If m ABD = 61, and m DBC = 59, then m ABC = ? PLS ASAP

The length of the function x = 2y is 2√5 units

According to the given question.

We have a function

x = 2y

Since, we know that the length of the function in the interval [a, b] is given by

l =    [tex]\int\limits^a_b\sqrt{1+(\frac{dx}{dy}) ^{2} } \,dy[/tex]

Where, l is the length of the function.

Now, differentiating the given function x = 2y w.r.t y.

Therefore,

dx/dy = 2

So, the length of the given function x = 2y  from y = -1 to y = 1 is given by

l =   [tex]\int\limits^1_{-1}{\sqrt{1+2^{2} } } \,dy[/tex]

⇒ l =   [tex]\int\limits^1_{-1} {\sqrt{1+4} } \,dy[/tex]

⇒ l =   [tex]\int\limits^1_{-1}{\sqrt{5} } \,dy[/tex]

⇒ l = √5[1 - (-1)]

⇒ l = √5(2)

⇒ l = 2√5

Hence, the length of the function x = 2y is 2√5 units.

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a. Expressing y in terms of x, y = 20/(x + 3)

b. When x = 5, the value of y is 2.5

The question has to do with inverse variation.

Inverse variation is variation in which one quantity varies inversely as the other.

Given that y is inversely as x + 3 and that y = 4 when x = 2.

Since y varies inversely as x + 3, we have

y ∝ 1/(x + 3)

y = k/(x + 3)

When y = 4, x = 3. So

y = k/(x + 3)

4 = k/(2 + 3)

4 = k/5

k = 4 × 5

k = 20

So, y = k/(x + 3)

y = 20/(x + 3)

So, expressing y in terms of x, y = 20/(x + 3)

Since  y = 20/(x + 3)

Substituting x = 5 into the equation, we have

y = 20/(x + 3)

y = 20/(5 + 3)

y = 20/8

y = 5/2

y = 2.5

So, when x = 5, the value of y is 2.5

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Answer:

no solution

Step-by-step explanation: because if it has no variables that are the same it has no solution.

Correct option is D) and E)

(3,7π/6),(3,11π/6)

Point of intersection is the point where two lines or two curves meet each other.

The point of intersection of two lines of two curves is a point.

If two planes meet each other then the point of intersection is a line.

The term "point of intersection" refers to the intersection of two lines. The equations a1x+b1y+c1=0 and a2x+b2y+c2=0, respectively, are used to represent these two lines. The two lines' intersection point is shown in the following figure. The intersection of three or more lines can also be located.

let

5 + 4 sin(θ) = −6 sin(θ)

Then get

θ= -1/2

Then you can make it

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I understand that the question you are looking for is:

On the interval [0, 2π), which points are intersections of r = 5 4 sin(θ) and r = −6 sin(θ)? check all that apply.

A) -3,7/6

B) (-3,11/6)

C) (3,7/6)

D) (3,11/6)

The quantity of the radioactive material which would remain 2 years from now is; 4 grams.

Since, it follows from the task content that after two year, the quantity of the radioactive substance decrease by 1 gram. Consequently, it follows from proportion that the quantity remaining in 2 years from now is; 5-1 = 4 grams.

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Answer:

I hope I've finally done justice to it.

Step-by-step explanation:

[tex]y=-5x^2 \sqrt{x}[/tex]

[tex]y=-5x^2(x)^\frac{1}{2}[/tex]

[tex]y=-5( {x}^{2 + \frac{1}{2} }) = - 5 {x}^{ \frac{5}{2} } [/tex]

[tex] \frac{dy}{dx} = - 5( \frac{5}{2}) {x}^{ \frac{5}{2} - 1 } [/tex]

[tex]\frac{dy}{dx} = ( \frac{ - 25}{2}) {x}^{ \frac{3}{2} } [/tex]

[tex]\frac{dy}{dx} = ( \frac{ - 25}{2}) \sqrt[3]{ {x}^{2} } [/tex]

[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=562\\ r=5 \end{cases}\implies 562=\cfrac{\pi (5)^2 h}{3}\implies 1686=25\pi h \\\\\\ \cfrac{1686}{25\pi }=h\implies 21.47\approx h[/tex]

Answer:

x(x-1)^2

Step-by-step explanation:

x(x^2-2x+1)

x(x-1)(x-1)

(x-1)(x-1)=(x-1)^2

The number of ways or permutations to select five unordered elements from a set with three elements when repetition is allowed is 243.

According to the given question.

The total number of elements, n = 3

The number of elements to be selected at a time when repetition is  allowed, r = 5

Since, we know that " the number of ways or permutations of n things taken r all at a time, when repetition of things are allowed, is [tex]n^{r}[/tex].

Therefore,

The number of ways or permutations to select five unordered elements from a set with three elements when repetition is allowed

= [tex]3^{5}[/tex]

= 243

Hence, the number of ways or permutations to select five unordered elements from a set with three elements when repetition is allowed is 243.

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The algebraic expression of the statement is 4x + 6

The statement is given as:

The sum of four times a number and six

Rewrite as:

The sum of 4 times a number and 6

Let the number be x

So, we have

The sum of 4 times x and 6

Evaluate the product

The sum of 4x and 6

Evaluate the sum

4x + 6

Hence, the algebraic expression of the statement is 4x + 6

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Answer:

-13x²+24x+6

Hope this helps:)

This is reverse percentage

8.4% = 420

÷8.4 both side

1% is now 50

1% =50

x100

100% is 5000

Check:

8.4/100 = 0.084 our decimal multiplier

5000 x 0.084 = 420

Thus, x is 5000

Hope this helps!

Answer: i believe the answer is 26

Step by step explanation

Total no. of observation = (12+13) = 25

Median = Average of 18/2 observation + (18/2+1)

=1/2 (12th observation + 13 observation)

1/2 × (25 +27) = 1/2 × 52

=26

To solve the given quadratic equation, a² - 5 = -2, the first step we need to do is to represent it in the standard form by adding 2 to both sides.

A quadratic equation is solved using the quadratic formula, [tex]x = \frac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex], when the equation is in the standard form, ax² + bx + c = 0, where, a, b, and c, are real numbers.

In the question, we are asked for the first step in solving a² - 5 = -2.

We can see that the provided equation is quadratic in the variable a.

To solve, the equation, we first need to represent the given equation in the standard form, ax² + bx + c = 0, where, a, b, and c, are real numbers.

To represent it in the standard form, we add 2 to both sides of the equation, to get a² - 5 + 2 = -2 + 2, or, a² - 3 = 0, which is a standard quadratic equation in the variable a.

Thus, to solve the given quadratic equation, a² - 5 = -2, the first step we need to do is to represent it in the standard form by adding 2 to both sides.

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In the hypothesis, based on the 90% confidence interval, (0.02, 0.12), there is convincing evidence that the new formula of laundry detergent is better because the interval is entirely above 0

Let's define the null hypothesis and alternative hypothesis first.

H0:p1-p2=0

Ha:p1-p2>0

Also, 90% CI is (0.02,0.12), we know that if the 0 of the null hypothesis is not in the confidence interval then we reject the null hypothesis.

In the given scenario 0 is not within the given interval, hence we reject the null hypothesis and accept the claim that new detergent A cleans better.

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Answer:

The number is 72.

Step-by-step explanation:

Let the number be xy.

x = y + 5

10x + y - 2(10y + x) = 0.25(10x + y)

10x - 2x + y - 20y = 2.5x + 0.25y

5.5x - 19.25y = 0

Substituting for x:

5.5y + 27.5  - 19.25y = 0

-13.75y = -27.5

y = 2.

So x = 2 + 5 = 7.

Using it's concept, the probability a person tests positive who does not actually have Tuberculosis is:

c. 49/148.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there are 198 + 98 = 296 people who test positive, which is the number of total outcomes, and of those, 98 do not have the disease, which is the number of desired outcomes. Hence the probability is given by:

p = 98/296 = 49/148.

Which means that option c is correct.

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The probability a person tests positive who does not actually have Tuberculosis is 1/100

The probability is given as:

The probability a person tests positive who does not actually have Tuberculosis.

This is a conditional probability, and it can be calculated using

P = n(Tests positive | Does not have Tuberculosis)/n(Does not have Tuberculosis)

Using the given table of values, we have:

P = 98/9800

Evaluate the quotient

P = 1/100

Hence, the probability a person tests positive who does not actually have Tuberculosis is 1/100

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Using it's concept, we have that the probability that both the first digit and the last digit of the three-digit number are even numbers is 2/27.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Considering that there are six numbers, out of which 4 are odd and 2 are even, we have that:

Hence the desired probability is:

p = 1/3 x 2/3 x 1/3 = 2/27.

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5. m∠C = 95°

6. m∠C = 70°

7. The other acute angle in the right triangle = 70°

8. m∠C = 70°

9. m∠C = 60° [equilateral triangle]

10. Measure of the exterior angle at ∠C = 110°

11. m∠B = 70°

12. m∠Z = 70°

A triangle is a 3-sided polygon with three sides and three angles. The sum of all its interior angles is 180 degrees. Some special triangles are:

5. m∠C = 180 - 50 - 35 [triangle sum theorem]

m∠C = 95°

6. m∠C = 180 - 25 - 85 [triangle sum theorem]

m∠C = 70°

7. The other acute angle in the right triangle = 180 - 90 - 25 [triangle sum theorem]

The other acute angle = 70°

8.  m∠C = 180 - 55 - 55 [isosceles triangle]

m∠C = 70°

9. m∠C = 60° [equilateral triangle]

10. Measure of the exterior angle at ∠C = 50 + 60

Measure of the exterior angle at ∠C = 110°

11. m∠B = 115 - 45

m∠B = 70°

12. m∠Z = 180 - 35 - 75

m∠Z = 70°

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The interpretation of f(30) is the distance travelled after 30 minutes

The function is given as:

A function representing distance (feet) as a function of time (minutes),

This means that, the dependent variable is the distance and the time is the independent variable

This in other words means that:

x = time

f(x) = distance

So, the interpretation of f(30) is:

The distance travelled after 30 minutes

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Answer:

[tex]\dfrac{8y-43}{(y-1)(y-8)}[/tex]

Explanation:

[tex]\rightarrow \dfrac{5}{y-1} +\dfrac{3}{y-8}[/tex]

make the denominators similar

[tex]\rightarrow \dfrac{5(y-8)}{(y-1)(y-8)} +\dfrac{3(y-1)}{(y-8)(y-1)}[/tex]

Join both the fraction

[tex]\rightarrow \dfrac{5(y-8)+3(y-1)}{(y-1)(y-8)}[/tex]

simplify the expression

[tex]\rightarrow \dfrac{5y-40+3y-3}{(y-1)(y-8)}[/tex]

[tex]\rightarrow \dfrac{8y-43}{(y-1)(y-8)}[/tex]

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's simplify ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{5}{y - 1} + \cfrac{3}{y - 8} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{5(y - 8) + 3(y - 1)}{(y - 1)(y - 8)} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{5y -40 + 3y - 3}{y {}^{2} - y - 8y + 8} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{8y -43}{y {}^{2} - 9y + 8} [/tex]

The quantity of meat and cheese sold by the deli according to the description accounts in the task content are; 4.5 and 2.5 pounds respectively.

The quantity of meat sold by the deli as represented by the variable X in the task content can be calculated by solving the systems of equations.

The quantity of cheese sold by the deli as represented by the variable y in the task content can be calculated by solving the systems of equations.

Consequently, solving the system of equations by means of substitution, we have;

y = (30.50-4x)/5

Hence, we have;

11x + 14((30.50-4x)/5) = 84.50

x = 4.5 pounds of meat and

y = 2.5 pounds of cheese.

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Answer: 77 - 10 = 67, and the additive inverse of 77 - 10 is 77 + 10. 77 + 10 = 87.

Hope this helps! This question was kind of confusing for me, because I didn’t understand why you said to add 77 - 10… is this is the incorrect answer sorry your question was worded weird

331.5 inches²  is the area of the octagon, rounded to the nearest square inch.

What is octagonal in shape?

Solving for an area of a regular octagon, we can make use of the formula shown below:

Area = 1/2 × apothem × perimeter

In this problem, the following values were given such as:

Apothem = 10 inches

Perimeter = 66.3 inches

Put the values in the formula

Area = 1/2 × 10 × 66.3

Area = 331.5 inches²  

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Answer: C). 332 in.2

Step-by-step explanation:

on edg

The equation of the line of best fit, using the least square method is v = 2.19t + 6.7, making the 2nd option as the right choice.

In the question, we are asked to find the equation of the line of BEST FIT for the given scatter plot.

We let the time be the independent variable x, and velocity is the dependent variable y.

We find the line of best fit using the least square method.

First, we calculate the mean:

Now, we find the slope of the line of best fit, using the formula:

m = {∑(x - μ(x))(y - μ(y))}/{∑(x - μ(x))²}.

Taking value from the tables, which is attached, we get:

m = 239.35/109.2683333 = 2.190479096.

Now, we calculate the y-intercept of the line of best fit, using the formula:

b = μ(y) - m.μ(x),

or, b = 20.5 - 2.190479096*6.283333 = 6.736489681.

Now, the equation of the line of best fit, in the form of y = mx + b, can be written as, y = 2.190479096x + 6.736489681, which on approximation, and making y as v, the velocity, and x as t, the time, we get: v = 2.19t + 6.7.

Thus, the equation of the line of best fit, using the least square method is v = 2.19t + 6.7, making the 2nd option as the right choice.

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The correct option is B.

Rank

The RANK function in a Microsoft Excel spreadsheet enables users to order the various pieces of data by their numerical values. By entering an absolute value for the range of cells the user wants to rank, they can also use the rank function. If an absolute value is not specified, the program's auto-formula may cause the rank of the various cells to alter.

A spreadsheet is a computer program used for organizing, organizing, analyzing, and storing tabular data. Spreadsheets were created as electronic alternatives to paper accounting worksheets. Data typed into table cells serves as the program's input.

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Answer:

n=2

Step-by-step explanation:

Create an equation.

9n=18

Divide 9 from both sides.

9n/9=18/9

n=2

Hope this helps!

Answer:

-8

Step-by-step explanation:

Remember pemdas

7 - 3*(10:2):1 =

7-3*5:1=

7-15:1=

7- 15=

-8

Answer:

-8

Step-by-step explanation:

7-3(10:2):1

We always solve what's in parenthesies first.

7 - 3*5:1

Multiplication and division have equal priority, so we solve that part from left to right:

7 - 15:1 =

= 7 - 15 =

= -8

Answer:

Step-by-step explanation:

The equation of a circle in standard form is (x - h)² + (y - k)² = r² ,

where (h, r) are coordinates of a center of a circle and "r" is a radius of a circle.

a² ± 2ab + b² = (a ± b)²

~~~~~~~~~~

x² + y² - 2x - 10y + 17 = 0

To rewrite the equation in standard form, need to group terms with the same variables, move the constant to the right side and complete the square for each grouping:

(x² - 2x) + ( y² - 10y) = - 17

( x² - 2x + 1 ) + ( y² - 10y + 25 ) = - 17 + 1 + 25

( x - 1 )² + ( y - 5 )² = 9

( x - 1 )² + ( y - 5 )² = 3²

The center of the given circle is

( 1 , 5 )

The radius of the given circle is

3 units