y))\\ = y(8x^2 + y^2 -6xy +4x)[/tex] using the same property above
(h)
[tex]a^6 -b^6 = (a^2)^3 - (b^2)^3 = (a^2-b^2)( a^4+b^4 +a^2b^2)\\ = (a-b)(a+b)( a^4+b^4 +a^2b^2)[/tex]
YOOOOO I NEED HELP QUESTION ON PICTURE !!!!!!!!!!
Answer:
Y intercept is -5
Step-by-step explanation:
It is negative five because it goes through the y axis at -5
Anyone????? That can help me answer these
Answer:
5. 3050ft³ (rounded to 3 s.f.)
6. 4190ft³(rounded to 3 s.f.)
7. 4600ft³(rounded to 3 s.f.)
Formulas (For easier reference):
Volume of a cone: pi×r²×[tex]\frac{h}{3}[/tex]
Volume of cylinder: pi×r²×h
Volume of a sphere: [tex]\frac{4}{3}[/tex]×pi×r³
Volume of a hemisphere: [tex]\frac{2}{3}[/tex]×pi×r³
Step-by-step explanation:
You can just apply the formulas to the question:
5. Volume of cone = pi×9²×[tex]\frac{(16-10)}{3}[/tex]
= 162pi
Volume of cylinder = pi×9²×10
= 810pi
Volume of figure = 162pi+810pi
= 972pi
= 3050ft³ (rounded to 3 s.f.)
6. Volume of sphere = [tex]\frac{4}{3}[/tex]×pi×10³
= 1333[tex]\frac{1}{3}[/tex]pi
= 4190ft³(rounded to 3 s.f.)
7. Volume of hemisphere = [tex]\frac{2}{3}[/tex]×pi×(26÷2)³
= 1464[tex]\frac{2}{3}[/tex]pi
= 4600ft³(rounded to 3 s.f.)
the length of a rectangle is 5 less than twice the width. If the perimeter of the rectangle is 146 centimeters, find the dimensions of the rectangle
Answer:
26x47
Step-by-step explanation:
To calculate the length of the rectangle we would do 2(2x - 5) + 2(x) = 146
We simplify and get 6x - 10 = 146,
then divide both side by 6 and plus 10 both sides,
we will get
x = 26
Now we've found one of the length,
to find the other side we do 26 * 2 = 52, and subtract 52 from 146,
which would get 94, then we divide it by 2
94/2 = 47
The dimensions is 26x47
Need help !!!! I would make you 100 edits if you answer this for me ! I need some help on this !! It’s due in a few minutes!! Help me !!
Answer:
6A7C8B
Step-by-step explanation:
Add them in and try to solve for 7 and 6, for 8. I usually put all number on one side and all x on other side.
grabriella volunteers at the hospital every 4th day.she volunteers at the food pantry every 6th day.she volunteered at the hospital and the food pantry both on march 31.On what date will she next volunteer at both?
Answer:
April 12th
Step-by-step explanation:
This table shows the total cost, t, in dollars, of a movie rental when the movie is rented d days.
Which equation represents the data in the table?
t=3d
t=d+6
t=2d+3
t=12d+9
t=3d based on the information given
Answer:
t=2d+3
Step-by-step explanation:
im bad at math so help ill mark the first person brainliest ty
Answer:
A. -x² + 2x + 8
General Formulas and Concepts:
Algebra I
Combining like termsStep-by-step explanation:
Step 1: Define
f(x) = 2x + 1
g(x) = x² - 7
(f - g)(x) is f(x) - g(x)
Step 2: Solve
Substitute: (f - g)(x) = 2x + 1 - (x² - 7)Distribute -1: (f - g)(x) = 2x + 1 - x² + 7Combine like terms: (f - g)(x) = -x² + 2x + 815. Lola jogs at a constant rate of 6 miles per hour. Which does not represent the relationship between the time Lola jogs, t, and the distance she jogs, d?
Is the sequence arithmetic? If yes, determine the common difference. *
(1 Point)
-14-9, -4, 1, 6, ...
O no, it does not increase or decrease the exact same amount
O yes, d = 5
O yes, d = -5
Answer:
Option 2: Yes, d= 5 is the correct answer
Step-by-step explanation:
An arithmetic sequence is a sequence where the common difference between the consecutive terms is same.
Given arithmetic sequence is:
-14, -9, -4, 1, 6
To check if it is an arithmetic sequence, we have to find the common difference d
[tex]a_1 = -14\\a_2 = -9\\a_3 = -4\\a_4 = 1[/tex]
Now,
[tex]d = a_2-a_1 = -9-(-14) = -9+14 = 5\\d = a_3 - a_2=-4-(-9) = -4+9 = 5\\d = a_4-a_3 = 1-(-4) = 1+4 = 5[/tex]
As the common difference is same, the given sequence is an arithmetic sequence.
Hence,
Option 2: Yes, d= 5 is the correct answer
Which statements about opposites are true?
Select each correct answer.
Answer:
(a) TRUE
(b) TRUE
(c) FALSE
(d) TRUE
Step-by-step explanation:
" The "opposite" of any number is also known as it's " additive inverse" i.e. for any number 'a' the additive inverse is 'a' ".
(a) TRUE
Since let us consider any negative number '-5' then it's opposite is '5' since (-5)+5=0
(b) TRUE
this could be seen clearly from the number line.
(c) FALSE
this statement is false since we can take example of zero.
the opposite of zero is 0 but 0×0≠1.
(d) TRUE
since 0-0=0.Step-by-step explanation:
help me please.
[tex]help \: me[/tex]
The solution is where the two lines cross each other:
(-1,3) and (2,6)
The answer is B.
Need help with this question. Thanks
Answer:
C
Step-by-step explanation:
-18x+2y>=-13
2y>= -13+18x
y>= -6.5+9x
Michael borrowed $4,500 from the bank. The bank charged a simple interest rate of 10.5% for the 3 years he had the bank loan. What was the total cost of the loan?
Answer:
142.85?
Step-by-step explanation:
Melissa earned $17 for 2 hours walking her dogs. Last week sh walking dogs for 8 hours how much did she make last week
Answer:
she made $68 last week.
Answer:
$68
Step-by-step explanation:
you need to divide 8 by 2 which is 4
then multiply 4 by 17 which equals 68.