1.) Prove that PAT is an isosceles triangle.
2.) State The Coordinates of R so that quadrilateral PART is a parallelogram.
( The image of the Question Is Given )
First one to answer with the correct answer gets marked
Answers
The triangle PAT is an isosceles triangle because the side lengths PA and AT are congruent
How to prove that the triangle is an isosceles triangle?The points are given as:
P = (1,6)
A = (4,5)
T = (5,2)
Calculate the distance between both points as follows:
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]
So, we have:
[tex]PA = \sqrt{(1 -4)^2 + (6-5)^2}[/tex]
[tex]PA = \sqrt{10}[/tex]
[tex]PT = \sqrt{(1 -5)^2 + (6-2)^2}[/tex]
[tex]PT = \sqrt{32}[/tex]
[tex]AT = \sqrt{(4 -5)^2 + (5-2)^2}[/tex]
[tex]AT = \sqrt{10}[/tex]
Because the side lengths PA and AT are congruent, i.e. √10, then the triangle is an isosceles triangle
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Related Questions
Someone help me.............asap
Answers
Answer:
11 h
Step-by-step explanation:
1/2 h
11h 1/2 will be need for a bike
What is the Surface area of a rectangle with a length of 3 width of 2 and a height of 12
Answers
Explain
See drawing not to scale.
Surface area is L x W
2 ends 2x12
4 sides 3x2
Nico is planting grass in his backyard. He is using 1 foot grass squares and has to cover an area that is 24 feet long and 20 feet wide.
How many 1 foot squares does Nico need?
pls help! Ill give brainly if possible! :)
Answers
The number of the grass squares of 1 square foot will be 480.
What is the area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called as the area of the rectangle.
The total area covered by the grass will be:-
A = L x W
A = 24 x 20 = 480 square feet
Number of the grass squares having an area of 1 square foot:-
N = Total area / area of one grass square
N = 480 square feet / 1 square feet
N = 480
Therefore the number of the grass squares of 1 square foot will be 480.
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Find the slope of the line through
the points (1, 4) and (7, 1).
A
1
2
B
-2
1
2
D
2.
Answers
For this, we can substitute the following to get this :
y2-y1 and x2-x1
1 - 4 and 7 - 1
-3 and 6
-3 / 6 gets you -1/2
Therefore the answer is :
The slope of the line is -1/2
What are the domain and range of f (x) = log (x minus 1) + 2?
domain: x > 1; range: y > 2
domain: x > 1; range: all real numbers
domain: all real numbers; range: y > 1
domain: all real numbers; range: all real numbers
Answers
Answer:
domain: x > 1; range: all real numbers
Step-by-step explanation:
Given function: [tex]f(x)=\log(x-1)+2[/tex]
Logarithms are not defined for zero or negative numbers.
[tex]\implies (x-1) > 0 \implies x > 1[/tex]
Therefore:
domain (input values): [tex]x > 1[/tex]range (output values): all real numbersAnswer:
B on edge
Step-by-step explanation:
Just took the test :)
Which of the following points is a possible solution to the system? y ≤ 3x − 1 y ≥ -x − 1
Answers
Plotting the inequalities y ≤ 3x − 1 and y ≥ -x − 1 using the geogebra graphing tool, a possible solution to the system is (3, 1)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the inequalities y ≤ 3x − 1 and y ≥ -x − 1
Plotting the inequalities y ≤ 3x − 1 and y ≥ -x − 1 using the geogebra graphing tool, a possible solution to the system is (3, 1)
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A number y increased by 5 is at least -21
Answers
- - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - -
[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Given question:-}}}}[/tex]
❖ A number y increased by 5 is at least -21.
[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]
❖ First, if you come across the word "increased" it means we
"increase" a number, or add something to that number, like
y increased by 5 [tex]\longmapsto[/tex] [tex]\sf{y+5}[/tex]
Now, we are also given that this expression is at least -21, which means it can't be -21; it can be -21 or it can be greater than -21.
So we have
[tex]\longmapsto\sf{y+5\geq -21}}[/tex]
Solving for y
Subtract 5 on both sides:-
[tex]\longmapsto\sf{y\geq -21-5}[/tex]
[tex]\longmapsto\sf{y\geq -26}[/tex]
So the values of y greater than or equal to -26 will make this inequality true.
Good luck with your studies.[tex]\rule{300}{1}[/tex]
Answer:
y >= - 26
Step-by-step explanation:
your equation at first looks like this
y + 5 >= -21
then you subtract 5 to both sides
y >= -26
Find the value of X
Answers
Answer:
x = 14
Step-by-step explanation:
By tangent secant theorem[tex] x^2 = 7(7+21)[/tex][tex]\implies x^2 = 7(28)[/tex][tex]\implies x ^2=196[/tex][tex]\implies x=\pm\sqrt{196}[/tex][tex]\implies x=\pm 14[/tex]x can not be negative[tex]\implies x=14[/tex]write down all the prime numbers
Answers
Answer:
The prime numbers from 1 to 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
Step-by-step explanation:
also it goes on and on so i dont think you meant but i hope this helps if it dosnt m very sorry
Given the function graphed below, find the average rate of change over the
interval x= 2 to x = 4. I’ve been stuck on this question for a little bit . Can’t seem to wrap my head around it
Answers
Answer:
Approximately 0.3.
Step-by-step explanation:
I can only estimate the value of the function when x = 2. it looks like it's about 2.4.
Average rate of change = [(f4) - f(2)] / (4 - 2)
= (3 - 2.4) / 2
= 0.6/2
= 0.3.
please help with this
Answers
Answer:
F = 53.1°
Step-by-step explanation:
When you consider F as your angle
cos F = adjacent / hypotaneous
or, cos F = EF/DF
We do not have DF right now,
so DF² = DE² + EF²
DF = √ (12² + 9²)
DF = 15
cos F = adjacent / hypotaneous
or, cos F = EF/DF
cos F = 9 / 15
F = cos ⁻¹ (9/15)
F = 53.1°
i'll give brainliest and points to whomever answers these two questions, thank you so much in advance!
Q8- what's the S.S of the inequality: x² + 4 > 2
a) R
b) ∅
c) R-
d) R+
Q9- if x + yi = (1 + i)⁴ , then x + y = ......
a) 4
b) - 4
c) 2
d) - 2
an explanation for future reference would be GREATLY appreciated, thank you again T^T
Answers
Answer:
8 Answer is a) R
9 Answer is b) -4
Step-by-step explanation:
Answer of your Question bro and good evening and please mark me as brainliest and thank u
what is the solution of 9 (x-8) = 3 (4x-12)
() = Exponents The things in perenthacys are exponents
Answers
Solving as exponents
[tex]\\ \rm\Rrightarrow 9^{(x-8)}=3^{(4x-12)}[/tex]
[tex]\\ \rm\Rrightarrow 3^{2(x-8)}=3^{2(x-6)}[/tex]
[tex]\\ \rm\Rrightarrow 2(x-8)=2(x-6)[/tex]
[tex]\\ \rm\Rrightarrow 2x-16=4x-12[/tex]
[tex]\\ \rm\Rrightarrow -2x=4[/tex]
[tex]\\ \rm\Rrightarrow x=-2[/tex]
Answer:
[tex]x=-2[/tex]
Step-by-step explanation:
Given equation:
[tex]9^{x-8}=3^{4x-12}[/tex]
Rewrite 9 as 3²:
[tex]\implies (3^2)^{x-8}=3^{4x-12}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 3^{2(x-8)}=3^{4x-12}[/tex]
[tex]\implies 3^{2x-16}=3^{4x-12}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]
[tex]\implies 2x-16=4x-12[/tex]
Subtract 2x from both sides:
[tex]\implies 2x-16-2x=4x-12-2x[/tex]
[tex]\implies -16=2x-12[/tex]
Add 12 to both sides:
[tex]\implies -16+12=2x-12+12[/tex]
[tex]\implies -4=2x[/tex]
Divide both sides by 2:
[tex]\implies \dfrac{-4}{2}=\dfrac{2x}{2}[/tex]
[tex]\implies x=-2[/tex]
Dexter is thinking of a number, x. Two more than three times his number is the same value as thirteen less than five times his number. Write this information as an equation in x. Solve your equation to find the value of x.
Answers
3x-5x=-13-2
-2x=-15
x=7.5
Dexter is thinking of a number, x. Two more than three times his number is the same value as thirteen less than five times his number. The number which he is thinking is 7.5.
What is equation?Two or more expressions with an equal sign is called as Equation.
Given that Dexter is thinking of a number, x. Two more than three times his number is the same value as thirteen less than five times his number.
Let the number which Dexter is thinking be x.
Two more than three times his number.
It means value two is added to the product of 3 and the number which he is thinking x.
3x+2
thirteen less than five times his number
It means value thirteen is subtracted from the product of 5 and the number which he is thinking x.
5x-13.
It is given Two more than three times his number is the same value as thirteen less than five times his number
3x+2=5x-13
Take the like terms to one side
13+2=5x-3x
15=2x
Divide both sides by 2.
x=7.5
Hence the value of x is 7.5.
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the bill at an electronics store was $52 before tax.
tax is 5 percent. what is the total price with tax?
Answers
Answer:
$54.6
Step-by-step explanation:
To solve the question, we need to find how much 5% of 52 is
For questions where we need to calculate the percentage, we will multiply the number by given percentage and then divide it by the whole, 100%
52*5/100 = 2.6
Now the price before the tax was 52 and the tax is 2.6
the total price:
2.6 + 52 = 54.6
Need help asap
the garcia family has a monthly car loan payment of $400, and their average monthly credit card bill is $4,800. mr. garcia
is also paying $1,000 per month to support his elderly parents. compute the back-end ratio to the nearest percentage.
type the correct answer in the box. use numerals instead of words.
Answers
Answer:
70%
Step-by-step explanation:
A guest was on holiday before going to the wedding at 6 o’ clock. He had to travel 120km to get to the venue. He travelled at an average of 100km/h . Verify if He will reach the dance on time if he leaves at 16:40
Answers
He will reach the dance before time if he leaves at 16:40.
What is speed- distance formula?The formula for speed is speed = distance ÷ time.
To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).
Given distance= 120 Km, speed= 100 km/h
For this speed,
time= distance/ speed
= 120/100
= 1.2 hours
If the guest leave at 4:40 p.m. then by the speed of 100 km/h he will reach the venue at 06:00 p.m.
Hence, he will reach before the time at wedding.
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i really need help on this. can you please solve
Answers
Answer:
371/999
Step-by-step explanation:
all repeating numbers like that just go over nines. Two repeating? Over 99. Four repeating? Over 9,999
Two points of a parallelogram are (1,2) and (2,5). The base of the parallelogram is parallel to the x axis and is 4 units long. Find the coordinates of the other two points of this parallelogram and also find the length of the other pair of parallel sides of the parallelogrma. What would the area of this parallelogram be?
Answers
Answer:
(5,2) and (6,5)
length of side = sqrt10 ~= 3.16 units
Area = 12 sq units
Step-by-step explanation:
It really helps to graph the given information. See image. The sides have the same slope bc they are parallel. If you go UP3 & OVER1 to get from the first point to the second point, then do that again on the right side. See image. Use distance formula or pythagorean thm to find the length:
c^2 = 3^2 + 1^2
c^2 = 9+1
c^2 = 10
c = root10 ~= 3.16
Area of a parallelogram is b•h
A = 4•3
= 12
see image.
Which is equivalent to cos-1(0)? give your answer in radians.
Answers
If cos90 is equivalent to zero, hence the cos inverse of 0 is 90 degrees which is equivalent to pi/2 in radians
Inverse of trigonometry functionInverse of a function are the opposite of the function. Given the inverse of cosine function as shown:
[tex]cos^{-1}x[/tex]
If x = 0, hence;
[tex]cos^{-1}{0[/tex]
If cos90 is equivalent to zero, hence the cos inverse of 0 is 90 degrees which is equivalent to pi/2 in radians
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Explain how you would graph the inequality, "b ≤ 0
Answers
Answer:
the inequality, b ≤ 0 has interval Notation of -∞,0
Step-by-step explanation:
the inequality, b ≤ 0 has interval Notation of -∞,0
I need the the number
Answers
y=3x+3
Step-by-step explanation:
The m is 3 because it is rise over run. For every 3 up it goes one over (3/1) or just 3. The b is 3 because b is where x equals 0 and it is at 3.
help with these 10th grade geometry angle problems? will reward brainliest!
Answers
Answer:
Step-by-step explanation:
PLEASe help math ...
Answers
Answer:
21.6 units² (nearest tenth)
Step-by-step explanation:
[tex]\textsf{Area of a trapezoid}=\dfrac{1}{2}(a+b)h \quad \textsf{(where a and b are the bases and h is the height)}[/tex][tex]\textsf{Area of a semicircle}=\dfrac12 \pi r^2 \quad \textsf{(where r is the radius)}[/tex]
Given:
a = 2b = 8h = 4r = 2 ÷ 2 = 1[tex]\begin{aligned}\textsf{Area of figure} & =\textsf{area of trapezoid + area of semicircle}\\& = \dfrac{1}{2}(a+b)h+\dfrac{1}{2} \pi r^2\\& = \dfrac{1}{2}(2+8)(4)+\dfrac{1}{2} \pi (1)^2\\& = 20+\dfrac{1}{2} \pi\\& = 21.6\: \sf units^2 \:(nearest\:tenth)\end{aligned}[/tex]
Area of the trapezium
1/2(Sum of parallel sides)×Height1/2(2+8)(4)2(10)20units²Area of semicircle
π(2/2)²/2π/21.57units²Total area
20+1.5721.6units²(Rounded)The sum of two numbers is 40 and the difference is 8. What are the numbers?
Answers
Answer:
24 and 16.
Step-by-step explanation:
They both are in between the sum of the two numbers.
The inside of a baking pan is to be lined with tinfoil. the pan is 12 inches long, 9 inches wide, and 1.5 inches tall. how many square inches of tinfoil are needed?
Answers
The inside of a baking pan is to be lined with tinfoil. Then the amount of tinfoil needed will be 171 square inches.
What is a rectangle?It is a polygon with four sides. The total interior angle is 360 degrees. A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.
The inside of a baking pan is to be lined with tinfoil. the pan is 12 inches long, 9 inches wide, and 1.5 inches tall.
Then the amount of the tinfoil will be
The surface area of the rectangle with an open lid is given as
Surface area = 2(LH + WH) + LW
Then the surface area of the tinfoil will be
Surface area = 2(12 x 1.5 + 9 x 1.5) + 12 x 9
Surface area = 2 (18 + 13.5) + 108
Surface area = 2 x 31.5 + 108
Surface area = 63 + 108
Surface area = 171 square inches
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Envision Geometry 10-1 Circles 22. page 425
Answers
The segment area of the circle that's given in the envision geometry is 2.568.
How to calculate the segment area?It should be noted that the segment area is given as:
= (a/360)π × R² - Area of triangle
= (90/360)π × 3² - (1/2 × 3²)
= 9π/4 - 9/2
= 2.568
In conclusion, the segment area of the circle that's given in the envision geometry is 2.568.
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The sum of two numbers is 23. The difference of the numbers is 7.4. What are the two numbers?
Answers
X-y=7.4
X+y=23
y=23-X
X-y=7.4
(23-y)-y=7.4
23-2y=7.4
-2y=-15.6
Y=7.8
X+y=23
X+7.8=23
X=15.2
Therefore the two numbers are 7.8 & 15.2
2 x (6÷2 +8) -4 Help me
Answers
Answer:
22x-4
Step-by-step explanation:
2x(3+8)−4
Simplify 3+8 to 11.
2x×11−4
Simplify 2x times 11 to 22x.
22x−4
Find the equation of the line shown
Answers
Answer: y = 1/2x + 1/2