Triangle XYZ has vertices X: (0,2) Y: (3,8), and Z: (6,2). Show that the triangle is isosceles by determining the length of each side.

[tex]\fbox{3x}[/tex]

Simplify:

[tex]x+y+2x+-y[/tex]

Combine Like Terms:

[tex](x+2x)+(y+-y)[/tex]

[tex]=3x[/tex]

Answer:

y - y = m(x - x)

y + 6 = 2(x + 1)

y + 6 = 2x + 2

y = 2x -4

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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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

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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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

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.

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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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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Answer:

95%

Step-by-step explanation:

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.

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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Answer:

3w - 2j

Step-by-step explanation:

twice the length j less of three times the width

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 :)

The measure of the obtuse angle is 128 degrees

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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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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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

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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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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Answer: D. 16/25

Step-by-step explanation:

The required slope of the given line is 1 which is shown in the graph.

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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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

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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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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The measure of ∠C using sine rule formula and as shown in the triangle is 39.8°.

The 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.

From the diagram,

Given:

Substitute these values into equation 1 and solve for angle C

Hence, ∠C is 39.8°.

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Answer: 40%

Step-by-step explanation:

100(175-125/125)

Simplify: 100(50/125)

Simplify: 100(0.4)=40

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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The width of the tent is twice the width of one side which is 10.5 feet.

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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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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