The two smaller triangles below were created by drawing an altitude in the larger triangle. Write a similarity statement
relating the 3 triangles.

A. CBD-CDA-DBA
B. ABD-DAC-DBA
C. ABC-DAC-DBA
D. CBA-CDA-DBA

Answer:

  n ∈ ℕ . . . (Natural numbers)

Step-by-step explanation:

You want the domain of the relation s(n) = 7+3n so that it defines the sequence 10, 13, 16, ....

The domain of a function is the set of "input" values for which the function is defined. Here, the function is intended for use with values of n that are Natural numbers:

  domain = ℕ

__

Additional comment

In general, the domain of any function that defines a sequence will be Natural numbers. That is, values of n will be 1, 2, 3, ....

Occasionally, the sequence represents a relation that is of interest for values of n other than positive integer values. In such a case, the domain may be Whole numbers, or Real numbers.

Answer: The distance between these two points is 5.

Step-by-step explanation:

Yay! Love doing distance formula questions!

Okay, so first off, the distance formula goes as follows:

d = [tex]\sqrt(x^{2} - x^1)^2 + (y^{2}-y^1)^2[/tex]

Basically you just plug in your coordinates to the formula.

Step 1:

[tex]\sqrt(-5 + 5)^{2} + (2-7)^{2}[/tex]

Step 2: Distribute the exponent to both parenthesis to get [tex]\sqrt{25}[/tex].

Step 3: Factor the number, which would result in [tex]\sqrt{5^2}[/tex].

As a result of this, your answer would be 5.

The zeroes of the given function are + 1 and - 1 respectively.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the function as -

y = x² - 1

For the zeros of the function substitute {y} = 0. We get -

x² - 1 = 0

x² = 1

x = ± 1

Therefore, the zeroes of the given function are + 1 and - 1 respectively.

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Answer:The student made a mistake and explain the specific error that was made. Support your answer using the correct vocabulary. The mistake has been done in Step 2.

PART A: There is a mistake in Step 2, Distributive Property has been employed incorrectly.

7 has to multiply by both the terms inside the bracket, but it has been multiplied with the first term only.

7(-2 x-8 y)=-14 x-56 y and 7(-2 x-8 y) -14 x-8 y

Hence, -5(x-16 y)+7(-2 x-8 y)=-5 x+80 y-14 x-56 y

PART B :

The given equation is

-5(x-16 y)+7(-2 x-8 y)

Applying distributive property to the above equation that states A(B+C)=AB+AC, we get :

-5 x+80 y-14 x-56 y

Now, Writing the terms with the same variable together, we get

(-5 x-14 x)+(80 y-56 y)

Proceeding with solving terms inside the brackets according to BODMAS, we get,

-19 x+24 y

Hence , −5(x − 16y) + 7(−2x − 8y) = -19x +24y

The number of star wars that Amy has is 255 and Carly has is 85

Linear equation:

The linear equation is a combination of algebraic terms that are used to find unknown quantities in a word problem. To solve the given problem represent the unknown value with a variable and form a linear equation according to the given condition. Now solve the equation for the value of the variable.

Here we have

Amy has three times as many star wars toys as Carly.  

Let Amy have 'x' star wars and Carly have 'y' star wars

From the given data, x = 3y  

It is also given that both have 340-star wars toys in total

=> y + 3y = 340

=> 4y = 340

=>  y = 85

Hence, the number of star wars that Carly has = 85

Number of star wars that Amy has = 3(85) = 255

Therefore,

The number of star wars that Amy has is 255 and Carly has is 85

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At least three functions can be called, including checkweather. The other two functions can be any other functions that the program contains.

The maximum number of functions that can be called when calling the checkweather function depends on the program. If the program contains other functions, then up to three functions can be called, including the checkweather function. When calling the checkweather function, the first function that will be called is the checkweather function itself. After the checkweather function is called, the program will then proceed to call any other functions that have been determined by the program. This means that the maximum number of functions that can be called is at least two, with the checkweather function being one of them.In addition, if the program contains additional functions, then the maximum number of functions that can be called increases to three. For example, if the program contains functions to display the weather forecast, to check the temperature and to generate an alert, then these functions can also be called in addition to the checkweather function. In this case, the maximum number of functions that can be called is three, with the checkweather function still being one of them.

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Step-by-step explanation:

To find the volume of this solid, we will use the method of cylindrical shells. We will integrate the cross-sectional area of the equilateral triangles over the height of the solid.

The height of the solid is given by the difference between the upper and lower bounds of the base, which are y = 4 and y = x^2, respectively. The cross-sectional area of an equilateral triangle with sides of length 2x is given by (x^2 * √3)/4.

So, the volume of the solid is given by the integral:

V = ∫[x^2, 4] (x^2 * √3)/4 dx

Using the antiderivative of x^2 * √3 / 4, which is (2x^3 * √3)/(12), we can find the definite integral:

V = [2x^3 * √3]/12 from x^2 to 4

Evaluating the definite integral and simplifying, we get:

V = 16 units^3

So, the volume of the solid is 16 units^3.

Answer:

the volume of the solid is 16 units^3

Step-by-step explanation:

Possible pair of measurements if they are congruent figures are,

⇒ ∠W = 140°

⇒ ∠X = 94°

⇒ ∠Y = 79°

⇒ ∠Z = 47°

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

Lincoln is measuring the angles of quadrilateral WXYZ to determine whether  it is congruent to the quadrilateral shown in figure.

Now, We know that;

If two figure are congruent to each other then there corresponding angles and side are equal to each other.

So, The angles of quadrilateral WXYZ are,

⇒ ∠W = 140°

⇒ ∠X = 94°

⇒ ∠Y = 79°

⇒ ∠Z = 47°

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Answer:

Question 3

First option:
[tex]\dfrac{\ensuremath{\dfrac{4}{5}\;in}}{\dfrac{2}{3}\;hr}[/tex]

Question 4
Third option:
[tex]\dfrac{1}{4} \div \dfrac{2}{5}[/tex]

Question 5

Second Option:
[tex]\dfrac{7}{10}[/tex]

Step-by-step explanation:

Question 3

If  [tex]\dfrac{4}{5}[/tex] inches of rain falls every  [tex]\dfrac{2}{3}[/tex] hours then the unit rate in inches per hour is inches [tex]\div[/tex] hours

This would be:
[tex]\dfrac{\ensuremath{\dfrac{4}{5}\;in}}{\dfrac{2}{3}\;hr}[/tex]

This is the first option in Question 3 answer choices

Question 4

[tex]\dfrac{\dfrac{1}{4}\;km}{\dfrac{2}{5}\;min}[/tex]

is nothing but the numerator ÷ denominator which would be:

[tex]\dfrac{1}{4} \div \dfrac{2}{5}[/tex]

This is the third option in Question 4 answer choices

Question 5

[tex]\dfrac{1}{2} \div \dfrac{5}{7}\\[/tex]

Flip the divisor [tex]\dfrac{5}{7}[/tex]; it comes [tex]\dfrac{7}{5}[/tex]

Multiply:
[tex]\dfrac{1}{2} \times \dfrac{7}{5}[/tex]

The result is
[tex]\dfrac{7}{10}[/tex]

This is the second option in Question 4 answer choices

Answers:

Question 3: [tex]\frac{\frac{4}{5}in.}{\frac{2}{3}hr.}[/tex]

Question 4: [tex]\frac{1}{4}[/tex] ÷ [tex]\frac{2}{5}[/tex]

Question 5: [tex]\frac{7}{10}[/tex]

Explanations:

Question 3: We're told that rain is falling at a rate of  [tex]\frac{4}{5} in.[/tex] every  [tex]\frac{2}{3} hr.[/tex], and the unit rate we're looking for is inches per hour (or more precisely, inches per 1 hour). Based on these parameters, we know that you have to divide the unit inches by the unit hours. So using the numbers above, the correct complex fraction to represent this situation would be [tex]\frac{\frac{4}{5} in.}{\frac{2}{3} hr.}[/tex] .

Question 4: In this question, we are given a complex fraction and asked to rewrite it as a simple division problem. The complex fraction is [tex]\frac{\frac{1}{4} km.}{\frac{2}{5} min.}[/tex], so in order to write this as a division expression, you simply take the numerator fraction and divide it by the denominator fraction, which will end up being [tex]\frac{1}{4}[/tex] ÷ [tex]\frac{2}{5}[/tex]. Therefore, that will be your answer.

Question 5: Now, we have a division expression and are asked to use the Keep, Change, Flip method to solve the problem. First and foremost, the Keep, Change, Flip method is essentially telling you that when you are dividing by a fraction, you keep the dividend the same, you change the divisor - specifically switching the numerator with the denominator, which is creating the reciprocal of that fraction - and multiply by the reciprocal of the original divisor instead.

                   A good example of the Keep, Change, Flip method from above would be [tex]\frac{1}{2}[/tex] ÷ [tex]\frac{1}{3}[/tex]. You keep the dividend, change the divisor, specifically flip the function around to create its reciprocal, and instead multiply by the divisor's reciprocal. Following those steps, [tex]\frac{1}{2}[/tex] ÷ [tex]\frac{1}{3}[/tex]  will become [tex]\frac{1}{2}[/tex] × [tex]\frac{3}{1}[/tex] or [tex]\frac{1}{2}[/tex] × [tex]3[/tex].

                  Now that we understand how to use the Keep, Change, Flip method, we can use it to solve the expression [tex]\frac{1}{2}[/tex] ÷ [tex]\frac{5}{7}[/tex]. We keep [tex]\frac{1}{2}[/tex] the same, flip [tex]\frac{5}{7}[/tex] to make its reciprocal, and multiply [tex]\frac{1}{2}[/tex] by that instead. So the final answer will be [tex]\frac{1}{2}[/tex] ÷ [tex]\frac{5}{7}[/tex] = [tex]\frac{1}{2}[/tex] × [tex]\frac{7}{5}[/tex] = [tex]\frac{7}{10}[/tex].

Have a great day! Feel free to let me know if you have any more questions :)

Answer:

Missing measure for angle B = 74°

Missing measure for angle C = 74°

Step-by-step explanation:

Side AB = Side AC

∴∠B° = ∠C°

Two sides out of three of this triangle are equal to each other, therefore this is an isosceles triangle

Let x° = ∠B° = ∠C°

Sum of interior angles of a triangle = 180°

                                      ∴32° + x° + x° = 180°

                                     = 32° + 2x° = 180°

                                      = 2x° = 180° - 32°

                                      = 2x° = 148°

                                      = x° = [tex]\frac{148}{2}[/tex]

                                      = x° = 74°                

                            ∴∠B° = ∠C° = 74°  

Answer:

[tex]5.98xy-8y[/tex]

Step-by-step explanation:

Distribute the y

[tex]5.98xy-5.81y-2.19y[/tex]

Combine like-terms

[tex]5.98xy-8y[/tex]

Due to length restrictions, we kindly invite to read the explanation below for further details on equivalence of trigonometric expressions.

In this problem we find five case of trigonometry expressions whose equivalence must be proved by means of algebra properties and trigonometric formulas. Now we proceed to show the solution for each case:

Case 3:

tan θ · cos θ

(sin θ / cos θ) · cos θ

sin θ

Case 5:

(1 - cos θ) · (1 + cos θ)

1 - cos² θ

sin² θ

Case 6:

(1 + sin θ) · (1 - sin θ)

1 - sin² θ

cos² θ

Case 7:

(sec θ + tan θ) · (sec θ - tan θ)

sec² θ - tan² θ

1

Case 10:

(tan θ + cot θ) / tan θ

1 + cot θ / tan θ

1 + cot² θ

csc² θ

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so the correct answer is the square route of it cause a anylis of a+b=c yup

Step-by-step explanation:

Answer: UTV

Step-by-step explanation:

When you join the lines U, T and V, the number 40 is written between it,

It means it is 40 degrees

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The length and the width of the playground 12 yards and 17 yards respectively.

As per the data given in the question the area of the playground is 204 square yards.

Area = 204 square yards.

The width of the playground is 5 yards longer than its length.

Let the length of the playground be 'l' yards.

Then the width of the playground will be (l + 5) yards.

The formula for the area of the playground is Length × Width.

A = Length × Width

204 = l (l + 5)

204 = [tex]l^{2}[/tex] + 5l

[tex]l^{2}[/tex] + 5l - 204 = 0

[tex]l^{2}[/tex] + 17l - 12l - 204 = 0

l (l + 17) -12 (l + 17) = 0

(l + 17) (l - 12) = 0

(l + 17) = 0 or (l - 12) = 0

l = -17 or l = 12

Length cannot be the negative value.

So the value of the length is 12 yards.

Then width = l + 5

Width = 12 + 5

Width = 17 yards

Therefore length is 12 yards and width is 17 yards.

Option (b) is correct.

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The area of a playground is 204 yd2. The width of the playground is 5 yd longer than its length. Find the length and width of the playground.

a.) length 17 yd, width 22 yd

b.) length 12 yd, width 17 yd

c.) length 22 yd, width 17 yd

d.) length 17 yd, width 12 yd

The number of arrangements of 6 balls with 2 red balls and 2 blue balls, we need to consider the number of ways to choose 2 red balls from the 4 available red balls and the number of ways to choose 2 blue balls from the 4 available blue balls.

These are both combinations, and we can use the formula for combinations to calculate them:

C(n, k) = n! / (k! (n-k)!).

For the red balls, C(4, 2) = 4! / (2! (4-2)!) = 6.

For the blue balls, C(4, 2) = 4! / (2! (4-2)!) = 6.

The total number of arrangements of 6 balls with 2 red balls and 2 blue balls is the product of the number of arrangements for each type of ball:

C(4, 2) * C(4, 2) = 6 * 6 = 36

So, there are 36 arrangements of 6 balls with 2 red balls and 2 blue balls.

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Alex will take 3.75 gallons of fuel to drive five hours to visit his family in city B.

First, let's convert the rate of 60 kilometers per hour to miles per hour:

60 kilometers per hour * (1 mile / 1.6 kilometers) = 37.5 miles per hour

Next, we'll use the rate to find out how many miles Alex will drive in 5 hours:

37.5 miles per hour * 5 hours = 187.5 miles

Now that we know the total distance Alex will drive, we can use the information about the fuel consumption (2 gallons every 50 miles) to calculate the number of gallons of fuel he will need:

187.5 miles / 50 miles per 2 gallons = 3.75 gallons

So, Alex will need 3.75 gallons of fuel to drive five hours to visit his family in city B.

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The ratio of votes for candidate B compared to candidate A is 1.3:1

What is Ratio?

A ratio in mathematics illustrates how many times one number contains another.

If there were a total of 64 votes and 28 votes went to candidate A, then the number of votes for candidate B can be found by subtracting the votes for candidate A from the total number of votes:

64 - 28 = 36

So, candidate B received 36 votes.

To find the ratio of votes for candidate B compared to candidate A, we divide the number of votes for candidate B by the number of votes for candidate A:

36 / 28 = 1.3

Therefore, The ratio of votes for candidate B compared to candidate A is 1.3:1

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a. Adding the same number to two numbers produces the same result. Example: 4 + 3 = 7, 7 + 3 = 10, b. Commutative Property: Order does not matter. Example: 4 + 7 = 7 + 4.

The Density Property of Real Numbers states that between any two real numbers, there are an infinite number of other real numbers. This means that for any two real numbers, no matter how close or far apart they are, there is always a third number between them. An example of this property would be if we have two numbers, 4 and 7. If we add 3 to each of these numbers, we will get the same result. 4 + 3 = 7, and 7 + 3 = 10. This shows that no matter what two real numbers we pick, there will always be a third number between them, and when we add the same number to both of them, we will get the same result. Another property of numbers is the Commutative Property, which states that the order of the numbers doesn’t matter when performing certain operations. For example, when adding two numbers, 4 + 7 = 7 + 4. This means that it doesn’t matter which number comes first when adding. This property applies to other operations as well, such as multiplication, division, and subtraction.

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Answer:

The equation that shows inverse variation is (Choice C) y = (1/8)x.

Step-by-step explanation:

The equation that shows inverse variation is (Choice C) y = (1/8)x.

Answer:

-4

Why? I subtract the numbers. How to do that is by looking at the table. You always use two ordered pairs. Let's choose (-3,12) and (-2,8).

Step 1: Choose two ordered pairs (you can choose any two, it doesn't matter).

Now, subtract the y's together and subtract that x's together. So, what is 12-8? That's obvious, it's 4. Alright, how about -3-(-2)? Well, two negatives make a positive, so the problem is actually -3+2. So, what's that? Correct, -1. And, since slope is y/x, the answer would be -4/1, or -4.

It depends on the thickness of the aluminum bar. Generally, a hacksaw blade with 18 teeth per inch is used to cut off aluminum from 1'' square bar.

The number of teeth a hacksaw blade should have to cut off a piece of aluminum from 1'' square bar depends on the thickness of the aluminum bar.

2. Generally, a hacksaw blade with 18 teeth per inch is used to cut off aluminum from 1'' square bar.

For example, if the aluminum bar being cut is thin (1/8'' or less) then a hacksaw blade with 18 teeth per inch should be used. On the other hand, if the aluminum bar is thicker (greater than 1/8''), then a hacksaw blade with fewer teeth per inch should be used. The fewer teeth per inch the hacksaw blade has, the thicker the aluminum bar it can cut through. It is important to choose the correct hacksaw blade for the job in order to ensure a clean and safe cut.

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It is formatted a bit weird.

u = the radius (im pretty sure)

area of a circle = pi(u)^2

circumference of a circle is 2pi(u)

22/7 = pi

Area = (22/7)(u)^2

Circumference = 2(22/7)u

Check the picture below.

so we know it has a vertex at (2 ,3 ) and it also passes through (-2 , -1), then

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=2\\ k=3\\ \end{cases}\implies y=a(~~x-2~~)^2 + 3\hspace{4em}\textit{we also know that} \begin{cases} x=-2\\ y=-1 \end{cases}[/tex]

[tex]-1=a(-2-2)^2 + 3\implies -4=a(-4)^2\implies -4=16a \\\\\\ \cfrac{-4}{16}=a\implies -\cfrac{1}{4}=a\hspace{10em}\boxed{y=-\cfrac{1}{4}(x-2)^2 + 3}[/tex]

The length of sides BC and XC in the triangle are 8.66 and 10 units respectively

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

Trigonometric ratio is used to show the relationship between the sides and angles of a right triangle.

From the triangle shown, using trigonometric ratio:

sin(30) = 5/XC

XC = 10

Also:

tan(30) = 5/BC

BC = 8.66

The length of BC and XC are 8.66 and 10 units respectively

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the total cost of fencing the garden will be Rs5400.

What is square?

Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognised by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.

area of the garden = 4a  ( a = side )

= 4(18)

= 72m

length of wire required to fence three rounds = 3 × perimeter

= 3 × 72

= 216 m

rate = 25 × 216

= 5400

Hence the total cost of fencing the garden will be Rs5400.

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Answer:

Let's call the travel fee "t" and the hourly fee "h". Then the total cost of a repair, y, can be represented as:

y = t + hx

We can use the two given pieces of information to write two equations and solve for t and h:

2h + t = 100

6h + t = 260

Subtracting the first equation from the second, we get:

4h = 160

Dividing both sides by 4, we get:

h = 40

Substituting this value of h back into the first equation, we get:

2h + t = 100

2(40) + t = 100

80 + t = 100

Subtracting 80 from both sides, we get:

t = 20

So the total cost of a repair, y, as a function of the number of hours spent fixing a leak, x, can be represented as:

y = 20 + 40x

Step-by-step explanation:

Answer:y=40x+20

Step-by-step explanation:

Answer:

C. 4

Step-by-step explanation:

The initial value would be four because that's what the value is at the start of the graph.

Answer:

Option 4
y = 2x + 3

Step-by-step explanation:

Equation of a line in slope intercept form is
y = mx + b
where m = slope and b = y-intercept

Slope m = rise/run = Δy/Δx with Δy = change in y values between any two points on the line and Δx = corresponding change in x values

b is the y-intercept, value of y when x = 0 and indicates the point at which the line crosses the y-axis

Let's take two distinguishable integer points on the line

(0, 3) and (1, 5) are two points

rise = Δy = 5 - 3 = 2
run = Δx = 1 - 0 = 1

So slope = 2/1 = 2

Since y = 3 at x = 0, y-intercept b = 3

Equation of line is
y = 2x + 3

Option 4)

Answer:

4)y=2x+3

You can see this clearly as the y-intercept is 3 and going two spaces up and one to the side is the slope.

Step-by-step explanation: