Given BD is the segment bisector of AC, complete the flowchart proof below. Note
that the last statement and reason have both been filled in for you.
D

The width of the dog run is 20 feet.

In the given problem, the length of the dog run is given as 30 feet.

The area of the dog run is also given as 240 square feet.

Using the formula for the area of a rectangle (A = lw), we can solve for the width (w).

Rearranging the formula, we have w = A / l.

Plugging in the values, we get w = 240 / 30 = 8 feet.

Since the width is given as (30 minus x) feet, we can set up an equation:

30 - x = 8. Solving for x, we find x = 22.

Therefore, the width of the dog run is 20 feet (30 - 22 = 8).

In this problem, the length and width of the dog run are defined by the dimensions of the fence being built around it.

The area of the dog run is given as 240 square feet.

By using the formula for the area of a rectangle, we can solve for the width. We are also given that the length is 30 feet.

Setting up an equation with the given width (30 minus x) and solving for x, we find that x is equal to 22.

This means that the width of the dog run is 8 feet. The main answer to the problem is that the width of the dog run is 20 feet (30 - 22 = 8).

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Answer:

Step-by-step explanation:

search it up

Answer: 20, 40, 60, 80, 100,....

Step-by-step explanation:

Given that :

It is possible to create teams of 4 for a relay race with no student leftover

Also,

It is possible to create teams of 5 for dodgeball with no student left over from the same class

To deduce the possible number of students in the class, then the number of students should be a multiple of both 4 and 5

Multiples of 4 include = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100,....

Multiples of 5 : 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100,....

Multiples common to both 4 and 5 : 20, 40, 60, 80, 100,....

Answer:

11.06

Step-by-step explanation:

The value of y is 4√3

Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.

Also , the ratio of corresponding sides of similar triangles are equal.

There are two triangles that are similar

Therefore;

y /16 = 4/y

y² = 48

y = √48

y = √16 × √ 3

y = 4√3

Therefore, the value of y is 4√3

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y = -2x is line parallel to given line.

What is line?

A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that are endlessly stretched in the opposing directions.

Main body:

The slope-intercept form is

y=mx+b, where

m is the slope and b is the y-intercept.

y=mx+b

Using the slope-intercept form, the slope is −2.

m=−2

To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.

Use the slope −2 and a given point (0,0) to substitute for

x₁ and y₁ in the point-slope form

y−y₁=m(x−x₁)

, which is derived from the slope equation

m=(y₂−y₁)/(x₂−x₁).

y−(0)=−2*(x−(0))

Simplify the equation and keep it in point-slope form.

y+0=−2⋅(x+0)

Solve for y.

y=−2x

Hence y = -2x is line parallel to given line.

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Answer:

1. x=1.25; y=1.75

2. x=15; y=4

3. x=3; y=2

Step-by-step explanation:

Because of the parallel lines, you're working with similar triangles. Therefore, the side lengths of the smaller triangle (in each figure) are proportional to those of the larger. Set up a proportion for x and solve; then for y.

Ex: \(\frac{10}{8}=\frac{x+5}{5}\)  ⇒  50=8(x+5)=8x+40  ⇒  10=8x  ⇒  x=1.25

     \(\frac{10}{8}=\frac{7+y}{7}\)  ⇒  35=28+4y  ⇒  7=4y  ⇒  y=1.75

NOTE: Be sure to set up the correct corresponding sides!

When three college students are randomly selected, the probability that ALL three buy their textbooks online is 0.227

The probability that at least one purchases their textbooks online is 1.

As per the question the probability of students purchase their textbooks online 61%.

\(=\frac{61}{100}\)

p = 0.61.

So, failure = 1 - 0.61 = 0.39

q = 0.39

When 3 students are selected(n = 3)

We know that, \($$p(x)={ }^n c_x p^x q^{n-x}$$\)

So, probability that all of them to purchase

\($$\begin{aligned}&(x=3) \\& p(3)={ }^3 c_3(0.61)^3(0.39)^{3-3} \\& p(3)=0.22698\end{aligned}$$\)

When 5 students are selected (n = 5)

And probability that at least one purchases books online

\(=P(x=1)+P(x=2)+P(x=3)$ $+P(x=4)+P(x=5)$\)

Now we know that probability of all equal to 1.

\(P(0)+P(1)+P(2)+P(3)+P(4)+P(5)=1\)

So, we can simply write

\($$\begin{aligned}P & =1-p(x=0)+p(x=1) \\& =1-\left[{ }^5 C_0(0.61)(0.35)^{50}+{ }^5 C_1(0.61)^1(0.39)^{5-1}\right] \\& =1-0.00902-0.07056 \\P& =0.92042\end{aligned}$$\)

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Answer:

8 weeks

Step-by-step explanation:

Betsy:

x=471-13y

Carlos:

x=15+44y

471-13y=15+44y

456=57y

y=8

288 ounces of water are left in the water tank.

What is arithmetic?

Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots

Here, we have

Given: Tom has a water tank that holds 5 gallons of water. tell me this is water for my footing to fill six bottles they each hold 16 ounces and a picture that holds one over 2 gallons.

1 gallon = 128 ounces, 2 gallon = 256 ounces

6 bottles × 16 ounces = 96 ounces

2 gallon + 96 ounces = 256 + 96 ounces = 352 ounces

5 gallon = 5 × 128 = 640 ounces

= 640 - 352 = 288 ounces

Hence,  288 ounces of water are left in the water tank.

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Answer:

Step-by-step explanation:

Based on the information in the image, it can be inferred that the sides of the box measure 5 cm each.

To find the measure of the sides of the box we must carry out the following mathematical procedure:

As we know the volume of a cube is the equivalent to the length of its sides raised to the cube (raised to the 3). In this case, to identify the value of the sides we must find the cube root of the volume and the result is the length of the sides.

So this cube has a volume of 125cm³, so its sides would be the cube root of 125.

\(\sqrt[3]{125} = 5\)

According to the above, the length of the sides is 5 taking into account that all the sides are equal.

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As we can see on the given graph, the domain of function F goes from x=3 to x=12. Then, the domain of F is

On the other hand, the domain of G goes from x=2 to x=11. Then, the domain of G is

Then, from the above results, we can see that the domain of F+G is the intersection of the domain of F and G, that is

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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Answer:

Okay so since she has 80 dollars, and already spent 25, then she would have 55 dollars remaining.

Now that she has 55 dollars, she will divide it up evenly between her 4 friends.

55/4 = 13.75

The most that she would be able to give them is $13.75

Step-by-step explanation:

Hope it helps! =D

Explanation

remember

Step-by-step explanation:

\( - 12u + 13 = 8w - 3 \\ - 12u + 13 + 3 = 8w \\ - 12u + 16 = 8w \\ w = \frac{ - 12u + 16}{8} \\ w = \frac{ - 3}{2} u + 2\)

I hope that is useful for you :)

Answer:

1.) R = 9 in

2.) R = 14.5 m

3.) D = 42 ft

4.) 26 mm

5.) 131.88 m

6.) 34.54 in

7.) 25.12 yd

8.) 28.26 mm

9.) 43.96 in

10.) 197.82 cm

11.) 263.76 cm

12.) 94.2 cm

13.) 97.34 m

14.) 138.16 cm

15.) 47.1 yd

16.) 285.74 cm

Step-by-step explanation:

2(pi)r... literally plugged in

Answer:

(3 x - 5)^{2}

Step-by-step explanation:

Rewrite the expression into the form of a^2\pm 2ab+b^2:(3 x)^{2} - 2 \times 3 x \times 5 + 5^{2}

Factor the expression using a^{2}\pm 2ab+b^{2}=(a\pm b)^{2}:(3 x - 5)^{2}

Answer: (3 x - 5)^{2}

Answer:

10% of 870 is 87

Step-by-step explanation:

I am so sorry if that wasn't the right answer!

have a blessed day!

The roots of the equation are : x = 0 an x= 13/5

A mathematical statement that has a "equal to" symbol between two expressions with equal-values is called an equation.

as in 3x + 5 Equals 15, for instance.

There are many different types of equations, including linear, quadratic, cubic, and others.

In the question, we have:

5x² = 13x

⇒ 5x² - 13x = 0

⇒ x(5x-13) = 0

So, solutions of the equation are: x =0 and x =13/5

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The rοοts οf the equatiοn are : x = 0 an x = 13/5

A mathematical statement that has a "equal tο" symbοl between twο expressiοns with equal-values is called an equatiοn.

There are numerοus ways in which οne may define an equatiοn. In its simplest fοrm in algebra, the definitiοn οf an equatiοn is a mathematical statement that shοws that twο mathematical expressiοns are equal. Fοr instance, 3x + 5 = 14 is an equatiοn, in which 3x + 5 and 14 are twο expressiοns separated by an ‘equal’ sign. The mοst basic and simple algebraic equatiοns cοnsist οf οne οr mοre variables in math.

as in 3x + 5 Equals 15, fοr instance.

There are many different types οf equatiοns, including linear, quadratic, cubic, and οthers.

In the questiοn, we have:

5x² = 13x

⇒ 5x² - 13x = 0

⇒ x(5x-13) = 0

Sο, sοlutiοns οf the equatiοn are: x =0 and x =13/5

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Answer:

C. 5

Step-by-step explanation:

Becuase the left figure is just a scaled down size of the right one, 3 x 2 = 6 so 10 ÷ 2 = 5

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Answer:

Annette should plan to spend 2.25 hours walking back.

Step-by-step explanation:

To solve this problem, we can use the formula:

Time = Distance / Speed

Let's assume the distance of the race is D miles.

Annette spends her time running the distance of the race, which takes:

Time running = D / 9 hours

She then walks back the same distance, which we need to find the time for:

Time walking = D / 3 hours

Since Annette has a total of 3 hours for her training, the sum of the running time and walking time should equal 3 hours:

D / 9 + D / 3 = 3

To simplify the equation, we can multiply all terms by 9 to eliminate the denominators:

D + 3D = 27

Combining like terms:

4D = 27

Dividing both sides of the equation by 4:

D = 6.75

So, the distance of the race is 6.75 miles.

To find the time Annette should spend walking back, we substitute the distance into the time-walking formula:

Time walking = D / 3 = 6.75 / 3 = 2.25 hours

Therefore, Annette should plan to spend 2.25 hours walking back.

Answer:

11:37am

Step-by-step explanation:

Answer:

11:22am

Step-by-step explanation:

Answer:

Please attach a photo to this so I can better answer your question

The domain and range of the graph above in interval notation include the following:

Domain = [-6, 3]

Range = [-3, 3]

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-6, 3] or -6 ≤ x < 3.

Range = [-3, 3] or -3 < y < 3

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In order to create 728 millilitres of the medication, 273 millilitres of component A are required.

A compound in chemistry is a material comprised of two or more separate chemical elements mixed together in a certain proportion. Chemical connections that are challenging to break are created when the elements interact with one another.

Compound A:Compound B ratio in the medication is 3:5. In other words, there are 3 millilitres of compound A and 5 millilitres of compound B for every 3+5=8 millilitres of the medicine.

We may set up a percentage using the ratio of compound A to the total volume of the medicine to determine how much compound A is required to make 728 millilitres of the drug:

3 ml x 3 ml x 3 ml

-------- = ----------

728 ml total, 8 ml overall

If we cross-multiply, we obtain:

8(x) = 3(728)

To find x, we use the formula x = 3(728)/8 = 273

In order to create 728 millilitres of the medication, 273 millilitres of component A are required.

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273 milliliters of compound A are needed to make 728 milliliters of the drug.

What are proportions?

In mathematics, a proportion is a statement that two ratios are equal. It expresses the relationship between two or more quantities that are directly proportional to each other. A proportion can be represented as an equation of the form:

a/b = c/d

To determine the amount of compound A needed to make 728 milliliters of the drug, we need to use the given ratio of 3 milliliters of compound A to 5 milliliters of compound B.

Let's start by finding the ratio of compound A to the total amount of ingredients (A+B) in the drug:

3 : (3+5) or 3:8

This means that for every 8 milliliters of the drug, 3 milliliters of compound A are used.

To find out how many milliliters of compound A are needed for 728 milliliters of the drug, we can set up a proportion:

3/8 = x/728

where x represents the amount of compound A needed.

To solve for x, we can cross-multiply:

8x = 3*728

8x = 2184

x = 273

Therefore, 273 milliliters of compound A are needed to make 728 milliliters of the drug.

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Answer:

a. Expected frequency of losses per semester = 0*0.08 + 5*0.16 + 10*0.28 + 15*0.32 + 20*0.14 + 25*0.02

Expected frequency of losses per semester = 11.7 losses per semester

b. Variance = (0-11.7)²*0.08 + (5-11.7)²*016 + (10-11.7)²*0.28 + (15-11.7)²*0.32 + (20-11.7)²*0.14 + (15-11.7)²*0.02

Variance = 10.9512 + 7.1824 + 0.8092 + 3.7848 + 9.6446 + 3.5378

Variance = 35.61

c. As losses equal $60, expected losses per semester = 11.7*$60 = $702

d. Expected losses of all textbooks per semester = 250*11.7*$60 = $175,500

Answer:

402 Meters

Step-by-step explanation:

Add 258+144 and you get 402.