B ABCD is a parallelogram and angle A< 90°. The height through the vertex D intersects the diagonal AC at point M. The height through vertex B intersects the diagonal AC at point N. Prove that MBND is a parallelogram.

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Explanation:

The parabola has its lowest point when either x = -8 or x = 8

Plug either value into the function

f(x) = -x^2 + 4

f(-8) = -(-8)^2 + 4

f(-8) = -60

You should find that f(8) = -60 as well

This is the lowest output possible. Confirmation of such can be done using a graph. Look for the lowest point and only focus on the interval [tex]-8 \le \text{x} \le 8[/tex]

The highest point is at the vertex (0, 4), so the largest output is y = 4

------------

We have the lowest output y = -60 and the highest output y = 4

The possible set of outputs is the interval [tex]-60 \le \text{y} \le 4[/tex] which turns into the interval notation [-60, 4]

Check out the graph below.

The polynomial equation is (x³ - 7x² + 20x - 24) = 0 and the Error that made by Andrew is incorrect factors of the roots.

Polynomial Equation:

The equations formed with variables, exponents and coefficients are called as polynomial equations.

Roots of the Polynomial:

Roots of a polynomial refer to the values of a variable for which the given polynomial is equal to zero.

Given,

Roots of the polynomial are: 3, 2 + 2i, 2 - 2i.

Here we need to find the error he made and the correct form of the equation.

According to the factor theorem, if a is a root of the polynomial P(x), then (x - a) is  a factor of P(x).

According to this definition:

=> (x - 3) , (x - (2 + 2i)) , (x - (2 - 2i))

are factors of the required polynomial.

Simplifying the brackets, we get:

=> (x - 3), (x - 2 - 2i), (x - 2 + 2i)

are factors of the required polynomial.

This is the step where Andrew made the error.

The factors will always be of the form (x - a) , not (x + a).

Andrew wrote the complex factors in form of (x + a)  which resulted in the wrong answer.

So, the polynomial would be:

=> (x - 3)(x - 2 - 2i)(x - 2 + 2i) = 0

=> (x - 3) (x² - 2x + 2xi - 2x + 4 - 4i - 2xi - 4i - 4i²) = 0

When we simplify it, then we get,

=> (x - 3)(x² - 4x + 4 + 4) = 0

=> (x - 3)(x² - 4x + 8) = 0

=> (x³ - 4x² + 8x - 3x² + 12x - 24) =0

=> (x³ - 7x² + 20x - 24) = 0.

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Answer:

Step-by-step explanation: Replace u with (3)

Multiply 5x3+3/2

Answer: 9

Step-by-step explanation:

remember, a variable is only a placeholder for an actual value.

so, when we get an actual value, we put it into every location of the variable in the expression and simply calculate.

6.

25/(r - 4) for r = 9

that means

25/(9 - 4) = 25/5 = 5

7.

(5u + 3)/2 for u = 3

that means

(5×3 + 3)/2 = (15 + 3)/2 = 18/2 = 9

Answer:

-3+(-6)= -9

Step-by-step explanation:

The function g(x) = - |x| + 2 is the result of applying a reflection about the x-axis and a translation 2 units up.

In this problem we find a resulting expression, that is, the function g(x) = - |x|   + 2. This is the result of a sequence of rigid transformations done on the parent absolute value function, that is, the function f(x) = |x|. Rigid transformations are transformations applied on functions such that Euclidean distance is conserved in the entire function.

After a quick inspection, we find that two rigid transformations were used in the following order:

Now we proceed prove this procedure:

f(x) = |x|

Step 1

f'(x) = - |x|

Step 2

g(x) = - |x| + 2

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Answer:

x= 0.9

step-by-step explanation:

LCM=3x

use the lcm to multiply each term

3x×1/3+3x×3=3x×3/x

cancel out

x+9x=9

10x=0

divide both side by the coefficient of x

10x/10=9/10

x=0.9

Answer:

see below

Step-by-step explanation:

1/11=0.0909....

3/11=0.090909...*3 or 0.27272727...

Scale factor for the drawing from actual park = 1/20

Area of the actual park = 1200 cm²

Area of a Rectangle. A = l × b. The area of any rectangle is calculated, once its length and width are known. By multiplying length and breadth, the rectangle's area will obtain in a square-unit dimension

Length of the rectangular city park = 5 cm

Width of the rectangular park = 6 cm

Using scale factor 1 cm = 20 meters

Scale factor = Length of the park in drawing/ actual length of park

⇒1/20.

5/actual length of park = 1/ 20

Actual length = 5 × 20 = 100 meters

Actual width = 6 × 20 = 120 meters

Area of the rectangular park = length × width

square meters

Therefore, Scale factor from actual length to the length in drawing = 1 : 20

Area of the rectangular park = 1200 square feet

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Answer:

8640in²

Step-by-step explanation:

A = I * W * H

A= 27*16*20

A=8640in²

All the data points are plotted on the number line and mentioned clearly as an image with the solution.

What is a number line?

For easy plotting on the number lines and for comparison of points, we will be converting all the fractions into decimals.

Kloee : [tex]3\frac{1}{4} = \frac{13}{4} =3.25[/tex]

High School :1.0

Middle School : 1.5

Football field : 5.7

KB: [tex]-4\frac{1}{8} = \frac{-33}{8} =-4.125[/tex]

Ben : -2.65

All the data points are plotted on the number line and mentioned clearly as an image with the solution.

(a) Distance between Ben and Kloee - 5.9

Plotted on the number line and mentioned clearly as an image with the solution.

(b) Distance of middle school from football field- 4.2

Plotted on the number line and mentioned clearly as an image with the solution.

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Astronauts brought back 500 lbs rock samples from the moon they brought back 227 kilograms of sample. The correct option is D.

Who, in brief, is an astronaut?

As the astronaut brought 550 lbs sample,

2.20lbs = 1 kg.

1 lbs = 1/2.20

1 lbs = 0.45

so, 500 lbs nearly implies 227kgs.

Thus, the correct option is D.

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Answer:

36%

Step-by-step explanation:

19.44 = ( ? percent ) × 54

This is the question in an equation form :

Divide both sides by 54 :

19.44 ÷ 54 = (? percent )

0.36 = ? percent

0.36 as a percentage is

0.36 ×100 = 36%

Hope this helped and have a good day

The value is 3600

According to question ,

given that, Depreciation for the current year is $ 3100

accumulated depreciation equipment is $ 6700

Unadjusted balance of December

 6700 - 3100 = 3600

Depreciation is the process of deducting the total cost of something expensive you bought for your business. But instead of doing it all in one tax year, you write off parts of it over time. When you depreciate assets, you can plan how much money is written off each year, giving you more control over your finances.

Formula: (asset cost – salvage value) / useful life

explain the formula:  You divide the cost of an asset, minus its salvage value, over its useful life. That determines how much depreciation you deduct each year.

Accumulated depreciation is the total amount an asset has been depreciated up until a single point. Each period, the depreciation expense recorded in that period is added to the beginning accumulated depreciation balance

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The float type of data stores real numbers (numbers with decimal values) such as 3.2, 5.67 and 48.42.

A data type, in programming, is a classification that specifies which type of value a variable has and what type of mathematical, relational or logical operations can be applied to it without causing an error.

All number types that allow for the possibility of a fractional component, such as 42.7 or pi, are known as floating point types.

The precision of various floating point data types varies depending on how many bits are utilized to represent the digits, which is directly proportional to the total number of bits in the number. In the IEEE standard, for instance:

Hence, the type of data is floating point.

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Answer:30x0

Step-by-step explanation:

Answer: f(k)=4k² - 6k +7

Step-by-step explanation:

f(x)=4x² - 6x +7

f(k)=4k² - 6k +7

The absolute value function is

|d - 140| = 30.

Using the absolute value function, we have that:

The minimum time is of 1.83 hours.

The maximum time is of 2.83 hours.

Absolute value function:

Basically, absolute value function providing the distance the number is from zero on a number line.

The absolute function is defined by:

|x| = x, x ≥ 0.

|x| = -x, x < 0.

It measures the distance of a point x to the origin,

For example,

|2| = |-2| = 2.

Given,

You are driving on a highway and are about 140 miles from a state borer. you set your cruise control at 60 miles per hour and plan to turn it off within 30 miles of the border on either side.

Here we need to  write and absolute value equation to model the situation. And we are also solve it to find the minimum and maximum numbers of hours you will have cruise control on.

In this problem, the minimum and maximum distances are within 30 miles of 140,

Hence, the absolute value function is,

|d - 140| = 30.

So, the minimum distance is of:

=> d - 140 = -30

=> d = -30 + 140

=> d = 110.

Hence the minimum time(distance divided by velocity) is:

=> 110/60 = 1.83 hours.

Then the maximum distance is of:

=> d - 140 = 30

=> d = 30 + 140

=> d = 170

Hence the maximum time(distance divided by velocity) is:

=> 170/60 = 2.83 hours.

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The rounded form of the number 9.19 which represents $9 and 19 cents to the nearest 25 cents is; 9.25

It follows from the task content that the number is required to be rounded off to the nearest 25 cents.

On this note, it follows that only 25 cent intervals are considered.

Hence, the number in discuss can either be rounded up to 9.25 or 9.00.

However, since the fractional 19 cents is closer to 25 more than it is to 0 on the number line, the rounded form of the number is;

= 9.25.

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We get that the solution to this scenario will be 50 t-shirts and 59 yearbooks.

Selling price of t shirts = $ 20

Selling price of year books = $ 24.

Let the number of t shirts sold be x and the number of yearbooks sold be y.

Goal to sell at least = $ 2400 in merchandise.

So, we get the equation as:

20 x + 24 y ≥ 2400

5 x + 6 y ≥ 600

Now, we are given some options:

50 t-shirts and 59 yearbooks

Substituting it, we get that:

5 ( 50) + 6 ( 59) ≥ 600

250 + 354 ≥ 600

604 ≥ 600

which is true.

51 t-shirts and 57 yearbooks

Substituting it, we get that:

5 ( 51) + 6 ( 57) ≥ 600

255 + 342 ≥ 600

597 ≥ 600

which is not true

60 t-shirts and 48 yearbooks

Substituting it, we get that:

5 ( 60) + 6 ( 48) ≥ 600

300 + 288 ≥ 600

588 ≥ 600

which is not true

62 t-shirts and 48 yearbooks

Substituting it, we get that:

5 ( 62) + 6 ( 48) ≥ 600

310 + 288 ≥ 600

598 ≥ 600

which is not true.

Therefore, we get that the solution to this scenario will be 50 t-shirts and 59 yearbooks.

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Answer:

50 tshirts and 59 yearbooks is the correct answer.

Step-by-step explanation:

Beginning with the graph of f(x) = x2, The transformations that are needed to form  [tex]g(x)=\frac{1}{2}(x+4)^2-3[/tex] is

The graph of g(x) is wider than f(x) and is shifted to the left 3 units and down 3 units

This is further explained below.

Generally, A point, a line, or a geometric figure may undergo one of these four distinct transformations in order for the point's, line's, or figure's shape and/or location to be altered.

The shape of the item as it was before the transformation is referred to as the Pre-Image, while the shape and location of the object after the change make up the Image.

In conclusion, The necessary transformations may be found by beginning with the graph of the function f(x) = x2.

[tex]g(x)=\frac{1}{2}(x+4)^2-3[/tex]

The graph of g(x) is bigger than the graph of f(x), and it is displaced 3 units to the left and 3 units down from its original position.

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Answer:

The graph of g(x) is wider than f(x) and is shifted to the left 4 units and down 3 units.

Step-by-step explanation:

I got it right.

Answer: 20

Step-by-step explanation:

The frequency of mice that are heterozygote is 0.3492

It is required to find the frequency.

The number of waves that pass a fixed point in unit time being, measured in hertz(Hz).The number of cycles or vibrations undergone during one unit of time by a body in periodic motion.

Given:

Population =200 mice

Gray fur mice= 120 mice

By the use of Hardy-Weinberg equation we have,

Hardy-Weinberg equation is given by

p² + 2pq + q² = 1 and p + q = 1

where, 2pq is the heterozygote frequency.

p² = 120/200

p = 0.7746

p + q = 1

q = 0.2254

Heterozygote frequency = 2pq = 2(0.2254)(0.7746) = 0.3492

Therefore, the frequency of mice that are heterozygote is 0.3492.

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There will be only 6  cubes with only one side painted red.

Cube : A cube is a 3D shape having 6 equal square sides. it has 6 faces , 8 vertices and 12 edges.

According to the question

A 3 cm cube is divided into one centimeter cube.

Every face will have 9 cube each and from that 9 cube there will be only one 1 cube that will have one side painted red.

Since there are 6 faces,

cubes painted one side red = 6x1=6.

Therefore , There will be only 6  cubes with only one side painted red.

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Answer: A= 2, B= −2, C= −2

Step-by-step explanation:

A = −1^2 −3 (−1) −2

= 1 + 3 -2 = 2

A = 2

B = 0^2 −3 (0) −2

= 0 − 0 − 2 = −2

B = −2

C = 3^2 −3 (3) −2

= 9 − 9 − 2

C = −2

Answer:

A = 2

B = -2

C = 16

Step-by-step explanation:

Plug in the numbers into the equation.

y = x^2 - 3x - 2

y = -1(-1) - 3 (-1) - 2

y = 1 + 3 - 2

y =2

y = 0^2 - 3(0) - 2

y = 0 - 0 - 2

y = -2

y = 3^2 - 3(3) - 2

y = 9 - 9 - 2

y = -2

Answer:

BC = 12

Step-by-step explanation:

from the diagram

AB + BC = AC , that is

18 + BC = 30 ( subtract 18 from both sides )

BC = 12

The total number of students in the four classes is 100 students.

From the information, the numbers of students in the four sixth-grade classes at Northside School are 26, 19, 34, and 21.

Therefore, the total number of students will be:

= 26 + 19 + 34 + 21

= 100

Therefore there are 100 students.

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1.738 kg of coffee are required to produce 200 cups of coffee.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal.

Now it is given that,

1 pound of coffee yield 50 cups.

Since 1 pound = 0.4535 kg

Therefore, 0.4535 kg of coffee yield 50 cups.

Let x be the kgs of coffee that yields 200 cups of coffee.

Thus by proportion we can write,

0.4345 / 50 = x / 200

By cross multiplication we get,

50 x = 0.4345 * 200

⇒ 50x = 86.9

⇒ x = 86.9 / 50

⇒ x = 1.738 kgs

which is the required amount of coffee need to yield 200 cups.

Thus, 1.738 kg of coffee are required to produce 200 cups of coffee.

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∠AOM ≅ ∠BOM  because they are both congruent to the same angle, not because they are vertical angles.

From the image of the angles attached, we are given that;

∠AOM ≅ ∠DON

Now, from the vertical angle theorem, we can say that;

∠AOM ≅ ∠CON

Similarly, by vertical angles theorem, we can also say that;

∠BOM ≅ ∠DON

From transitive property of congruence, we can equally say that since ∠AOM and ∠BOM are equal to the same angle, then;

∠AOM ≅ ∠BOM

From transitive property of congruence, we can equally say that since ∠CON and ∠BOM are equal to the same angle, then;

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Answer: ∠AOM≅ ∠BOM because they are both congruent to the same angle, not because they are vertical angles.

Step-by-step explanation:

cause I did the mastery test

The value of k(10) is 6.

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