PLEASE HELP ME 50 points

The length of side BD is, 40

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In figure,

⇒ AB = 20

⇒ BC = 10

In triangle ABC;

We can find the side AC by using Pythagoras theorem as;

⇒ AB² = AC² + CB²

⇒ 20² = AC² + 10²

⇒ 400 - 100 = AC²

⇒ AC² = 300

⇒ AC = 10√3

Now, By using proportional relationship in triangles ABC and triangle ACD;

⇒ Hypotenuse / Short

⇒ AB / BC = AD / AC

Substitute all the values, we get;

⇒ 20 / 10 = AD/10√3

⇒ 2 × 10√3 = AD

⇒ AD = 20√3

In triangle ACD;

We an find CD by using Pythagoras theorem as;

⇒ AD² = AC² + CD²

⇒ (20√3)² = (10√3)² + CD²

⇒ 1200 - 300 = CD²

⇒ CD² = 900

⇒ CD = 30

Hence, Length of BD is,

⇒ BD = BC + CD

⇒ BD = 10 + 30

⇒ BD = 40

Thus, The length of side BD is, 40

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Answer:

school who study French also study Japanese, do more students at the school study french than Japanese? (1) 16 students at

The statement can be proved by the property of similarity and adjacent angles of a line property.

An orthocenter can be defined as the point of intersection of altitudes that are drawn perpendicular from the vertex to the opposite sides of a triangle. In a triangle, it is that point where all the three altitudes of a triangle intersect.

Given here: A triangle ABC with an orthocenter O.

Now let BD and A-F be the altitudes that intersect on the sides of AC and BC

then we have in the triangles AOD and ACF we have

∠ADO=∠AFC=90 and ∠A is common and therefore ΔAOD≈ΔACF

thus ∠AOD=∠ACF=∠ACB

now ∠ACB and ∠AOB lie on a line BD thus we must have

∠ACB +∠AOB=180

Hence, The statement  ∠ACB +∠AOB=180 is proved.

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An inequality to represent the regular price of snacks, if i can buy using the coupon, x ≤ $13

Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.

We use these symbols to represent inequalities, '>' , '<', '≥', '≤'

Given that,

There are two coupons available, $8 and a $5 off on buying snacks

Let's call the regular price of the snacks "x".

Since you have a $5 off coupon,

the price you would actually pay would be x - $5.

And since you only have $8, the price you pay for the snacks cannot be greater than $8:

x - $5 ≤ $8

Adding $5 to both sides:

x ≤ $13

So, the regular price of the snacks must be less than or equal to $13 if you want to use the coupon and still have enough money to pay for them.

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The time needed when the bacteria count reaches 8621 is approximately 19.97 hours.

The composite function of the bacteria count in a refrigerated food product with respect to time can be found by combining the two functions given. The first function is the number of bacteria in the food, which is given by , where is the temperature of the food. The second function is the temperature of the food when it is removed from the refrigerator, which is given by , where is the time in hours. Combining these two functions, we can form the composite function , where is the number of bacteria and is the time in hours.

To find the time when the bacteria count reaches 8621, we can rearrange the composite function to solve for . Doing this gives us , which can be solved for to obtain . Therefore, the time needed when the bacteria count reaches 8621 is approximately 19.97 hours.

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The largest possible Norman window with a perimeter of 43 feet has an area of approximately 324.71 square feet

Let the width of the rectangle be x. Then, the height of the rectangle is (43 - 2x)/2, and the radius of the semicircle is x. The area of the Norman window is then given by:

A = x * (43 - 2x)/2 + (π/4) * x^2.

We want to maximize A subject to the constraint that the perimeter is 43 feet, which we have expressed as:

x + (43 - 2x)/2 = 43/2.

Solving for x, we find x = 12. The height of the rectangle is then 15.5, and the area of the Norman window is:

A = 12 * 15.5 + (π/4) * 12^2 = 180 + 144π.

So the largest possible Norman window with a perimeter of 43 feet has an area of approximately 324.71 square feet.

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Since the values of [tex]\hat{p}_1, \hat{p}_2, n_1[/tex], and n_2 are not given, it is not possible to determine the exact 95% confidence interval estimate.

A 95% confidence interval estimate of the difference between the proportion of women and men who trust recommendations made on a social networking site can be calculated using the formula for a difference in proportions:

[tex]$$\hat{p}_1 - \hat{p}_2 \pm z^* \sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}$$[/tex]

where [tex]$\hat{p}_1$[/tex] and [tex]$\hat{p}_2$[/tex] are the sample proportions of women and men who trust recommendations, respectively, n_1 and n_2 are the sample sizes of women and men, and z^* is the critical value from the standard normal distribution for a 95% confidence level (approximately equal to 1.96).

Since the values of [tex]\hat{p}_1, \hat{p}_2, n_1[/tex], and n_2 are not given, it is not possible to determine the exact 95% confidence interval estimate.

However, this formula can be used to calculate the estimate once the sample data is available.

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The length of the sides a and b are respectively 19.67 and 20.21 approximately to 2 decimal place, using the sine rule.

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

For the triangle ABC, by sine rule;

a/sinA = b/sinB = c/sinC

We first derive the angle A as follows:

75° + 35° + A = 180° {sum of interior angles of a triangle}

A = 180° - 110°

A = 70°

Thus by sine rule;

b/sin75° = 12/sin35°

b = (12× sin75°)/sin35° {cross multiplication}

b = 20.21

a/sin70° = 12/sin35°

a = (12× sin70°)/sin35° {cross multiplication}

a = 19.67

Therefore, the length of the sides a and b are respectively 19.67 and 20.21 approximately to 2 decimal place, using the sine rule.

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A researcher should follow all of the rules when presenting quantitative data with a histogram. This includes starting the frequency/proportion at zero, putting a break in the y-axis, and putting gaps between intervals.

When creating a histogram, there are several important rules to follow in order to ensure that the data is accurately presented. These rules include starting the frequency/proportion at zero, putting a break in the y-axis, and putting gaps between intervals. Additionally, the bin width should be uniform and the x-axis should have a label. Furthermore, the histogram should have a title that describes the data being presented. Finally, the researcher should be sure to include a legend that explains the different colors and symbols used in the histogram. Following these guidelines will ensure that the data is accurately and effectively presented.

The complete question is :

When presenting quantitative data with a histogram, which of the following rules should a researcher follow? Start the frequency/proportion at zero. Put a break in they-axis. Put gaps between intervals. All of the above. None of the above.

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1. The ordered pair (1, 5) is a solution to the system of equations.

2. The ordered pair (-2, 0) is NOT a solution to the system of equations.

To determine if the ordered pair (1, 5) is a solution to the system of equations, we substitute the values into the equations and see if they hold true.

-5(1) + 6(5) = 25

25 = 25 (holds true)

-7(1) + 8(5) = 33

33 = 33 (holds true)

Since both equations hold true for the values of m=1 and n=5, we can conclude that the ordered pair (1, 5) is a solution to the system of equations.

To determine if the ordered pair (-2, 0) is a solution to the system of equations, we substitute the values into the equations and see if they hold true.

8(-2) - 3(0) = -16

-16 = -16 (holds true)

-9(-2) - 2(0) = 50

4 ≠ 50 (does not hold true)

Since one of the equations does not hold true for the values of x=-2 and y=0, we can conclude that the ordered pair (-2, 0) is NOT a solution to the system of equations.

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[tex]\huge\begin{array}{ccc}y=\dfrac{4}{x}&\text{for}&x\neq0\end{array}[/tex]

We have:

[tex]xy=4[/tex]

We need:

[tex]y=?[/tex]

Let's transform the equation:

[tex]xy=4\\\\\dfrac{xy}{x}=\dfrac{4}{x}\qquad\text{for}\ x\neq0\\\\\boxed{y=\dfrac{4}{x}}[/tex]

The equation of the line through the point(6,7) and (2,-1) is y = -2x + 3

The formula for the equation of a line is expressed as;

y = mx + c

Such that;

From the information given, the slope is expressed as;

Slope = y₂ -y₁/x₂ - x₁

Substitute the values

Slope = 8/-4 =-2

Then, substitute the values

-1 = -4 + c

collect like terms

c = 3

Hence, the equation is y = -2x + 3

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The number of hamburgers sold was 275.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Hamburgers = x

Cheeseburgers = y

There were 58 fewer cheeseburgers sold than hamburgers.

This means,

y = x - 58 ______(1)

A local hamburger shop sold a combined total of 492 hamburgers and cheeseburgers on Saturday.

This means,

x + y = 492 _______(2)

Substituting (1) in (2)

x + y = 492

x + x - 58 = 492

2x = 492 + 58

2x = 550

x = 275

Thus,

275 hamburgers were sold.

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Answer:

R10.00

Step-by-step explanation:

Purchase:

10 apples at R2.50 each = 10 × R2.50 = R25.00

He spent R25.00 on the 10 apples.

Sales:

25% discount on R4.00 is 0.75 × R4.00 = R3.00

5 apples at R4.00 = 5 × R4.00 = R20.00

5 apples at R3.00 = 5 × R3.00 = R15.00

Total sales = R20.00 + R15.00 = R35.00

Profit:

R35.00 - R25.00 = R10.00

Jackson could use control theory to explore how to design and analyze systems that are able to maintain a desired state or behavior in the face of varying environmental conditions and disturbances.

One line of research Jackson could pursue to explore the scientific goal of control is control theory. Control theory is the study of how to design and analyze systems that are able to maintain a desired state or behavior in the face of varying environmental conditions and disturbances. Control theory uses mathematical models to describe the behavior of a system and the effects of control inputs on the system. For example, a simple linear control system can be modeled using the transfer function, which is a mathematical expression that describes how a system responds to an input signal. The transfer function can then be used to calculate the output of the system in response to different inputs. Jackson could use control theory to explore how to design and analyze systems that are able to maintain a desired state or behavior.

Jackson could use control theory to explore how to design and analyze systems that are able to maintain a desired state or behavior in the face of varying environmental conditions and disturbances.

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Complete question: Which of the following lines of research should Jackson pursue in order to explore the scientific goal of control?

The percentage of the combined volume of 4 equal spheres stacked in a tetrahedral arrangement with a triangular base will be ~43.30%

Given that the normal tetrahedron's (Vt) side-S volume,

Vt = S3/(6*(square(2))

Considering a regular tetrahedron with side S and the radius (r) of a sphere,

the proportion of the total volume of four identical spheres stacked in a tetrahedral pattern with a triangular base

r = (S) / (2 + (2*sqrt(6))

S =[tex](2 + 2(sqrt(6)*r)[/tex]

S = r times 6.898979486

for S = 1

r = ~0.144948974

Sphere volume = (4*pi*r3)/3

Vsphere = 0.012756574 (Vs).

Vs = [tex]((2+(2*sqrt(6)/(2+(2*sqrt(6)3/3[/tex]

Vs equals 0.012756574 when S = 1.

4 spheres' volume equals 0.051026296.

Tetrahedron volume = Vt = S3/(6*(sqrt(2))

When S = 1, Vt equals 0.11785113.

4Vs/Vt = ~0.432972475

4Vs/Vt = ~43.30%

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The complete question:

What is the percentage of the combined volume of 4 equal spheres stacked in a tetrahedral arrangement with a triangular base, inscribed within a regular tetrahedron, to the volume of the tetrahedron?

The number of words Gillan can read in 1 minute is,  165

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.

Given that,

Gillan read 3,135 words in 19 minutes

The number of words read each minute = w

Now, it has given,

Total words = 3135

Time taken = 19 minutes

For words per minute,

we need to take ratio of total words and total time taken,

Ratio =  Total words/Time taken

         =   3135/19

         =   165

Hence, the number of words in 1 minute is 165

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The coordinates for hector's position are (137.78, 47.72) for (x, y)

Tre's position as the point on the pitcher's mound (42.78, 42.78). Hector is approximately 95 feet away from the pitcher's mound horizontally (x axis).

We must solve for the correct x-coordinate because we already have the correct y-coordinate.

Now all that is required of you is to write down the coordinates.

The coordinates of Hector are (137.72, 47.78).

The coordinate values of a point on a graph can be represented by (x, y), with x being referred to as the abscissa, indicating the horizontal distance from the origin or x-axis, and y being referred to as the ordinate, signifying the vertical distance from the origin or the x-axis.

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Complete Question:

Hector was standing halfway between first and second base, at the grass line. The

grass line is 95 feet from the pitcher's mound.

6. Calculate the coordinates for Hector's position. [Note: We can assume that 95

feet is an approximately horizontal distance from the pitcher's mound to the grass

line.] (2 points: 1 for x, 1 for y)

Hector was standing at the coordinate ( __, _).

Answer: 0>-6

Step-by-step explanation:

2x+8>2x+2     Distribute and subtract numbers.

2x+8-8 > 2x+2-8  Subtract eight from both sides.

2x > 2x-6  Then, simplify the expression. Subtract the numbers.

Answer: 0>-6

Hoping this helps!

The correct solution of the expression is, 31/40.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

The expression is,

⇒ 2/5 + 3/8

Now, We can add the fraction as;

⇒ 2/5 + 3/8

⇒ (16 + 15) / 40

⇒ 31/40

Thus, The solution of fraction = 31/40

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The term of the sequence is Tn = 200[(e^0.09959)^1/12]^(n-1)

From the question, we have the following parameters that can be used in our computation:

200 + 200(e^0.09959)^1/12 + 200(e^0.09959)^2/12 + 200(e^0.09959)^3/12 + ... + 200(e^0.09959)^58/12 + 200(e^0.09959)^59/12

In the above sequence, we have

T1 = 200

T2 = 200(e^0.09959)^1/12

So, the common ratio (r) is

r = 200(e^0.09959)^1/12/200

Evaluate

r = (e^0.09959)^1/12

The sequence is then calculated as

Tn = T1 * r^(n - 1)

Substitute the known values in the above equation, so, we have the following representation

Tn = 200[(e^0.09959)^1/12]^(n-1)

Hence, the term is Tn = 200[(e^0.09959)^1/12]^(n-1)

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This question is based on the concept of statistics. Hence, the correct option is  (c) The mean of all sample proportions of those who make a donation from all random samples of 100 people contacted by phone is 0.05.

A national charity contacted 100 randomly selected people by phone, and 7 percent of those contacted made a donation to the charity. The population proportion p=0.05. For samples of size 100.

According to the question of statistics,

Mean of  sampling distribution of the sample proportion = p (Population proportion.)

It is given that, the population proportion of those who make donation when contacted by phone is known to be p=0.05.

Thus, Mean = p = 0.05

Hence, the correct option is  (c) The mean of all sample proportions of those who make a donation from all random samples of 100 people contacted by phone is 0.05.

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The function 4^n + 15n - 1  is divisible by 9 if n is a natural number.

A number is divisible by 9 if the sum of its digits is divisible by 9.

The given number = 4^n + 15n - 1

so we are going to test different natural numbers as n, to check if the resulting number is divisible  by 9.

let n = 1

4^(1) + 15(1) - 1 = 4 + 15 - 1 = 18

sum of 18 = 1 + 8 = 9

9 is divisible by 9

let n = 2

4^(2) + 15(2) - 1 = 16 + 30 - 1 = 45

sum of 45 = 4 + 5 = 9

9 is divisible by 9

Thus, if is proved that 4^n + 15n - 1 is divisible by 9 if n is a natural number. ​

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The transformations to prove the relationships between the angles formed by parallel lines and a transversal are as follows

10. A translation of [tex]\overleftrightarrow{BF}[/tex] to [tex]\overleftrightarrow{AD}[/tex] and rotation of the image, indicates that the alternate interior angles ∠3 and ∠6 are congruent

11. The translation of [tex]\overleftrightarrow{BF}[/tex] to [tex]\overleftrightarrow{AD}[/tex], and the linear pair angles, ∠3 and ∠1, indicates that the same-side interior angles ∠3 and ∠5 are supplementary

Alternate interior angles are angles formed in the interior part but on opposite side of the common transversal to (two) parallel lines.

10. To prove that alternate interior angles are congruent using (rigid) transformations, the specified parameters for the parallel lines [tex]\overleftrightarrow{BF}[/tex] and [tex]\overleftrightarrow{AD}[/tex], are used as follows;

[tex]\overleftrightarrow{BF}[/tex] ║ [tex]\overleftrightarrow{AD}[/tex]

The alternate interior angles are ∠3 and ∠6

A transformation that can be used to prove that the alternate interior angles, ∠3 and ∠6 are congruent is the translation of the line [tex]\overleftrightarrow{BF}[/tex] along the transversal [tex]\overleftrightarrow{AB}[/tex] to coincide with the line [tex]\overleftrightarrow{AD}[/tex], such that the the image of angle ∠3 following the translation is angle ∠7

Angle ∠3 is then indicated to be congruent to ∠7

∠3 ≅ ∠7

Rotating the resulting figure, 180°, we get, the image of angle ∠3, (∠7) is congruent to ∠6, ∠7 ≅ ∠6

Therefore, by transitive property of congruency, ∠3 is congruent to ∠6

11. The parallel sides are; [tex]\overleftrightarrow{BF}[/tex] and [tex]\overleftrightarrow{AD}[/tex]

[tex]\overleftrightarrow{BF}[/tex] ║ [tex]\overleftrightarrow{AD}[/tex]

The translation of [tex]\overleftrightarrow{BF}[/tex] to [tex]\overleftrightarrow{AD}[/tex] indicates that ∠1 is congruent to ∠5

∠1 ≅ ∠5

∠1 = ∠5, (definition of congruency)

∠3 and ∠1 are linear pair angles, therefore, angle ∠3 and ∠1 are supplementary angles

∠3 + ∠1 = 180° (definition of supplementary angles)

∠3 + ∠5 = 180° (substitution property)

Therefore, Same-side interior angles, angle ∠3 and angle ∠5 are supplementary angles by definition of supplementary angles

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The solution is Option C.

The value of the equation is y' = y/2x

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

y² = cx   be equation (1)

Now , dividing by x on both sides of the equation , we get

c = y²/x

Differentiating the equation with respect to x , we get

0 = ( x ( 2yy' ) - y² ) / x²

Multiply by x² on both sides of the equation , we get

x ( 2yy' ) - y² = 0

Adding y² on both sides of the equation , we get

y² = x ( 2yy' )

Divide by 2xy on both sides of the equation , we get

y' = ( y² ) / 2xy

y' = y/2x

Hence , the equation is y' = y/2x

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Union of set A and set B' is A ∪ B' = {a, c, e, f, g}      

What is union of sets?

Union of two or more sets is the set containing all the elements of the given sets. Union of sets can be written using the symbol “⋃”

Given sets,

U = {a, b, c, d, e, f, g}

A = {a, c, e, g}

B = {a, b, c, d}

⇒ B' = {e, f, g}

A ∪ B' =  {a, c, e, g} ∪ {e, f, g}

A ∪ B' =  {a, c, e, f, g}          

Hence, A U B = {a, c, e, f, g} which union of both sets.

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Answer:

1. Rational

2. False

Step-by-step explanation:

1. You will always get a rational number when you add, subtract, multiply, or divide rational numbers.
2. All whole numbers, integers, and natural numbers are rationals, but not all rational numbers are integers, natural numbers, or whole numbers.
Hope it helps!

The least positive integer n for which [tex]$\triangle A_nB_nC_n$[/tex] is obtuse is 15.

Since the angles of[tex]$\triangle A_0B_0C_0$[/tex]  are [tex]$59.999^\circ$, $60^\circ[/tex]  and [tex]$60.001^\circ$[/tex], the triangle is very close to being equilateral. Therefore, each time an altitude is drawn from one of the vertices, the triangle will become more acute, and it will take many iterations before an obtuse triangle is formed. The least positive integer n for which [tex]$\triangle A_nB_nC_n$[/tex]  is obtuse is 15. To confirm this, we can use the Law of Cosines. For [tex]$\triangle A_15B_15C_15$[/tex] , we have [tex]$A_{15}B_{15} = 90 - 60.001 = 29.999$ and $B_{15}C_{15} = 90 - 59.999 = 30.001$[/tex]. Therefore,  [tex]$A_{15}C_{15}^2 = 29.999^2 + 30.001^2 - 2(29.999)(30.001)\cos \angle A_{15}B_{15}C_{15} = 899.998^2$[/tex] . Since [tex]$A_{15}C_{15}^2 > 899.997^2$, $\angle A_{15}B_{15}C_{15}$[/tex] is obtuse, and therefore the answer is (E) 15.

The least positive integer n for which [tex]$\triangle A_nB_nC_n$[/tex] is obtuse is 15.

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The lateral surface area of a rectangular prism is 2(l + w)h sq units.

A rectangular prism is a three-dimensional shape, that has six faces (two at the top and bottom and four are lateral faces).

The lateral surface area of a rectangular prism is given by

Where l, w, and h are the length, width, and height, respectively. To find the lateral surface area, we need the values of l, w, and h.

Without these values, it is not possible to determine the lateral surface area of the rectangular prism.

Therefore, the lateral surface area of a rectangular prism is 2(l + w)h sq units.

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