Note that sides AD and BE are perpendicular on the same side AC. So the angles CAD and CBE, both are equal to 90 degrees.

Beig the corresponding angles, ADC and BEC are also equal.

And the angle ACD is the common angle in both the triangles.

Therefore by the AAA criteria, the triangles CAD and CBE are similar.

So their corresponding sides must be proportional,

[tex]\begin{gathered} \frac{AD}{BE}=\frac{AC}{BC} \\ \frac{4\sqrt[]{138}}{\sqrt[]{138}}=\frac{6\sqrt[]{3}+BC}{BC} \\ 4=\frac{6\sqrt[]{3}+BC}{BC} \\ 4BC=6\sqrt[]{3}+BC \\ 3BC=6\sqrt[]{3} \\ BC=2\sqrt[]{3} \end{gathered}[/tex]A house has decreased in value by 35% since it was purchased. If the current value is $78,000, what was the value when it was purchased?

**Answer: The value of the house when it was purchased was 120,000**

**Step-by-step explanation:**

**1) Set up the equation. Let x be the house.**

x-x*35%= 78,000

**First, the house decreases 35% of the cost of the original house. It now costs 78,000.**

**2) Solve the equation. **

x-x*0.35 = 78,000

x-0.35x=78,000

0.65x = 78,000

**x= 120,000**

If triangle LMN has an obtuse angle at vertex M, which statements could be true? Check all that apply.

Triangle LMN is an obtuse angle then, **the angle at vertex L is acute, the angle at vertex N is acute.**

The triangle LMN is an obtuse angle at the vertex M. So by the definition of obtuse angle triangle LMN is an obtuse angle.

As ∠M is an obtuse angle

So 90° < m∠M < 180°

By the **property of a triangle**,

m∠L + m∠M + m∠N = 180°

m∠M = 180° - (m∠L + m∠N)

90° < 180° - (m∠L + m∠N) < 180°

90° - 180° < -(m∠L + m∠N) < 0

-90° < -(m∠L + m∠N) < 0

90° >(m∠L + m∠N) > 0

**90° > m∠L and 90° > m∠N**

Therefore both angles L and N are acute angles.

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**Answer:**

1, 2 and 5

**Step-by-step explanation:**

see picture

find the area under the standard normal distribution curve to the right of . use a ti-83 plus/ti-84 plus calculator and round the answer to at least four decimal places.

using calculator

**Area** right to the right of the 2=2.12

P(Z > 2.12)

• P(Z < -2.12)

= 0.0170

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Use the intersect method to solve the equation. x^2 - 3x = x^2 -1

The** coordinate **that represent the **solution **of the equation -

x² - 3x = x² - 1 is **(0.333, -0.8889)**.

An equation is a formula that expresses the **equality **of two expressions, by connecting them with the **equals sign =**.

Given is the following equation -

**x² - 3x = x² - 1**

In order to solve it using** intersect method,** we will plot the graphs of both** functions** and find the point of **intersection** of graphs of both the equations.

Assume -

**f(x) = x² - 3x**

**g(x) = x² - 1**

Now, the point of **intersection** of both the graphs will be the solution to the equation given by -

**f(x) = g(x)**

It can be seen from the graph that, both the **graphs intersect** at the coordinate **(0.333, -0.8889)**. This coordinate will be the **solution set** of the equation -

**f(x) = g(x)**

Therefore, the** coordinate **that represent the **solution **of the equation -

x² - 3x = x² - 1 is **(0.333, -0.8889)**.

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7th grade students were asked to choose their

favorite color. The table shows the fraction of

students that choose each color. What DECIMAL

shows the difference between the most and least

favorite colors?

Color

Fraction

Red Yellow Blue Green

5/18

1/6

4/9

1/9

**Answer:**

**Step-by-step explanation:**

Please help and provide an explanation for why the answer is f(x) = -1/3x - 4

What is the equation of the line that passes through Point (-6, -2) and has a Slope of -1/3.

y=-1/3-4

**Step-by-step explanation:**

point slope form!

y-y=m(x-x)

with the point (-6,-2) and the slope (-1/3) replace the 2nd variables of each variable and replace m with the slope

y-(-2)=-1/3(x-(-6))

then solve that normally

y-(-2)=-1/3(x-(-6))

y+2=-1/3x -2

y=-1/3x-4

I didnt use officially math symbols but i hope you can still read it!

What is the US GDP for the first quarter and second quarter of 2020? What is the personal consumption expenditures for the first quarter and second quarter of 2020?

The US GDP for the first quarter of 2020 was **21.54 trillion dollars**, and the US GDP for the second quarter of 2020 was **19.49 trillion dollars.**

The personal consumption expenditures for the first quarter of 2020 are **13.02 trillion dollars.**

the personal consumption expenditures for the second quarter of 2020 are **11.82 trillion dollars.**

What are **the personal consumption expenditures?**

Personal consumption expenditures are the price that citizens of the US pay for goods and services. This is a crucial index that indicates inflation or deflation and consumer behavior over some time.

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write and solve a real world problem in which you find the commission

A car salesman earns a 3% commission on sales. If he sells a car for $27,990, how much** commission **will he earn?

($27,990)*(0.03) = $839.70

The Jones family will pay their** insurance **broker a commission of $1,750.00.

Commission is an amount of money paid to an employee or company as an **incentive** to sell more. A straight commission is a percentage of sales.

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a $52 video game is adversited for 20% of it sales tax is 6%

What is the rest of the question?

Answer:

39 dollars

Step-by-step explanation: 20 perrcent of 52

Create three probability application problems of your own. Solve your problems. Explain your answers.

In the above question, we need to from 3 **probability **questions and then give solutions for them

Example 1 : A coin is tossed three times. What is the **probability **of getting at least one head?

Solution : A coin is tossed 3 times then

Sample space = [HHH, HHT, HTH, THH, TTH, THT, HTT, TTT]

Total number of ways = 2 × 2 × 2 = 8

Favorable Cases = 7

P (A) = 7/8

OR

**Probability ** (of getting at least one head) = 1 – P (no head)⇒ 1 – (1/8) = 7/8

Example 2 : Three red and four black balls are contained in a bag. Randomly, one ball gets taken out of the bag. Determine the **probability **that the drawn ball is

(i) black

(ii) not black

Solution :

Total number of balls in the bag are = 3 + 4 = 7 balls

Number of favorable outcomes or number of black balls in the bag = 4

(i) **Probability **getting black balls = [tex]\frac{number of favorable outcomes}{number of total outcomes}[/tex]

P(black ball) = [tex]\frac{4}{7}[/tex]

(ii) **Probability **getting no black balls = 1 - P(black ball)

= 1 - [tex]\frac{4}{7}[/tex]

= [tex]\frac{3}{7}[/tex]

Example 3 : Given two dice, what is the likelihood of receiving the number 7?

Mathematical **probability **- There are 36 ways in all, or 6 times 6. Favorable scenarios are (1, 6) (6, 1) (2, 5) (5, 2) (3, 4) (4, 3), etc., in six different ways. P (A) = 6/36 = 1/6

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Hillsboro Street and Manchester Avenue intersect. If the diagonal distance across the

intersection is 73 feet and Hillsboro Street is 55 feet wide, how wide is Manchester Avenue?

The **intersection's** two opposing corners are 91.40 feet apart.

Since the given data are:

Width of the Hillsboro Street = 73 feet

Width of Manchester Avenue = 55 feet

When Hillsboro Street and Manchester Avenue cross, calculate the distance between the intersection's two opposing corners,

Because the junction of Hillsboro Street and Manchester Avenue created a **right-angled triangle**:

Using **Pythagoras's Theorem**,

H² = B² + P²

H² = (55)² + (73)²

H² = 3025 + 5329

H² = 8354

H = √8354

H = 91.40

As a result, the distance between the intersection's two opposing corners is 91.40 feet.

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How do I solve number 4 and 5 to get the correct answer?

**Answer:**

4. (d)

5. (b)

**Step-by-step explanation:**

You want to apply the **secant and chord rules** to the **circles** given in the **diagram**.

The secant rule is "the product of distances from the point of intersection of secants to the two points of intersection of the secant with the circle is the same for both secants." A tangent can be considered to be a secant that has both points of intersection with the circle in the same place.

The chord rule is similar to the secant rule: "The product of distances from the point of intersection of the chords to their intersection with the circle is the same for both chords."

4.The diagram shows a tangent of length 12, so the product of distances to the two points of intersection with the circle is 12(12).

The secant has length 8 to the near point of intersection, and (x+8) to the far point of intersection. That product is the same as for the tangent:

** 8(x +8) = 12(12)** . . . . . . matches choice D

One chord has lengths of 14 and x, so the product of those is 14x.

The other chord has lengths of 12 and 21, so the product of those is 12(21).

The product is the same for both chords, meaning ...

** 14x = 12(21)** . . . . . . matches choice B

__

*Additional comment*

We have purposely tried to write the rules in "parallel" fashion, because we find them easier to remember that way. Considering a tangent to be a secant with the points of intersection with the circle merged means the *same rule can be used for all three cases*:

describe five occupations you want to do, and how you prepare for your dream job. And list the average salary, and then, combine your family cost per month, make a reasonable saving plan.

architecture, invest money so that I can pay fr fees

The product of -2 and a number is at most 10.

Find the possible numbers.

On<-5

Ons-5

Onz-5

On>-5

**Answer:**

n ≥ -5

**Step-by-step explanation:**

-2n ≤ 10

Divide both sides by -2. Remember to flip ≤ to ≥.

-2n/(-2) ≥ 10/(-2)

n ≥ -5

Arnold plants a tree sapling in his yard and measures its height every year. His measurements so far are shown in the scatterplot.

The equation of the **scatter plot **is y = 5/3x + 2 and the tree will be 18.7 feet in ten years

**Linear equations **are equations that have constant average rates of change.

Note that the constant **average rates **of change can also be regarded as the slope or the gradient

The information that completes the question is added as an attachment

From the **scatter plot**, we have the following points

(x, y) = (0, 2) and (6, 12)

The equation of the line is calculated as

y = (y2 - y1)/(x2 - x1) * (x - x1) + y1

Substitute the known values in the above equation

So, we have

y = (12 - 2)/(6 - 0) * (x - 0) + 2

So, we have

y = 5/3x + 2

In ten years, the value of x is

x = 10

So, we have

y = 5/3 x 10 + 2

Evaluate

y = 18.7

Hence, the **height **of the tree is 18.7 feet

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Givin f(x) = 1/x+5 and g(x)=x-2. What are the restrictions of the domain of f(g(x))?

OX≠ -5

OX≠ -3

OX≠ 2

OThere are no restrictions

**Answer:**

**Step-by-step explanation:**

x cannot be -3 or 2

Step-by-step explanation:

f(g(x)) = 1 / (( x-2) +5)

= 1/ (x+3)

g(x) cannot have x=2

The domain is restricted where

f(x) has an restriction that x cannot be 5

so g(x) cannot be -5

-5 = x-2

Add 2 to each side

-5+2 = x

-3

Write 41% as a fraction in simplest form.

**Answer:**

[tex]\frac{41}{100}[/tex]

**Step-by-step explanation:**

It cannot be simplified.

Ex: 50% can be simplified to [tex]\frac{1}{2}[/tex]

Make x the subject of the formula. 5d cubed= d squared (2b-3cx)

The **value of x** = [tex]\frac{2b-5d}{3c}[/tex] .

Algebraically speaking, an **equation **is a statement that shows the equality of two mathematical **expressions**. For instance, the two equations** 3x + 5 and 14, **which are separated by the** 'equal' sign**, make up the equation **3x + 5 = 14.**

The given equation is

[tex]5d^{3}=d^{2}(2b-3cx)[/tex]

5[tex]d^{3}= d^{2}2b-3cd^{2}x[/tex]

3c[tex]d^{2}x = d^{2}2b-5d^{3}[/tex]

x = [tex]\frac{d^{2}(2b-5d) }{3cd^{2} }[/tex]

x = [tex]\frac{2b-5d}{3c}[/tex]

Hence, The** value of x **= [tex]\frac{2b-5d}{3c}[/tex] .

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ANSWER QUICK I WILL GIVE BRAINLIEST!

Solve k over negative 1.8 is less than negative 4.9 for k.

k < −8.82

k > 8.82

k < −6.7

k > −6.7

**Answer:**

k<-8.82

**Step-by-step explanation:**

k/1.8<-4.9

k<-8.82

**Answer:k<-8.82**

**Step-by-step explanation:**

PLEASE HELP ME ILL LITERALLY AND I PROMISE ON GOD TO RATE YOU 5 STARS AND GIVE U POINTS

**Answer:**

1. 12hrs

2. 2hrs

**Step-by-step explanation:**

4:00pm is 2 hrs from 6:00pm

5:00am is 12hrs from 5:00pm

Price-club sells a 12-ounce package of spaghetti noodles for $3.44 and Shop Mart sells a 2 1/2-pound box of spaghetti noodles for $8.35.

The unit price per ounce at Price-Club is $ and the unit price per ounce at

Shop Mart is $

0.28 0.21

0.30 0.20

0.29 0.19

The **unit price** per ounce at Price-Club is $0.29 per ounce and the **unit price** per ounce at Shop Mart is $0.21 per ounce.

Th**e unit price **can be determined by **dividing **the total cost by the total ounce that is purchased.

**Division **is the process of putting a number into equal groups using another number. The sign used to denote **division** is ÷.** Division** is one of the basic mathematical operations. The result of the **division **process is known as the quotient.** **Other mathematical operations include addition, subtraction and multiplication.

**Unit price ** = total cost / total ounce sold

**Unit price **of Price-Club = $3.44 / 12 = $0.29 per ounce

In order to determine the u**nit price **of Shop Mart, pounds have to be converted to ounces

1 pound = 16 ounces

To convert 2 1/2 pounds to ounces, multiply 2 1/2 by 16. Multiplication is the mathematical operation that is used to determine the product of two or more numbers.

16 x 2 1/2

16 x 5/2 = 40 ounces

**Unit price **of Shop Mart = $8.35 ÷ 40 = $0.21 per ounce

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For this exponential function,

what is the output value (y),

when the input value (x) is 3?

y = 5.2x

(3, [?])

Enter

**Answer:**

40

**Step-by-step explanation:**

5*(2^3)=40

2/3 ÷ -5/6 yo nesecesito dividir

**Answer:**

-4/5

**Step-by-step explanation:**

2/3 * -6/5 = -4/5

:]

Find the values of a,b and c that would make the statements true.

1) (ax+2)(5x+b)=10x^2+bx+c

The **values **of a, b and c are a = 2, b = -10 and c = -20

The **equation **is given as

(ax + 2)(5x + b) = 10x^2 + bx + c

Open the brackets

So, we have

5ax^2 + 10x + abx + 2b = 10x^2 + bx + c

By comparing the above **equation**.

We have the following **set **of equations

5a = 10

10 + ab = b

2b = c

By solving the equations, we have

a = 2

Substitute a = 2 in 10 + ab = b

10 + 2b = b

So, we have

b = -10

Substitute b = -10 in 2b = c

2(-10) = c

Evaluate

c = -20

Hence, the **values **of the **variables **are a = 2, b = -10 and c = -20

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Wilbur landed his plane.

The plane's elevation relative to the ground

(in meters) as a function of time (in seconds)

is graphed.

How high was the plane after 1000 seconds?

At 1000 **seconds **the graph **shows **the **height **of 3500 **meter**.

The **graph **is simply a structured **representation **of the **data**. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.

Following the **creation** of a **research question**, **data **is continuously **gathered **through **observation**. The information is subsequently arranged, condensed, categorised, and visually portrayed.

In a **line graph**, the **information **or **data **is **represented **as a series of **markers**, or **dots**, and is then **connected** to one another by a **straight line**.

Usually, data that varies over time is represented with a line graph.

Given:

The graph gives the relation between Elevation and Time.

As, if at 400 **seconds **the **height **is 6500 meters.

and, at 800 **seconds **the **height **is 4500 meters.

Thus, at 1000 **seconds **the graph shows the **height **of 3500 **meter**.

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inverse of (1/4x) +2

**Answer:**

Inverse Function = 4x -8

**Step-by-step explanation:**

replace x with y and replace x with y

solve for y (meaning isolate y)

y=(1/4x) +2

x= (1/4y) +2

x-2 = 1/4y

multiply by 4 on each side to remove 1/4 from the right side

4(x-2) = y

y= 4(x-2)

y= 4x -8

Inverse Function = 4x -8

1/16 - ( -7/16)

Write your answer as a fraction in simplest form.

You just add both fractions because you’re subtracting a negative.

Answer: 1/2

Answer: 1/2

question is in the picture

in slope intercept form the equation is y=-3x-3

A store has two types of animal feed available. Type A contains 3 pounds of oats and 3 pounds of corn per bag. Type B contains 1 pound of oats and 7 pounds of

corn per bag. A farmer wants to combine the two types so that the resulting mixture has at least 18 pounds of oats and at least 54 pounds of corn. The store

only has 11 bags of type A feed and 12 bags of type B feed in stock. Type A costs $4 per bag, and type B costs $1 per bag. How many bags of each type should

the farmer buy to minimize her cost?

Note that the ALEKS graphing calculator can be used to make computations easier.

Type A feed:

Type B feed:

bag(s)

bag(s)

The farmer will **purchase** five bags of kind A and six bags of type B.

Per bag, Type A includes 9 pounds of oats and 3 pounds of maize.

Per bag, Type B includes 2 pounds of oats and 10 pounds of maize.

The farmer is looking for a** blend** that comprises at least 57 pounds of oats and 75 pounds of maize.

Allow the farmer to mix type A feed = x pounds.

and feed type B = y pounds

(9x + 2y) pounds of oats when blended

Corn amount when **combined**: (3x + 10y) pounds

Oats equation: 9x + 2y = 57 ———— (1)

Corn equation: 3x + 10y = 75 ————- (2)

Subtract equation (2) from equation (2) by multiplying it by three (1)

3(3x + 10y) - (9x + 2y) = 75×3 - 57

9x + 30y - 9x - 2y = 225 - 57

28y = 168

y = 6 bags

**derived** from the equation (1)

9x + 2×6 = 57

9x + 12 = 57

9x = 57 - 12

9x = 45

x = 5 bags

Because the business has 15 bags of each sort, each bag costs $4.

As a result, the cost of 5 bags of type A and 6 bags of type B is = (54) + (64)

= 20 + 24

= $44

The farmer intends to buy** five** bags of kind A and **six** bags of type B.

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You take a $4,500 loan to pay for a trip

to the Amazon rainforest to photograph

wild animals. If the loan's interest rate is

8% for 1 year, what is the interest for the

first payment?

A $12.58

C $30.00

Vincent Fal

B $26.00

D $80.99

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$4500\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &1 \end{cases} \\\\\\ I = (4500)(0.08)(1) \implies I = 360~\hfill \underset{monthly~payment}{\stackrel{360 ~~ \div ~~ 12}{\text{\LARGE 30}}}[/tex]

**c.**

**PRT/100**

**4500×8×1/100=360**

**per month=360÷12**

**=30**

WILL GIVE BRAINLIEST FOR CORRECT ANSWER!In types of attribute tables, dBASE files, Excel files, or Access files are examples of A. Object attribute table B. Non-spatial attribute tableC. Vector attribute table
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at spatial scales, north american bird populations are . at spatial scales, north american bird populations are . large, random large, clumped small, random small, regular
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the following data were obtained for days required to reach 230 lb and backfat thickness of a sample of 10 pigs: pig no. days to 230 lb, days backfat thickness, in 1 164 1.0 2 180 1.1 3 158 1.2 4 160 1.4 5 198 1.2 6 172 1.3 7 186 1.1 8 178 1.3 9 178 1.4 10 186 1.0 calculate the covariance between days to 230 lb and backfat thickness.
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