What is the vertex form of the equation? y = – x 2 + 12 x – 4 show steps of how you solved please

Answers

Answer 1

The vertex form of the equation is in the form of y = a(x-h)^2 + k.

Step 1: Use the formula below to solve for a.

a = -1/4 * (4 - 12) = -1

Step 2: Use the formula below to solve for h.

h = -b/(2a) = 12/(2(-1)) = -6

Step 3: Use the formula below to solve for k.

k = f(h) = -(-6)^2 + 12(-6) - 4 = 36

Therefore, the vertex form of the equation is y = -(x+6)^2 + 36.

In mathematics, what is the vertex?

A vertex, or particular point, is a place where two or more lines or edges meet in a mathematical object. Angles, polygons, polyhedra, and graphs are where vertices are most frequently seen. Nodes and vertices in a graph are the same thing.

What is the vertex location?

Recall that a parabola's General Form is y = ax2 + bx + c. The x-coordinate of the vertices, which is x = - b/2a, must first be discovered in order to find the vertex from this form. You will use this number to replace x in the parabola equation once you have determined the x-coordinate of the vertex.

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Related Questions

Two students are looking at their phones while walking in the hallway. This results in them colliding head on with one another. The first student has a mass of 62 kg and is moving to the right at 3.80 m/s while the second student has a mass of 67 kg and is moving to the left at 2.59 m/s. After the collision, student A bounces backwards at 1.17 m/s. Determine the final velocity of student B. (Treat velocity to the right as positive and velocity to the left as negative.)

Answers

The final velocity of student B is -1.05 m/s. This value is negative, indicating that student B is moving to the left after the collision.

What is Velocity?

Velocity is a term that describes the speed and direction of a point's motion.

Conservation of momentum states that the total momentum of a system remains constant unless acted upon by an external force. In this case, the two students can be considered a closed system, since no external forces are acting on them.

Therefore, the total momentum of the system before the collision must be equal to the total momentum of the system after the collision.

We can represent the momentum of each student as a vector, where the magnitude is equal to the mass of the student times their velocity and the direction is the direction in which the student is moving. The total momentum of the system before the collision can be found by adding the individual momenta of the two students:

Momentum before collision = (62 kg * 3.80 m/s) + (67 kg * -2.59 m/s)

= 233.6 kg m/s + (-174.53 kg m/s)

= 59.07 kg m/s

After the collision, student A bounces backwards at 1.17 m/s, while student B moves with an unknown velocity in the opposite direction. We can represent the total momentum of the system after the collision as:

Momentum after collision = (62 kg * -1.17 m/s) + (67 kg * v)

where v is the velocity of student B after the collision. We can set the two expressions for total momentum equal to each other and solve for v:

59.07 kg m/s = (62 kg * -1.17 m/s) + (67 kg * v)

v = (59.07 kg m/s + 62 kg * -1.17 m/s) / 67 kg

= (-70.34 kg m/s) / 67 kg

= -1.05 m/s

Therefore, The final velocity of student B is -1.05 m/s. This value is negative, indicating that student B is moving to the left after the collision.

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can someone please help?
does it represent a function
yes or no

Answers

Answer:

No

Step-by-step explanation:

Functions must have only one answer for each x. However, in all the x values in this graph there are two answers.

No since there are 2 answers

(Solving Equations Using Square and Cube Roots LC)

Solve y3 = −1.

y = −0.5
y = 0.5
y = −1
y = ±1

Answers

Answer:

Step-by-step explanation:

J Square Roots and Cube Roots To find the square root of a number, you want to find some number that when multiplied by itself gives you the original number. In other words, to find the square root of 25, you want to find the number that when multiplied by itself gives you 25. The square root of 25, then, is 5. The symbol for square root is equation.

Which of the following equations has 2 as a root? (a) `x^(2)-4x+5=0`, (b) `x^(2)+3x-12=0`
(c) `2x^(2)-7x+6=0`, (d) `3x^(2)-6x-2=0`

Answers

The given equation (C) 2x² - 7x + 6 = 0 has 2 roots in it.

What are equations?

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

Ax+By=C is the usual form for two-variable linear equations.

A standard form linear equation is, for instance, 2x+3y=5.

(A) x² - 4x + 5 = 0

LHS: x² - 4x + 5

= (2)² - 4(2) + 5

= 4 - 8 + 5

= -4 + 5

= 1

RHS = 0

LHS ≠ RHS

Has no root that is 2 in it.

(B) x² + 3x - 12 = 0

LHS: x² + 3x - 12

= (2)² + 3(2) - 12

= 4 + 6 - 12

= 10 - 12

= -2

RHS = 0

LHS ≠ RHS

Has no root that is 2 in it.

(C) 2x² - 7x + 6 = 0

Put x = 2

= 2(2)² - 7(2) + 6

= 8 - 14 + 6

= 14 - 14

= 0

RHS = 0

LHS = RHS

It has 2 roots.

(D) 3x² - 6x - 2 = 0

LHS: 3x² - 6x - 2

= 3(2)² - 6(2) - 2

= 12 - 12 - 2

= -2

RHS = 0

LHS ≠ RHS

Has no root that is 2 in it.

Therefore, the given equation (C) 2x² - 7x + 6 = 0 has 2 roots in it.

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The selling price of an item is $720. It is marked down by 30%, but this sale price is still marked up from the cost $420. What is the markup from cost to sale price

Answers

The markup from cost to sale price was originally 245%.

What is the markup?

The markup is the addition put on the cost of an item.

Goods are marked-up to take care of other selling and administrative costs and to achieve an estimated profit.

The cost of the item plus the markup equals the retail selling price.

Selling price = $720

Markdown percentage = 30%

Marked-up selling price before the markdown = $1,029 ($720/0.7)

Markup cost = $420

Markup difference = $609 ($1,029 - $420)

Markup = 245% ($1,029/$420 x 100)

Thus, the item was marked-up by 245% before it was marked down by 30% to $720.

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How do you convert 0.23 (3 repeating) as a fraction?

Answers

[tex] \frac{7}{30} [/tex]

The solution is attached to the answer.

Hope understands

An investor invested a total of $2,300 in two mutual funds. One fund earned a 6% profit while the other eamed a 4% profit. If the investor's total profit was $102, how much was invested in each mutual fund?​

Answers

The amounts in each mutual fund are $500 and $1800. By using a system of equations, the required values are evaluated.

What is a system of equations?

The system of equations is a set of one or more equations that intersects at locations called solutions of the system.

The system of equations is solved for solutions in three different methods. They are the Elimination method, Substitution method, and Graphing method.

Calculation:

It is given that, an investor invested $2300 in two mutual funds.

Consider the amount invested in two mutual funds as fund1 = x and fund2 = y.

So, we can write the equation for the total investment is

x + y = 2300 ...(1)

The percentage of profit earned from the fund1 = 6% = 0.06

The percentage of profit earned from the fund2 = 4% = 0.04

The total profit for the investor = $102

Then, the equation from this statement is

0.06x + 0.04y = 102 ...(2)

Then the system of equations is

x + y = 2300 ...(1)

0.06x + 0.04y = 102 ...(2)

Applying the substitution method to solve the obtained system of equations.

So, from (1), we can write x = 2300 - y

Then, equation (2) becomes

0.06(2300 - y) + 0.04y = 102

⇒ 6(2300 - y) + 4y = 10200

⇒ 13800 - 6y + 4y = 10200

⇒ 13800 - 2y = 10200

⇒ 2y = 13800 - 10200 = 3600

∴ y = 3600/2 = $1800

So, the value of x is x = 2300 - 1800 = $500

Thus, the amount of investment in two mutual funds is $500 and $1800.

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just these 2 questions

Answers

Answer:

nnnn

Step-by-step explanation:

hh

n a survey of 3102 ​adults, 1443 say they have started paying bills online in the last year. Construct a​ 99% confidence interval for the population proportion. Interpret the results.

A​ 99% confidence interval for the population proportion is ( ),( ).

​(Round to three decimal places as​ needed.)

Interpret your results. Choose the correct answer below.

A. With​ 99% confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.

B. The endpoints of the given confidence interval show that adults pay bills online​ 99% of the time.

C. With​ 99% confidence, it can be said that the sample proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.

Answers

With 99% certainty, the population proportion of adults who say they have started paying bills online in the last year is between the given confidence interval's endpoints.

What is confidence interval?

We have the following confidence interval of proportions in a sample of n people surveyed with a success probability of π and a confidence level of 1 - α.

Confidence interval = [tex]\pi[/tex] ± z [tex]\sqrt{\(\pi (1 - \pi ))/n}[/tex]

z = 1 - α/2

Here given, According to a survey of 3102adults, 1443 have begun paying bills online in the last year.

That is, n = 3102 and x = 1443

p = x / n

  = 1443 / 3102

  = 0.465

significance level = α

= 1 - confidence

= 1 - 0.99

= 0.01

zα/2 = z0.01 / 2 = 2.58

By substituting in confidence interval formula,

The lower limit is :

0.465 - 2.58[tex]\sqrt{(0.465 * 0.535) / 3102}[/tex]

= -0.01894056008

The upper limit is:

0.465 + 2.58[tex]\sqrt{(0.465 * 0.535) / 3102}[/tex]  

= 0.02722425658

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The lower limit is 0.456 and upper limit is 0.474

What is confidence interval?

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.

As confidence interval (C) = π ± z√[π(1-π)/n]

In the above expression, z = 1 - α/2, where α is the significance level.

Given in the question, n=3102 as the survey was conducted on 3102 adults. Also, x=1443, as 1443 people have started paying bills online in last year.

π = x/n

Substituting the values, we get,

π = 1443/3102

⇒ π = 0.465

Confidence level(α) = 1 - confidence

= 1 - 0.99

= 0.01

Since, z = 1 - α/2

⇒ z = 1 - 0.01/2

⇒ z = 1 - 0.005

⇒ z = 0.995

By substituting in confidence interval formula,

The lower limit is = 0.465 - 0.995√[(0.465*0.535)/3102]

= 0.456

The upper limit is = 0.465 + 0.995√[(0.465*0.535)/3102]

= 0.474

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Draw the net diagram of the the 3-object below and determine the total surface area

Answers

Answer:

see below for the netarea: 168 cm²

Step-by-step explanation:

You want the net and total surface area for the triangular prism shown.

Net

The net diagram is attached. It consists of three rectangles with triangles attached to the ends of the widest rectangle. Of course, these parts can be arranged in any order you find convenient, as long as the common edges match the original prism.

Area

The net shows the area can be computed as the sum of a rectangle 9 cm high and 5+6+5 = 16 cm wide, together with two triangles of base 6 cm and height 4 cm.

  A = (9 cm)(16 cm) +2(1/2)(6 cm)(4 cm)

  = 144 cm² +24 cm²

  = 168 cm²

The total surface area of the prism is 168 cm².

__

Additional comment

The formulas for the area of a rectangle and triangle are ...

  A = LW . . . . . area of a rectangle of length L and width W

  A = 1/2bh . . . . area of a triangle of base b and height h

what is the value of tan a?

Answers

The value of tanA is always less than 1.

What is a number's tan of?

Tangent is the ratio of the side opposite the angle we know or want to know over the side next to that angle, and is sometimes abbreviated as T-A-N.

Describe tan angle A.

The trigonometric ratio between the opposite and adjacent sides of a right triangle that contains an angle is its tangent.

                     Tangent is the mathematical term for the length of the leg that faces the angle and is often abbreviated as "tan." For instance, in the triangle above, tan(A) = 68 or 34 and tan(B) = 86 or 43.

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At the school carnival, Mike will play a game in which he will toss a penny, a nickel, and a dime at the same time. He will be awarded 3 points for each coin that lands with heads faceup. Let the random variable x represent the total number of points awarded on any toss of the coins. What is the expected value of x?

Answers

The expected value of x for the awarded 3 points for each coin that lands with heads faceup is 27/8.

How do you determine the likelihood of an event?Assume that there are a finite number of elementary events that are all equally likely to occur in the sample space of the experiment under consideration.Probability (E) = favourable outcome/ total outcome

In this instance, we are informed that:

Three coins were tossed, and the result was three heads.X is the overall point total.X now has a total of 4 possible values: 0, 1, 2, and 3.

The probability of each of them is calculated as:

Situation 1: No heads

That implies that all three coins must land on the tail.

Thus, there is only one method to accomplish this. While the whole range of potential outcomes is;

= 2x 2x 2

= 8

via the product rule (because each coin has two alternative outcomes).

The result is:

P(x =0) = 1/8

Situation 2: One head

Single head means three points, or X = three.

Total outcomes possible = 8,

Single head can occur in 3 different ways, as other two needs to be strictly tails.

Thus,

P(x = 3) = 2/8

Situation 3: Two heads

Two heads equals 3+3 = 6.

X = 6

8 outcomes are possible in total.

Single tail means two heads. Three separate scenarios can lead to a single tail.

Therefore,

P(x = 6) = 2/8

Situation 4: Three heads

Three heads signifies that X = 9 or 3+3+3 = 9 points.

8 outcomes are possible in total.

Three heads means there is only one way to do it and no tail.

Thus,

P(x = 9) = 1/8

As a result, the expectation of X is determined as follows:

E(x) = 0. 1/8 + 3. 2/8 + 6. 2/8 + 9. 1/8

E(x) = 27/8

Therefore, 27/8 is the expected value of X.

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2. Tino charges $2 for the first mile, plus 50 cents for
each additional mile. Is this a proportional
relationship?

Answers

The given situation for the price according to the distance is not proportional.

Describe the term proportional relationship?Relationships between 2 factors that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, each variable is consistently equal to the other's constant value.

Let the total distance covered by Tino is 'x'.

Let the total price be 'y'.

Then,

y = fixed price + additional price

y = $2 + $0.5x

For x = 1; y = $2.5   ---> x/y = 1/2.5

for x = 1; y = $3   ---> x/y = 2/3

for x = 3; y = $3.5   -----> x/y = 3/3.5

In all situations, ratio x/y is not constant.

Thus, the given situation for the price according to the distance is not proportional.

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the time to fly between new york city and chicago is uniformly distributed with a minimum of 66 minutes and a maximum of 100 minutes. what is the probability that a flight is less than 71 minutes? a) 1.00 b) 0.15 c) 0.07 d) 0.00

Answers

The probability that the flight is less than 71 minutes is 0.1471

Let the distribution of the time to fly between New York City and Chicago be X

X~U(66,100)

where,

66 = minimum

100 = maximum

We need to find P(X<71)

We know that in the case of uniform distribution,

P(X<x) = (x - a) / b -a

where,

a = min value

b = max value.

Hence P(X<71)

= (71 - 66) / (100 - 66)

= 5/34

= 0.1471

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Which of the following transformations is non-rigid? A.translationB.dilationC.reflectionD.rotation

Answers

From the question the transformations that non-rigid is dilation. The correct answer is B.

what is nonrigid transformation?

Any transformation of a geometric object that alters the size but not the shape is referred to as a nonrigid transformation. Examples of non-rigid types of transformation include stretching and dilation. Any action taken on a shape is referred to as a metamorphosis.

Rigid transformation is When a figure undergoes a stiff transformation, its size and shape are left unaltered. Because the image is unchanged, stiff transformations include translations, rotations, and reflections.

As a result, a dilation is a non-rigid transformation because the size of the image is changing.

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The simple interest formula is I=Prt, where I is the interest, P is the principal, r is the interest rate, and t is the time.

What is the interest if the principal is $10,000, the interest rate is 2%, and the time is 8 years?

options:

$160
$200
$1600
$16,000

Answers

Answer:

1600$

Step-by-step explanation:

By using the SI formula,

[tex]SI={PXRXT}/{100} \\SI=10000X2X8/100\\SI = 1600$\\\\Hence, the interest is 1600$[/tex]$

Option C) 1600$ is correct

Mark me brainliest

45 POINTS ANSWER FOR BRAINLIST AND HEARTS

Answers

The graph of the linear function y = 36 - 4x that represents this function is given by the image shown at the end of the answer.

How to graph the linear function?

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the parameters are listed as follows:

m is the slope, representing by how much y changes when x is increased by one.b is the intercept, representing the value of y when x = 0.

Initially, he has 36 overdue activities, hence the intercept is of:

b = 36.

Each day, he can do 4 activities, hence the number of remaining activities decays by 4, and thus the slope is of:

m = -4.

Thus the function is given as follows:

y = -4x + 36.

The y-intercept is given by the following point:

(0, 36).

The x-intercept is given by the following point:

(9,0).

As:

-4x + 36 = 0

4x = 36

x = 9.

Then a line is traced connecting the intercepts.

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What is the diameter of a P210/60R17 tire?

Answers

the diameter of a P210/ 60R17 is 26.9" where width is 8.3" , sidewall 5" overall diameter of the tire is indicated by the first digit.

What is diameter of tire ?

Remembering that the tire diameter is made up of two sidewalls—the one above the wheel and the one below the wheel hitting the ground—and adding the diameter of the wheel, the sidewall height must be multiplied by two to determine the tire's overall diameter.

given ,

size = 210 / 60R17

The overall diameter of the tire is indicated by the first digit. The tire diameter or "height" in this illustration is 210 inches tall. The tire's breadth is shown by the second digit. When using tires with inch measurements, the width will typically contain a.50 decimal after the first digit.

the diameter of a P210/ 60R17 is 26.9" where width is 8.3" , sidewall 5"

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which expression shows a way to factor 16 + 72

Answers

The expression that shows a way to factor 16 + 72 is 8(2 + 9)

How to determine the way to factor the expression?

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

16 + 72

Express the terms of the expression as products

So, we have the following representation

16 + 72 = 8 * 2 + 8 * 9

Factor out 8 from the expression

This gives

16 + 72 = 8 * (2 +  9)

Hence, the factored expression of 16 + 72 is 8 * (2 +  9)

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35% of 350 is what number?

Answers

Answer: 122.5

Step-by-step explanation:

In addition to the 407 inch diagonal, the rectangle slab is 379 inches wide.
What is the length of the side of the slab in inches?

Answers

By using  Pythagorean theorem ,148  is the length of the side of the slab in inches .

What is the Pythagorean theorem in plain English?

The Pythagorean Theorem states that the squares on the hypotenuse of a right triangle, which is the side that faces the right angle, are equal when added together.

                    This is written as a2 + b2 = c2 in the usual algebraic notation.

12 inches = 1 feet  

 feet measurment = 407/12  = 33.91 feet

In triangle ABC

Using PYTHAOREAN THEOREM

               l² + b² = h²

             l = √h²  -  b²

            l =  √407² - 379²

            l = √165649 - 143641

            l = √22008

           l = 148.35

           l ≈ 148

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How do I do this? , it’s making me confused

Answers

Answer:

you remember vertex: h,k in (x-h)²+k..

replace in that. In that graph vertex: (10, -20)

So in that Equation, a(x-10)²-20, a<0 since it is maximum graph.

I cannot find the full Equation but from what I can see you can find h,k and the fact that a<0

Geometry-need help i dont get it

Answers

Answer:

z = 11

Step-by-step explanation:

To find the answer we need to set up an expression with the two values they gave us:

8z = z + 77

This works because side IJ is the same length as side JK. So, all we have to do is solve for z:

8z = z + 77

-z    - z

7z = 77

/7     /7

z = 11

Find the value of the variable BC, if B is between A and C. AB=19, BC = 4y, AC = 8y-1

Answers

The value of the variable BC will be equal to 20.

What is a line segment?

A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.


Given that B is between A and C. AB=19, BC = 4y, AC = 8y-1.

Here If B is between the segment AC the value of BC will be calculated as,

BC = AC - AB

Substitute the values in the above equation and solve for the value of y,

4y = 8y - 1 - 19

4y = 8y - 20

8y - 4y = 20

4y = 20

y = 5

The value of segment BC will be.

BC = 4y

BC = 4 x 5

BC = 20

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a report on the nightly news broadcast stated that 10 out of 105 households with pet dogs were burglarized and 24 out of 212 without pet dogs were burglarized. suppose that this sample data is used to test the claim that there is a difference in the proportion of homes with dogs that are burglarized and the proportion of homes without dogs that are burglarized. find the test statistic for the test. group of answer choices -0.195 -0.828 -0.487 -0.001

Answers

Therefore the solution to this problem is the test statistic for the test  is  -0.487

What is test statistics ?

In statistical hypothesis testing, a test statistic is a statistic that is employed. A hypothesis test is often defined in terms of a test statistic, which is a numerical summary of a data set that can be used to execute the test and reduces the data to one value.

Here,

According to a report on the evening news show, burglaries occurred in 23 out of 197 residences without pets and 10 out of 129 homes with pets.

Let p1 represent the percentage of dog-owning homes who experienced burglaries.

p2 is the population proportion of burglarized homes without canine companions.

Since both population proportions are equal, the null hypothesis (H) is that p1=p2.

A Different Hypothesis, K:p1≠p2 indicates that there is an imbalance between the two population proportions.

The test results that would be utilized in this z-test for proportions with two samples;

                          T.S. = [tex]\frac{(p1^{'} -p2^{'} )-(p1-p2)}{\sqrt{\frac{p1^{'}1-p1^{'}()}{n1} +\frac{p2^{'}(1-p2^{'})}{n2} } }[/tex]~ N(0,1)

where,  p1= sample proportion of households with pet dogs who were burglarized =10/105  = 0.095

p2= sample proportion of households without pet dogs who were burglarized = 24/212 = 0.11

n1= sample of households with pet dogs = 105

n2 = sample of households without pet dogs = 212

So, the test statistics  =  [tex]\frac{(0.0095 -0.11 )-(0)}{\sqrt{\frac{0.095(1-0.095)}{105} +\frac{0.11(1-0.11)}{212} } }[/tex]

                                                                      =  -0.487

Therefore  ,the test statistic for the test is  -0.487

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How do you use demoivre's theorem to simplify (1−i)^12?

Answers

The correct answer is 64

Demoivre's theorem states that for all complex numbers z and all positive integers n:

z^n = (r^n) × (cos(n∅) + isin(n×∅))

where r is the magnitude of z and theta is the argument of z.

To use Demoivre's theorem to simplify (1−i)^12, we can first write (1−i) in polar form as r × cis(∅). where r is the magnitude and cis(∅) is the size complex number. is 1, the argument ∅. In this case the size of (1−i) is √(1^2 + (-1)^2) = √(2) and the argument of (1−i) can be found using the arctangent function.

∅ = arctan(-1÷1) = -45 degrees.

So (1−i) can be written as sqrt(2) × cis(-45 degrees). Applying this to Demoivre's theorem, we get:

(1−i)^12 = (√(2)^12) × (cos(-540°) + i×sin(-540°))

We can simplify this to:

(1−i)^12 = 2^6 × cis(-180°)

This can be further simplified as follows.

(1−i)^12 = 64 × (-1)

the final answer is -64.

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Desde un punto en tierra ubicado a 4m de un poste, se divisa su parte alta con un ángulo de elevación de 37°. ¿Cuál es la altura del poste?

Answers

The height of the pole will be 3m (approx.)

What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.

We have the ground located 4 m from a pole, its upper part can be seen with an elevation angle of 37°.

We can write the height of the pole as -

h = 4 tan(37°)

h = 4 x 0.75

h = 3 m (approx.)

Therefore, the height of the pole will be 3m (approx.)

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[Question in english -

From a point on the ground located 4m from a pole, its upper part can be seen with an elevation angle of 37°. What is the height of the pole?]

AD is the median of triangle ABC . E is the mid – point of AD. BE produced to meet AC at F. DG║BF Show that AC=3AF

Answers

From the various triangle proofs below, we have been able to show that; 3A F = AC

How to prove the median of a triangle?

A median of a triangle is defined as a line segment from a vertex of the triangle to the midpoint of the side opposite that vertex.

We are given that;

AD is the median of ΔABC.

E is the midpoint of AD

Through D, we draw DG parallel to BF

In ΔADG, E is the midpoint of AD and EF is parallel to DG

By using the converse of midpoint theorem, we have;

F is midpoint of AG and A F = FG     ------(eq 1)

Likewise, In ΔBCF ;

D is the midpoint of BC and DG is parallel to BF  

G is midpoint of CF and FG is congruent to GC (FG ≅ GC) .........(eq 2)

From equations 1 and 2, we will get;

A F = FG = GC     -------(3)

Thus;

A F + FG + GC = AC

A F + A F + A F = AC (from eq 3)

3A F = AC

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Which pairs of rectangles are similar polygons? Rectangle A: 100cm & 80cm Rectangle B: 120cm & 100cm Rectangle C: 90cm & 72cm. A and B - similar or not similar? B and C similar or not similar? A and C similar or not similar?

Answers

Answer:

A and C similar

Step-by-step explanation:

A: 80/100 = 0.8

B: 100/120 = 0.833...

C: 72/90 = 0.8

Since the ratio of the lengths of the sides of rectangle A and C are equal, the only similar rectangles are A and C.

Answer: A and C similar

You make two separate investments for a total of $4000. The percent return on Charles Schwab & co. At the end of the year was 5% and the percent return on merill lynch was 7%. The combined return on both funds was $256. How much did you invest in each fund.

Answers

The required funds invested in Charles Schwab & co and Merrill lynch are 1200 and 2800 respectively.

Given that,
Make two separate investments for a total of $4000. The percent return on Charles Schwab & co. At the end of the year was 5% and the percent return on Merill lynch was 7%. The combined return on both funds was $256.

here,
let x be the invested amount on Charles Schwab & co and y be the invested amount on Merrill lynch.
According to the question,
x + y = 4000
x = 4000 - y   - - - - - (1)
And
0.05x +0.07y = 256 - - - - (2)
From equation 1 and 2
x=1200 and y=2800

Thus, the required funds invested in Charles Schwab & co and Merrill lynch are 1200 and 2800 respectively.

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