Answer:
Step-by-step explanation:
formula used= [tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
XY= [tex]\sqrt{(3-0)^2+(8-2)^2}[/tex] = [tex]\sqrt{9+36} =\sqrt{45}[/tex] (here x1=0, x2=3, y1=2, y2=8)
YZ= [tex]\sqrt{(6-3)^2+(2-8)^2}[/tex] = [tex]\sqrt{9+36} = \sqrt{45}[/tex]
ZX= [tex]\sqrt{(6-0)^2+(2-2)^2}[/tex] = [tex]\sqrt{36+0} = \sqrt{36}[/tex]
as you can see side XY=YZ=45
so triangle XYZ is an isosceles triangle
hope this helps :)
Can you guys help me ??
Simplify: x+y+2x-y
PLEASE HELP!!!
[tex]\fbox{3x}[/tex]
Simplify:
[tex]x+y+2x+-y[/tex]
Combine Like Terms:
[tex](x+2x)+(y+-y)[/tex]
[tex]=3x[/tex]
What is the area of a triangle with vertices at (-3, 1), (-6, 5), and (1, 1)?
Enter your answer in the box.
The area of a triangle is 8.
What is the area of a triangle?
Area of a triangle = [s(s - a)(s - b)(s - c)], where s is the triangle's semi-perimeter and a, b, and c are the lengths of the triangle's three sides.
We know that the area of the triangle whose vertices are (x1 ,y1),(x2 ,y2), and (x3, y3) is:
1/2 |x1(y2−y3)+x2(y3−y1)+x3 (y1−y2)|
Area of triangle = 1/2 |-3(5 − 1)+ (-6)(1−1) + 1(1 − 5)|
Area of triangle = 1/2 |-12 + (-4)|
Area of triangle = 8
Hence, the area of a triangle is 8.
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Which equation has no solution?
O
-3(x+5)= x - 15 - 2x
-3(x+5) = x - 15 - 4x
O c-3(x+5)= x − 10 - 4x
OD -3(x+5)= x −10+2x
Equation with option B and C has no solution.
What is equation?
When two expressions are connected with the equals sign, a formula known as an equation is created.
Main Body:
A) -3(x+5) = x-15 -2x
⇒ -3x -15 = x-15-2x
⇒ -3x = -x
⇒ -2x= 0
⇒ x = 0, this means it has a solution.
B) -3(x+5) = x- 15 -4x
⇒ -3x -15 = -3x -15
So this equation also has no solution.
as L.H.S cancels out R.H.S completely so this equation has no solution.
C) -3(x+5) = x-10 -4x
⇒ -3x -15 = -3x -10
⇒ -15 ≠ 10
hence the equation with no solution is option b and c.
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Quiz scores
Data set: 5, 6, 6, 7, 7, 7, 8, 8, 8, 9, 10, 10, 10, 10, 11, 11, 13, 15, 15
Calculate the mean of the data set.
Calculate the range.
If you scored 7 on the quiz, how far did you deviate from the mean?
If you scored 15 on the quiz, how far did you deviate from the mean?
The mean of the data set is 9.26
The range is 10
The deviation when we scored 7 is 2.26 and when we scored 15 is 5.74.
Given, the quiz scores of a class.
Data set: 5, 6, 6, 7, 7, 7, 8, 8, 8, 9, 10, 10, 10, 10, 11, 11, 13, 15, 15
Mean = (Sum of all values)/(Total no. of values)
Mean = 176/19
Mean = 9.26
The range = 15 - 5 = 10
If I scored 7 on the quiz, then I will deviate (9.26 - 7) = 2.26
Similarly, If we scored 15 on the quiz, then I will deviate (9.26 - 15) = 5.74
Hence, the mean of the data set is 9.26
the range is 10
and the deviation when we scored 7 is 2.26 and when we scored 15 is 5.74.
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Find the value of c to make the trinomial a perfect square.
x^2−22x+c
Answer:
c = 121
Step-by-step explanation:
Take half of the middle term coefficient: -22/2 = -11
Now square it: (-11)² = 121
c = 121
Brothers Bob and Tom Katz buy a tent that has a center pole 6.25 feet high. If the sides of the tent are supposed to make a 50° angle with the ground, how wide is the tent?
2.1 ft
10.5 ft
5.6 ft
18.4 ft
The width of the tent is twice the width of one side which is 10.5 feet.
What are trigonometric ratios in terms of a right-angle triangle?We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjecen/hypotenuse and
tan = opposite/adjacent.
Given, Brothers Bob and Tom Katz buy a tent that has a center pole 6.25 feet high and the sides of the tent make a 50° angle with the ground.
Here the opposite is the height with the reference angle of 50° and we have to determine the adjacent which is the width of the tent.
∴ tan50° = Height of the pole/width.
1.19 = 6.25/width.
width = 6.25/1.19.
width = 5.25 feet.
But the total width of the tent will be twice as we have obtained only one side width.
∴ Total width is (2×5.25) = 10.5 feet.
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Jemmy throws the dice twice. What is the probability of getting 3 on the top for both dice?.
A bank account starts with a balance of £8000 and pays compound interest of 5% per year. Work out the balance of the account after 1 year and after 2 years.
The balance of the account after 1 year and after 2 years 16400 and 16820 is respectively.
A bank account starts with a balance, P = $8000
rate of interest = 5%
compound interest for 1 year is :
[tex]CI = P(1 + R/100)^n[/tex]
CI = 8000(1 + 5/100)
CI = 8000(1 + 1/20)
CI = 8000(21/20) = 8400
A = CI + P = 8000 + 8400 = 16400
compound interest for 1 year is :
[tex]CI = P(1 + R/100)^{2n}[/tex]
CI = 8000(1 + 5/100)^2
CI = 8000(1 + 1/20)^2
CI = 8000(21/20)^2 = 8820
A = CI + P = 8000 + 8820 = 16820
The balance of the account after 1 year and after 2 years 16400 and 16820 is respectively.
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a) Write an equation for a line in point-slope form that is parallel to the line y=2/3x-5 and passes through the point (3, 4).
b) Explain what would be different in part (a) if you were asked to write an equation for a line that is perpendicular instead of parallel.
Answer: a) y - 4 = 2/3(x) - 2
b) y - 4 = -3/2(x) -2
Step-by-step explanation:
equation of original line: y = 2/3x -5
point on a line parallel to original line: (3,4)
The slope of a line parallel to a given line has the same slope, so the equation of the parallel line (in point-slope form) is:
(y - y1) = 2/3(x - x1)
point (x1, y1) is (3, 4)
plug (3,4) into the equation:
y - 4 = 2/3(x - 3)
y - 4 = 2/3(x) - 2
rewrite in slope-intercept form: y = 2/3(x) + 2
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the first line: - 1/m
Therefore, the slope of the perpendicular line = -3/2
Equation for the perpendicular line is:
y - 4 = -3/2(x) -2
Natasha is making a bookshelf she begin with 120  inches of oak boards she use 50.75 inches for shelves she bought 36 1/4 more inches 00 boards she didn’t use 40 1/2 inches for the top is 60.5 inches for the sides how many inches of oak boards does Natasha have left 
Natasha has left with 4.5 inches of oak boards.
What is a simplification?
The act of simplifying something such that it is simpler to carry out or understand, or the thing that is the product of this simplifying process: The group offers suggestions for streamlining trade processes.
Here, we have
120 inches of oak boards
50.75 inches for shelves, 36 1/4 more inches of oak boards, and she didn’t use 401/2 inches for the top and 60.5 inches for the sides.
We have to find how many inches of oak boards Natasha has left.
We use here simplification, we get
= 120 + 36 1/4 - 50.75 - 40 1/2 - 60.5
= 4.5 inches
Hence, Natasha has left with 4.5 inches of oak boards.
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Abe jogs 1. 8 miles on monday, 1. 3 miles on tuesday, and 1. 2 miles on wednesday. If beth jogs twice as far as abe, how many miles does beth jog?.
Abe jogs 1. 8 miles on Monday, 1. 3 miles on Tuesday, and 1. 2 miles on Wednesday.
Beth will jog 8.6 miles, if she jogs twice as far as Abe.
The answer provided below has been developed in a clear step by step manner.
Step: 1
Given that,
Abe jogs 1.8 miles on Monday, 1.3 miles on Tuesday and 1.2 miles on Wednesday.
So,
Total miles jog by Abe =1.8+1.3+1.2
Step: 2
Adding, we get,
Total miles jog by Abe = 4.3 miles
To find :-
The number of miles Beth jogged.
Step: 3
Since Beth jogs twice as far as Abe, we have,
Number of miles Beth jog = 2×4.3 miles = 8.6 miles
Since Abe jog 4.3 miles in total, Beth will jog (2* 4.3) miles
Hence the answer is, Beth will jog 8.6 miles, if she jogs twice as far as Abe.
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A line has a slope of 2 and passes through the point (–1, –6) . What is its equation in slope -intercept form?
Answer:
y - y = m(x - x)
y + 6 = 2(x + 1)
y + 6 = 2x + 2
y = 2x -4
The price of an item yesterday was 125 . Today, the price rose to 175 . Find the percentage increase.
Answer: 40%
Step-by-step explanation:
100(175-125/125)
Simplify: 100(50/125)
Simplify: 100(0.4)=40
Martina spent a total of $60 at the grocery store. Of this amount, she spent $57 on fruit. What percentage of the total did she spend on fruit?
Answer:
95%
Step-by-step explanation:
I need help answering the question…
Find expressions for the slope and x- and y- intercepts for Ax + By = C, where A, B, and C are nonzero integers.
First of all, I do not understand any word in that, so the answer and an explanation with get brainiest.
I gotchu :)
So, the base equation is: ax+by=c
x int is c/a
y int is c/b
and the slope is -a/b
So basically, what I wrote above is how to get each aspect of the line using the standard form formula.
The "nonzero" part means that each integer (the A, B, AND C in the formula above) cannot be 0, as that would mean that everything will end up equaling to 0, which does not create the line. So basically, the answer would be:
x int is c/a
y int is c/b
and the slope is -a/b
^ if you apply these to any standard form, you will get the thing I stated next to it. For example, if the standard form equation is:
5x+6y=5
if you want to find the slope, you will do -a/b, and that will give you -5/6, which is your slope
Hope this helps :)
consider . the function is a. continuous on . b. discontinuous but piecewise continuous on . c. neither. is exponentially bounded on ? ? does the laplace transform of exist (on some domain)?
The function f(x)=x³-e⁻⁷ˣ is continuous function. That is a continuous function is one whose graph is continuous throughout without any pauses or leaps.
Given that,
The function is f(x)=x³-e⁻⁷ˣ
We have to find the function f(t) is it continuation on 0≤t<8.
We know that,
Take the function f(x)=x³-e⁻⁷ˣ
What is continuous function?As the name implies, a continuous function is one whose graph is continuous throughout without any pauses or leaps. To put it another way, we say that a function is continuous if we can draw the curve (graph) of the function without ever picking up the pencil.
Therefore, The function f(x)=x³-e⁻⁷ˣ is continuous function. That is a continuous function is one whose graph is continuous throughout without any pauses or leaps.
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Calculate the measure of
The measure of ∠C using sine rule formula and as shown in the triangle is 39.8°.
SINE RULE FORMULAThe sine rule formula gives the ratio of the sides and angles of a triangle. The sine rule can be explained using the expression, a/sinA = b/sinB = c/sinC,
From the diagram, to calculate the measure of the ∠C, we use the sine rule formula.
b/sinB = c/SinC............ Equation 1
From the diagram,
Given:
b = 9c = 6B = 105°Substitute these values into equation 1 and solve for angle C
9/sin105° = 6/sinCsinC = (sin105°×6)/9sinC = 0.64C = sin⁻¹(0.64)C = 39.8°Hence, ∠C is 39.8°.
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A bird is at the very top of a 35 feet tree. He spies a worm that is 50 feet from the base of the tree. Set up a right triangle picture to find the distance from the bird to the worm.
The distance from the bird to the worm is approximately 61.06 feet.
To set up a right triangle picture to find the distance from the bird to the worm, we can use the given information about the bird's position and the worm's position.
Let's consider the bird at the top of the tree as the highest point of the triangle. The height of the tree, 35 feet, represents the vertical side of the triangle. The worm's position, which is 50 feet from the base of the tree, represents the horizontal side of the triangle.
Now, to find the distance from the bird to the worm, we need to find the hypotenuse of the right triangle, which represents the direct line from the bird to the worm.
By using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides, we can set up the equation:
h² = 35² + 50²,
where h represents the length of the hypotenuse.
Solving this equation, we find:
h² = 1225 + 2500,
h² = 3725.
Taking the square root of both sides, we get:
h ≈ √3725 ≈ 61.06 feet.
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Twice the length (į) less three times the width (w)
Answer:
3w - 2j
Step-by-step explanation:
twice the length j less of three times the width
there are 8 members on a committee. if they must form a subcommittee of 3 members, how many different subcommittees are possible
Out of 8 members of the committee, it is possible to create two subcommittees only.
We know that in order to create subcommittees. we need to divide the total number of people on the committee into equal parts so that they form subcommittees.
Here, it is given that there are 8 members on the committee.
A subcommittee needs to have 3 people in it.
On dividing 8 people into groups of three, we get
⇒ [tex]\frac{8}{3}[/tex]
⇒ 2.66..
Here, it is obvious that the 0.66... can not be considered because it is not a whole number and hence, does not mean any number of people.
So, we can create only two different subcommittees from 8 members on the main committee.
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Kami received 2,300 votes in a town election. She received 190 more than 2/5 of the total number of votes. Determine the total number of residents that voted in the town election.
The total number of residents that voted in the town election is 5275 votes
Total number of votes received = 2300 votes
Consider the total number of votes in the town election = x
She received 190 more than 2/5 of the total number of votes
2/5 of the total number of votes = (2/5)x
190 more than 2/5 of the total number of votes = (2/5)x + 190
The equation will be
(2/5)x + 190 = 2300
Move 190 to the right hand side of the equation
(2/5)x = 2300 - 190
(2/5)x = 2110
0.4x = 2110
x = 2110 / 0.4
x = 5275 votes
Hence, the total number of residents that voted in the town election is 5275 votes
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Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
The required slope of the given line is 1 which is shown in the graph.
What is the slope of the line?The slope of the line is represented as the rise of the line.
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Grab two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)
We take the two points (4, 10) and (9, 22)
Let
x₁ = 0, y₁ = 1
x₂ = 8, y₂ = 9
∵ Slope m = (y₂ - y₁)/(x₂ -x₁ )
Substitute values in the formula
m = (9 - 1) / (8 - 0)
m = (8)/(8)
m = 1
Thus, the required slope of the given line is 1 which is shown in the graph.
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Write an expression for the following situation: A man earns a $5000 dividend from an investment and distributes it equally amongst his children.
Which expression is not equivalent to (5^2x)^3
Answer:
#3
Step-by-step explanation:
For this... you just multiply the exponents together to get 6x
any of the others that do NOT have 6x as a product of exponents is not equiv ..... so #3 is not equivalent
Option 3 is not equivalent to the given expression.
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
The given expression is (5²ˣ)³.
Now, (5⁶ˣ)
(5ˣ)⁶
(5²)³ˣ
Therefore, option 3 is not equivalent to the given expression.
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14) WINDOWS This window is designed in the shape of a right trapezoid If the acute angle measures 52", what is the measure of the obtuse angle?
The measure of the obtuse angle is 128 degrees
How to determine the measure of the obtuse angle?From the question, we have the following statement that can be used in our computation:
Acute angle = 52 degrees
The measure of the obtuse angle is calculated as
Obtuse angle = 180 - Acute angle
Substitute the known values in the above equation So, we have the following equation
Obtuse angle = 180 - 52
Evaluate
Obtuse angle = 128
Hence, the angle is 128 degrees
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Given the points (3,5),(2,4),(9,0) and (?,6). What could be replace the ? to create a function.
Any number apart from 3 can be used to replace the ? to create a function.
In a function, the inputs do not repeat that is the input in all cases should be unique in nature.
The inputs are assigned to exactly one output for each.
Three is one of the options to create a non function as three is already an input in the given function.
Replacing the ? with 3 would create the a function would be to replace it with any number but 3.
(3,5) (2, 4) (9, 0) (3,6)
Any number apart from 3 can be used to replace the ? to create a function.
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A doctor prescribes 250 milligrams of a therapeutic drug that decays by about 10% each hour. Write an exponential model representing the amount A in milligrams of the drug remaining in the
patient's system after t hours.
A(t)=
Use the formula to find the amount of the drug that would remain in the patient's system after 3 hours. Round to the nearest milligram.
mg
A(3) = 185mg
Formula for exponential growth/decay is
A(t) = A0 * e^(xt)
Where A0 is your initial amount
x is your percentage
t is the time
A(3) = 250 * e^(-0.1*3)
A(3) = 185.2mg
Key point x is negative in this case as it's a decaying function. If it was growth it would be positive
I NEED HELP ASAP RN
What fraction can not be simplified?
A. 9/15
B. 18/30
C. 8/12
D. 16/25
Answer: D. 16/25
Step-by-step explanation:
Harley davidson offers 3 different motorcycle models. Each of these is available in 6 different colors. How many different combinations of model and color are available? 9 12 18 24.
A different combination of models and colors available is 18.
Combination:
the act of combining or the state of being combined. a number of things combined: a combination of ideas. something formed by combining: A chord is a combination of notes. an alliance of persons or parties: a combination in restraint of trade.
Here it is given 6 different colors. Harley Davidson offers 3 different motorcycle models.
We have to find the number of different combinations of models and colors available.
Based on the above-given data we get the:
Different combination = 3 × 6
= 18
Therefore the number of combinations is 18.
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