Answer:
(i) In △ABD and △ACD,
AB=AC ....(since △ABC is isosceles)
AD=AD ....(common side)
BD=DC ....(since △BDC is isosceles)
ΔABD≅ΔACD .....SSS test of congruence,
∴∠BAD=∠CAD i.e. ∠BAP=∠PAC .....[c.a.c.t]......(i)
(ii) In △ABP and △ACP,
AB=AC ...(since △ABC is isosceles)
AP=AP ...(common side)
∠BAP=∠PAC ....from (i)
△ABP≅△ACP .... SAS test of congruence
∴BP=PC ...[c.s.c.t].....(ii)
∠APB=∠APC ....c.a.c.t.
(iii) Since △ABD≅△ACD
∠BAD=∠CAD ....from (i)
So, AD bisects ∠A
i.e. AP bisects∠A.....(iii)
In △BDP and △CDP,
DP=DP ...common side
BP=PC ...from (ii)
BD=CD ...(since △BDC is isosceles)
△BDP≅△CDP ....SSS test of congruence
∴∠BDP=∠CDP ....c.a.c.t.
∴ DP bisects∠D
So, AP bisects ∠D ....(iv)
From (iii) and (iv),
AP bisects ∠A as well as ∠D.
(iv) We know that
∠APB+∠APC=180
∘
....(angles in linear pair)
Also, ∠APB=∠APC ...from (ii)
∴∠APB=∠APC=
2
180
∘
=90
∘
BP=PC and ∠APB=∠APC=90
∘
Hence, AP is perpendicular bisector of
Step-by-step explanation:
HOPE ITS HELP YOU
Y+2= 1/3(x+6)
Solve for y
Answer:
y = 1/3x
Step-by-step explanation:
Alright, so we have an equation with two variables (y and x) and I need to solve for y in terms of x. That is, I need to isolate y one one side with all the other terms on the other side.
First, let's distribute the 1/3 on the right side of the equation onto the x and 6 inside the parentheses.
y + 2 = 1/3(x + 6)
y + 2 = 1/3(x) + 1/3(6)
y + 2 = 1/3x + 2
Now, let's isolate y on the left side by removing 2 from both sides.
y + 2 = 1/3x + 2
y + 2 - 2 = 1/3x + 2 - 2
y = 1/3x
So, y is equal to 1/3x. Hopefully that's helpful! :)
help please anybody PLEASE
Answer:
18 dimes
Step-by-step explanation:
Since Leon has ”16 fewer than” it’s a symbol to subtract
34-16=18
Answer:
34-16=18 leon has 18 dimes
Step-by-step explanation:
hope this helps
Evaluate the expression when B = -4 and C = 6
C-8B
A 9-foot roll of waxed paper costs $4.32. What is the price per inch?
The price per foot is $0.91
Step-by-step explanation:
A 6-yard roll of butcher paper costs 16.38
1 yard = 3 foot
6 yards = 3 times 6 = 18 foot
the cost of 18 foot is $16.38
To find price per foot, we divide the cost of 6 yards by 18
16.38÷ 18 = 0.91
The price per foot is $0.91
If (6^2]^p = 6^10, what is the value of p?
A.) 2
B.) 3
C.) 4
D.) 5
please try looking at the picture :(( i’m really struggling so much!!
Answer:
4- true
5-true
6-false
7-false
8-true
9-true
Step-by-step explanation:
Follow the letters and the sign of congruence
≅
When is it best to solve a system of equations using substitution?
Answer:
The easiest way to solve this system would be to use substitution since x is already isolated in the first equation. Whenever one equation is already solved for a variable, substitution will be the quickest and easiest method
What is the number in standard form (8 x 10) + (2 x 1 /100) + ( 9 x 1/1,000
Answer:
8.0029 x[tex]10^{1}[/tex]
Step-by-step explanation:
8 x 10=80
2 x [tex]\frac{1}{100}[/tex]=0.02
9x[tex]\frac{1}{1,000}[/tex]= 0.009
add all ur answers together and u get 80.029
then in standard form that nwould be 8.0029 x[tex]10^{1}[/tex]
Hoped that helped:P
Write the equation for 5x+ 2 y= 3 in slope-intercept form PLEASE HELP ME
y= -5/2x+ 3x
y=5/3x -3/5
y= -2/5x + 3/5
Answer:
y=-5/2x+3/2
Step-by-step explanation:
5x+2y=3
2y=3-5x
2y=-5x+3
y=-5/2x+3/2
equivalent ratio tables
Answer:
11, 44, 24
Step-by-step explanation:
On the right side column you are adding 11 every time you add 4 on the left side column
For example :
4:11
8:22
12:33
16:44
20:55
24:66
Hope this helps!!! :)))
Express 29 and 37 as the sum of two squares.
If you can answer the correct answer first, then I will mark brainliest.
Answer:
See below
Step-by-step explanation:
[tex] {5}^{2} + {2}^{2} = 25 + 4 = 29 \\ \\ {6}^{2} + {1}^{2} = 36 + 1 = 37[/tex]
The values are 29 = 5² + 2² and 37 = 6² + 1².
What is square of number?The definition of a square number states that they are numbers that have been multiplied by themselves. In other terms, a natural number is referred to as a square number if it is multiplied by itself.
Decimal squares are fairly simple to calculate, and the process is the same for both whole numbers (integers) and decimals.
Given numbers 29 and 37
to express in form of sum of two square
let = 29 = a² + b²
the perfect square number near 29 is 25
29 = 25 + 4
29 = 5² + 2²
and 37 = a² + b²
the perfect square near 37 is 36
37 = 36 + 1
37 = 6² + 1²
Hence the numbers in sum of two squares are,
29 = 5² + 2² and 37 = 6² + 1²
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Simplify this question
[tex]4 + \sqrt{ - 16} \\ = 4 + \sqrt{ - 2 \times 2 \times 2 \times 2} \\ = 4 + 2\sqrt{ - 4} \\ = 2(2 + \sqrt{ - 4} )[/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
[tex]\\ \sf\longmapsto 4+√-16[/tex]
[tex]\\ \sf\longmapsto 4+√16i[/tex]
[tex]\\ \sf\longmapsto 4+4i[/tex]
Take 4common[tex]\\ \sf\longmapsto 4(1+i)[/tex]
6 less than the quotient of y and 5.
Answer:
(y/5)-6
Step-by-step explanation:
quotient is dividing, less than is subtracting
A hybrid car can go 400 miles on 8 gallons of gas. How far can the car take you with 1 gallon of gas?
Step-by-step explanation:
In 8 gallons of gas the car can go = 400 miles
In 1 gallon of gas the car can go = 400/8
In 1 gallon of gas the car can go = 50 miles
How far can the car take you with 1 gallon of gas? With 1 gallon of gas, the car can go 50 miles.
Step by Step calculations:
We know that
With 8 gallons of gas, the car can go 400 miles
Then,
With 1 gallon of gas, the car can go
= 400 / 8
= 50 miles
Therefore, with 1 gallon of gas, the car can go 50 miles.
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A triangle has side lengths of 2 feet, 5.4 feet, and 5 feet. The angle measures are 90 degrees, 73 degrees, 17 degrees. Another triangle has side lengths of 3 feet, 8.1 feet, 7.5 feet. The angle measures are 90 degrees, 73 degrees, 17 degrees. Are the triangles similar? If so, what is the scale factor going from the top triangle to the bottom triangle?
Answer:
Yes. The factor is 3/2 (=1,5)
Step-by-step explanation:
They have all the 3 angles congruent, so they are similar. You calculate the scale factor by dividing the hypotenuse (for example) of the second triangle by the hypotenuse of the first one.
Answer:
1) yes 2) 1.5
Step-by-step explanation:
have a nice day! <:
Combine the like terms to create an equivalent expression.
large 9p+3p
Answer:
12p
Step-by-step explanation:
9p+3p=12p
Crystal's yearly income is $25,000, and the cost
of her rent for the year is $7,500. What fraction
of her yearly income does she spend on rent?
A. 1/4
B. 3/10
C. 2/5
D. 2/7
A solid wood cone 12 cm in diameter and 8 cm high sells for $1.19. A second wood cone is 17 cm in diameter and 12 cm high. the fair price for this second cone rounded to the nearest cent, is
a) $2.53,
b) $3.58
c) $5.06
d) $10.75
e) $14.33
Answer:
Answer is a
Step-by-step explanation:
I think it's "A", im looking for answer as well :(
PLEASE HELP ME!!!
Maggie's brother is 7 years younger than four times her age. The sum of their ages is 68.
How old is Maggie?
=============================================
Explanation:
m = Maggie's age (some positive whole number)
4m = four times her age
4m-7 = seven years younger than 4m = brother's age
Add up her age (m) and her brother's age (4m-7) to get a sum of 68.
m+(4m-7) = 68
5m-7 = 68
5m = 68+7
5m = 75
m = 75/5
m = 15
Maggie is currently 15 years old.
Her brother is currently 4m-7 = 4*15-7 = 60-7 = 53 years old.
Their current year ages add to: 15+53 = 68 which confirms the answer.
how to solve the following system y=(1/2)x^2+2x-1 and 3x-y=1
Answer:
(0,-1),(2,5)
Step-by-step explanation:
3x-y=1
0.5[tex]x^{2}[/tex]+2x-1=y
Substitute the equation of y into the other equation
3x-(0.5[tex]x^{2}[/tex]+2x-1)=1
3x-0.5[tex]x^{2}[/tex]-2x+1=1
collect like terms
-0.5[tex]x^{2}[/tex]+x=0
Solve for x
x(-0.5x+1)=0
0=-0.5x+1
-1=-0.5x
x=2 x=0
Back substitute into the other original equation and solve for y
3(2)-y=1
6-y=1
y=5
(2,5)
3(0)-y=1
-1(-y)=-1(1)
y=-1
(0,-1)
2. List the like terms in each of the following
i) 4x2 , -5x , 6 , 7x , -2x2 , -3
he is the best way to get a free agent and I ask 6262626
after sales tax a 33 dollar photo album cost 35.97 dollars. What is the sales tax percentage
Answer:
9%
Step-by-step explanation:
Set up a ratio:
[tex]\frac{33}{100}[/tex] = [tex]\frac{35.97}{x}[/tex]
Cross multiply: 33x = 35.97 * 100
33x = 3597
Divide by 33: x = 109
That means the tax is 9%.
EASY 9TH GRADE MATH
Write an equation in point-slope form that passes through the point (1,-10) and
is perpendicular to y = -1/3 x + 5.
Do NOT type spaces between numbers and symbols.
Til
ALE
11
SE
Answer:
y = 3x - 13
Step-by-step explanation:
which of the following equations could be parallel to the equation x = 5
A. y = 5x
B. x = -2
C. y = 5
D. y = x
Answer:
B
Step-by-step explanation:
x = 5 is the equation of a vertical line parallel to the y- axis
The equation of a line parallel to it must have the same form, that is
x = - 2 ← vertical line parallel to x = 5
PLSSSS HELPPPP ASAPPPP. REWARDING BRAINLIEST. PLS SHOW WORK
3. What are the exact measures of the other two sides of the triangle? Use special right triangles ratios and show your work.
Answer: B = 90°; C = 60°
Step-by-step explanation:
B is obviously 90° because of the right angle quadrant.
Since it is a right triangle and A is already 30°, just subtract 30 from 90.
90 - 30 = 60
Thus, C is 60°.
Correct me if I am incorrect.
A tram moved downward 9 meters per second for 54 seconds. What was the total change in the tram's elevation?
Answer:
6
Step-by-step explanation:
Answer:
-486
Step-by-step explanation:
A sequence of numbers is shown below :
1 5 9 13 17
explain why 95 will not be a term in this sequence
Answer:
95 is not a term here as the next verse should be 98 as it is a 94 term in this pattern
95 will not be a term in the sequence 1, 5, 9, 13, 17, ....., as the value of n for the nth term is not integer.
What is arithmetic sequence ?An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence.
The given sequence of numbers is,
1, 5, 9, 13, 17, .....
The first term of the given sequence a₁ =1,
From the given sequence, the common difference pair of two consecutive terms d = 4,
Let nth term of the sequence aₙ= 95,
By arithmetic sequence formula,
aₙ = a₁ + (n-1).d
Substitute the value of aₙ and d,
95 = 1 + (n-1).4
94 = (n-1). 4
(n-1) = 23.5
n = 24.5
The value of n can't be decimal, so 95 can't be a term of the given sequence.
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(2w2+4w)÷(w–2) divide
the answer is 4
someone please help this is due in 25 minutes
Because it is an isosceles triangle, the 2 sides that are given will be equal to each other.
15=4x+3
(subtract 3 on both sides)
12=4x
(divide by 4 on both sides)
x=3
Hope it helps!
Answer:
x = 3.
Step-by-step explanation:
1. 4x + 3 = 15
2. Subtract 3 from both sides.
3. Divide by 4 from both sides.
Write (5/3)³ as a quotient of powers.
Answer:
The number (5/3)³ written as a quotient of powers is; 5³/3³
According to the question;
We are required to determine write the number, (5/3)³ as a quotient of powers
The number (5/3)³ can be evaluated as;
= 125/27
= 5³/3³
Step-by-step explanation: