Answers
The area of the given triangle will be [tex]\dfrac{5\sqrt{2}}{2}[/tex]
What is the triangle?Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.
Given points of the triangle are:-
( -6,5 ) (-5,3 ) and (-8, 2)
Now we will apply the area formula for the triangle:-
[tex]A = \dfrac{1}{2} \times B\times H[/tex]
The base will be = [tex]\sqrt{(-5++8)^2+(3-2)^2)}=\sqrt{9+1}=\sqrt{10}}[/tex]
The Height will be = [tex]\sqrt{(-5+6)^2+(5-3)^2}=\sqrt5[/tex]
The area will be calculated as:-
[tex]A =\dfrac{1}{2}\times \sqrt{10}\times \sqrt{5}=\dfrac{5\sqrt{2}}{2}}[/tex]
Therefore the area of the given triangle will be [tex]\dfrac{5\sqrt{2}}{2}[/tex]
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Related Questions
Which algebraic expression represents the situation "add seven to the product of a number and ten"?
Answers
7 (10 - X)
Find the sum of the first 200 terms of the arithmetic sequence that begins: 12, 18, 24, ...
Answers
Answer:
S₂₀₀ = 121800
Step-by-step explanation:
the sum to n term of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
here a₁ = 12 and d = a₂ - a₁ = 18 - 12 = 6 , then
S₂₀₀ = [tex]\frac{200}{2}[/tex] [ (2 × 12) + (199 × 6) ]
= 100(24 + 1194)
= 100 ×1218
= 121800
Beg someone helps me w this question
Answers
Answer:
[tex](x+1)^{2} +4[/tex]
a = 1
b = 4
Step-by-step explanation:
hope this helps!! p.s. i really need brainliest :)
Find the area and the area of the figure.
Answers
Answer:
352
Step-by-step explanation:
sssplit the shapes and then do regular formula
a = lh
Find f(4) given f(x) = 2x^2 - 7
Answers
Answer:
f(4) = 25
Step-by-step explanation:
substitute x = 4 into f(x)
f(4) = 2(4)² - 7 = 2(16) - 7 = 32 - 7 = 25
Which inequality represents the domain of the exponential piece?
a x>3
b x greater than or equal to -1
c x>1
d x less than or equal to -2
Answers
Using it's concept, it is found that the inequality represents the domain of the exponential piece is:
d) [tex]x \leq -2[/tex].
What is the domain of a function?The domain of a function is the set that contains all possible input values.
Researching this problem on the internet, we have that the function is divided as follows:
For [tex]x \leq -2[/tex], it has exponential behavior.For x > 2, it has polynomial behavior.Hence, for the domain of the exponential piece, option d is correct.
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In parallelogram HIJK, the measure of angle H is 45∘.
Find the measure of angle J. Explain how you know.
Find the measure of angle K. Explain how you know.
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Answer:
Step-by-step explanation:
Please help me solve for Z
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The correct value of z in this figure is 190⁰
The image given in this question is of a circle. To solve it, let's calculate it as an equation of the first degree.
– First, let's: add the data that are on the circle and equate the equality as 360⁰, which is the value of the degree of a circle.
145 + 24 + z = 360⁰
– Now, let's: add the natural terms to each other. And finally, we'll isolate z and subtract 360⁰ by the number that's left.
145 + 24 + z = 360⁰
170 + z = 360⁰
z = 360⁰ - 170
z = 190⁰
So, the value of z, will be 190⁰
1. Which is a set of collinear points? (1 point)
J, H, I
L, H, J
J, G, L
L, K, H
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first correct answer gets brainleist pls help asap
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Answer:
The angle is acute. This type of angle must be between 0° and 90°, and Orla's estimate is not.
Need help please answer ASAP!
Answers
Perimeter of larger sail
10+24+2660ftNow
Let shorter sail's Perimeter be x
x/6=60/10x/6=6x=36#2
Let they be 2x and 7x
2x+7x=1809x=180x=20Smaller angle
20(2)=40What is the answer to this question?
Answers
Answer:
[tex]\huge\boxed{\bf\:tan \: Z= \frac{4}{3}}[/tex]
Step-by-step explanation:
We know that, tan θ = opposite side of ∠θ / adjacent side of ∠θ.
Here, we need to find tan Z,
In this triangle for ∠Z,
Opposite side = 28Adjacent side = 21Then,
tan Z
= opposite side / adjacent side
= 28 / 21
= 4 / 3
[tex]\rule{150pt}{2pt}[/tex]
Find the value of x in the given figure
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[tex]~~~~~~(2x+34)+(x+71) = 180\\\\\implies 3x + 105=180\\\\\implies 3x = 180-105\\\\\implies 3x = 75\\\\\implies x = \dfrac{75}3\\\\\implies x = 25[/tex]
Find the gradient of the line joining (-1,9) and (3,5)
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[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]
Find the gradient of the line joining (-1,9) and (3,5)
[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]
Use the slope formula:-
[tex]\boxed{\frac{y_2-y_1}{x_2-x_1}}[/tex]
Replace the letters with the numbers:-
[tex]\boxed{\frac{5-9}{3-(-1)}}[/tex]
[tex]\circ[/tex] On simplification,
[tex]\boxed{\frac{-4}{3+1}}[/tex]
[tex]\circ[/tex] On further simplification,
[tex]\boxed{\frac{-4}{4}}[/tex]
[tex]\circ\sf{SLOPE=-1}[/tex]
Good luck with your studies.[tex]\rule{300}{1}[/tex]
12.3 Write the first five terms of the sequence whose general term is [tex]a_{n}=3^{n}+4[/tex] .
Answers
Answer:
7,13,31,85,247......
Step-by-step explanation:
[tex]a_n =3^n + 4[/tex]
[tex]\sf a_1=3^1 + 4 = 3 + 4 = 7\\\\a_2 = 3^2 + 4 = 9 + 4 = 13\\\\a_3 = 3^3 + 4 = 27 + 4 = 31\\\\a_4 = 3^4 + 4 = 81 + 4 = 85\\\\a_5 = 3^5 + 4 = 243 + 4 = 247[/tex]
if you have 48 apples and you gave your friend molly 20 and you gave your brother and mom 18 each how much apples do you have now?
Answers
Answer:
10
Step-by-step explanation:
48-20=28
28-18=10
that is how I see it at least
One-third of the Socer training participants are four-fifths of the Dance training
students. Twelve Dance training students do not participate in the Soccer training.
What is the total number of students who participate in the Soccer training?
Answers
Answer:
There are a total of 144 students in soccer training.
Step-by-step explanation:
12x5=60
60-12=48
48=4/5
4/5=1/3
1/3 = 48
48x3= 144
What is the common difference between successive terms in the sequence? 2, 8, 14, 20, 26,. –6 –4 4 6.
Answers
Answer:
The common difference is the difference between any two consecutive terms in an arithmetic sequence.
The formula which is used to find the common difference in AP is
d = an - an-1
Here the common difference is
d = a2 - a1 = 8 - 2 = 6
d = a3 - a2 = 14 - 8 = 6
d = a4 - a3 = 20 - 14 = 6
d = a5 - a4 = 26 - 20 = 6
2, 8, 14, 20, 26 … = 2, (2 + 6), (8 + 6), (14 + 6), (20+ 6) …
Therefore, the common difference is 6.
Step-by-step explanation:
The graph of a sinusoidal function intersects its midline at (0, 1) and then has a maximum point at
Write the formula of the function, where is entered in radians.
f(x) =
Answers
Answer:
f(x) = 4·sin(2/7x) +1
Step-by-step explanation:
The sinusoidal function y = a·sin(kx) +b will have cross its midline at (0, b), and a peak value of (x, y) = (π/(2k), a+b). We can use these facts to find the values of a, k, and b for the sinusoidal function.
__
midline(0, b) = (0, 1) ⇒ b = 1
peak value(7π/4, 5) = (π/(2k), a+1)
This gives rise to two equations:
7π/4 = π/(2k)
k = π/(2(7π/4)) = 2/7
and
a+1 = 5
a = 4
equationUsing the found values for the parameters of the function, we have ...
f(x) = 4·sin(2/7x) +1
When you use the slope formula, does it matter what point you choose as (x1 , y1) and what point you choose as (x2, y2)? Explain why or why not.
Answers
Answer:
It does not matter.
Step-by-step explanation:
How to find a slope with just two points,
Step One: Identify two points on the line.
Step Two: Select one to be (x1, y1) and the other to be (x2, y2).
Step Three: Use the slope equation to calculate the slope.
Example
Let's say that points (15, 8) and (10, 7) are on a straight line. What is the slope of this line?
Step One: Identify two points on the line.
In this example, we are given two points, (15, 8) and (10, 7), on a straight line.
Step Two: Select one to be (x1, y1) and the other to be (x2, y2).
It doesn't matter which we choose, so let's take (15, 8) to be (x2, y2). Let's take the point (10, 7) to be the point (x1, y1).
Step Three: Use the equation to calculate the slope.
Once we've completed step 2, we are ready to calculate the slope using the equation for a slope:
[tex]slope=\frac{y2-y1}{x2-x1} =\frac{8-7}{15-10} =\frac{1}{5}[/tex]
We said that it really doesn't matter which point we choose as (x1, y1) and the which to be (x2, y2). Let's show that this is true. Take the same two points (15, 8) and (10, 7), but this time we will calculate the slope using (15, 8) as (x1, y1) and (10, 7) as the point (x2, y2). Then substitute these into the equation for slope:
[tex]slope=\frac{y2-y1}{x2-x1} =\frac{7-8}{10-15} =\frac{-1}{-5}=\frac{1}{5}[/tex]
We get the same answer as before!
Often you will not be given the two points but will need to identify two points from a graph. In this case, the process is the same, the first step being to identify the points from the graph. Below is an example that begins with a graph.
So therefore it does not matter.
No, it does not matter which point you choose as (x₁, y₁) and which point you choose as (x₂, y₂) when using slope formula. Slope between two points on line remains same regardless of order in which you choose points.
The slope formula is given by slope = (y₂ - y₁) / (x₂ - x₁)
This is because the slope represents the rate at which the y-coordinate changes with respect to the x-coordinate.
If you swap the points (x₁, y₁) and (x₂, y₂), the change in y and the change in x will simply swap as well, but their ratio, which is the slope, will remain unchanged. For example, if the slope between (x₁, y₁) and (x₂, y₂) is m, then the slope between (x₂, y₂) and (x₁, y₁) will also be m.
This property of the slope formula makes it convenient and efficient to calculate the slope between two points, regardless of their order, as it will yield the same result.
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What is the midpoint of AB?
Answers
Answer:
[tex](-4, -\frac{1}{2} )[/tex]
Step-by-step explanation:
A (-5, -4)
B (-3, 3)
We can apply the midpoint formula: [tex](\frac{-5 + -3}{2} , \frac{-4 + 3}{2} )[/tex]
[tex]= (-4, -\frac{1}{2} )[/tex]
hope this helped! :)
19. Solve for the angle x.
sin²(2x) = 1
Answers
Answer: Е
Step-by-step explanation:
▪︎ a^2 - b^2 = (a-b)(a+b)
sin^2(2x) = 1
sin^2(2x) - 1 = 0
(sin2x - 1)(sin2x + 1) = 0
sin2x - 1 = 0 or sin2x + 1 = 0
sin2x - 1 = 0
sin2x = 1
2x = 90° + 360°n
x = 45° + 180°n
▪︎180° means half of the unit circle, therefore,
x = 45° + 360°n and
x = 45° + 180° + 360°n = 225° + 360°n
sin2x + 1 = 0
sin2x = -1
2x = 270° + 360°n
x = 135° + 180°n
therefore,
x = 135° + 360°n and
x = 135° + 180° + 360°n = 315° + 360°n
n is an integer
Select all angle measures for which
sin 0=-
❌
✅
✅
❌
✅
Answers
If the trigonometric expression is sin θ = -√2/2. Then the value of angle θ will be 5π/4, 7π/4, and 13π/4.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
The trigonometric expression is given below.
sin θ = -√2/2
The expression can be written as
sin θ = -1/√2
Then the value of angle θ will be
θ = sin⁻¹ (-1/√2)
θ = 5π/4, 7π/4, and 13π/4.
Thus, the correct options are B, C, and E.
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Answer:
B,C,E
Step-by-step explanation:
The _____ is the price of an item that is being offered at a lower price than usual.
Answers
Answer:
sale price
Step-by-step explanation:
price of an item that is being offered at a lower price than usual
How do the average rates of change for f(x) = -0.5x² and g(x) = -1.5x² over the interval -5 ≤ x ≤ -2 compare?
Answers
reflection across y = 1
Answers
Answer:
Vertical Reflection Apply a reflection over the line y=-1 The procedure to determine the coordinate points of the image is the same as that of the previous example with minor differences in that the change will be applied to the y-value and the x-value stays the same.
Step-by-step explanation:
BRAINLIST PLEASEFor each graphically defined function below, state the domain, the range, and the intervals on which the function is increasing, decreasing, or constant.
Domain:
Range:
Increasing:
Decreasing:
Constant Intervals?
Answers
Answer:
Domain: [tex]-3\leq x\leq 3[/tex]
Range: [tex]0\leq y\leq 1.5[/tex]
Increasing: [tex]0\leq x\leq 3[/tex]
Decreasing: [tex]-3\leq x\leq 0[/tex]
No constant intervals
Step-by-step explanation:
Hope this helped
Swimming Pool On a certain hot summer's day, 366 people used the public swimming pool. The
daily prices are $1.25 for children and $2.25 for adults. The receipts for admission totaled $767.50.
How many children and how many adults swam at the public pool that day? There were
children at the public pool.
Answers
Answer:
c=__ and a=__
Step-by-step explanation:
767.50=1.25(c)+2.25(a).
366=c+a
normally from here, I would just guess the number of adults and children. It does take a while doing it that way, but maybe you know a quicker way. Hope this helps :)
50/9 as a mixed fraction
Answers
Answer:
5 5/9
Step-by-step explanation:
9 goes into 50 4 times and the subtract that from 50
Answer :
5 [tex]\frac{5}{9}[/tex]
Explanation:
50/9= 5.5555555555556 = 5
Now that we have our whole number for the mixed fraction, we need to find our new numerator for the fraction part of the mixed number.
Step 2: Get the new numerator
To work this out we'll use the whole number we calculated in step one (5) and multiply it by the original denominator (9). The result of that multiplication is then subtracted from the original numerator:
50 - (9 x 5) = 5
Step 3: Our mixed fraction
We've now simplified 50/9 to a mixed number. To see it, we just need to put the whole number together with our new numerator and original denominator:
5 [tex]\frac{5}{9}[/tex]
Find the volume of the prism.
Answers
Answer:
172.8 m^2
Step-by-step explanation:
7.2/2 = 3.6
3.6*4.8 = 17.28
17.28*10 = 172.8