Is √35 rational or irrational

MBND is a parallelogram as BN=MD and BN║MD.

A parallelogram is a quadrilateral whose both pair of opposite side are equal and parallel. Few examples of parallelograms are square, Rhombus  and rectangle.

Given ABCD is a parallelogram and ∠A=90°

Now we have to prove that MBND is a parallelogram

Given BN⊥AC and DM⊥AC

Since BN and DM are both perpendicular to the same straight line AC then we cam say that BN║DM.

Again we know  from the properties of parallelogram that the diagonal divides a parallelogram into two equal triangles.

Therefore the diagonal AC divides the parallelogram into two equal triangles ΔABC and ΔADC.

Now we know that the area of a triangle is given by [tex]\frac{1}{2}[/tex] ×base ×height .

Area of  ΔABC =Area of ΔADC

Since BN⊥AC and DM⊥AC

∴[tex]\frac{1}{2}[/tex]×BN×AC=[tex]\frac{1}{2}[/tex]×DM×AC

This above equation can be simplified as

BN=MD

Hence BMND is a parallelogram as we know from the properties of parallelogram that when a pair of opposite sides are equal and parallel in a quadrilateral it is a parallelogram.

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Answer:

- 14

Step-by-step explanation:

You can substitute the given values into the expression.

b - 3x

= -2 - 3(4)

= -2 - 12

= - 14

Hope this helped! ^^

Answer:

give the other person the brainliest the answer is -14

Step-by-step explanation:

The value of x is 108. If the mean of the data set 100, 122, 107, 115, 107, x is 108.

According to the given question.

We have a data set 100, 122, 105, 115, 107, x .

Also, the mean of the data set is 108.

As we know that, mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Therefore, the mean of the data set 100, 122, 105, 115, 107, x is given by

Mean = [100 + 122 + 107 + 115+ 107 + x]/6

⇒ 108  × 6 = (551 + x)

⇒ 648  = 551 + x

⇒ x = 648 - 551

⇒ x = 97

Hence,the value of x is 108. If the mean of the data set 100, 122, 107, 115, 107, x is 108.

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Answer:

90.29

Step-by-step explanation:

I did math

Answer:

Step-by-step explanation:

what is the question>

Answer:

x = 0.3384663

Step-by-step explanation:

The correct answer to the exponential expression which is as given in the task content is; 8³.

Based on the given task content, Gina's error from her workings is dividing the bases of the exponent.

Gina's working:

8^12 / 8^9

= 0^12 / 0^9

The Correct workings:

8^12 / 8^9

= 8^(12-9)

= 8³

So therefore, the correct answer to the exponential expression which is given in the above expression is 8³.

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If Kevin has a total of 81 hours of service, then he volunteered for 0.48 weeks.

As per the question statement, Kevin served as a volunteer for 81 hours.

We are required to find out the number of weeks, he volunteered his service.

To solve this question, we just need to know that a week consists of how many hours ?

We can proceed with the facts that a week consists of 7 days and each day consists of 24 hours. Therefore, a week consists of [tex](24*7)=168[/tex] hours, of which, Kevin volunteered for 81 hours.

Therefore, as per the unitary method, we get that,

168 hours make 1 week, then

1 hour makes [tex](\frac{1}{168})[/tex] weeks, and

81 hours make [tex](\frac{81}{168})=0.48[/tex] weeks approximately.

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Answer:102

Step-by-step explanation:

The interior angles of a triangle have to measure 180 degrees, which is an isosceles triangle, and 39+39=78.

180-78=102.Therefore the  answer is 102

Answer:

32028464937583748374

The profit percentage for the lawn owner is 15.8%

Profit Percentage:

Profit means, if the selling price of a product is more than its cost price, there is a profit earned in the transaction.

So, it can be calculated as,

Profit = Selling Price - Cost Price

The formulas for profit percentage is,

Profit percentage(P%) = (Profit /Cost Price) × 100

Given,

Here we need to find the profit percentage, If a lawnmower has a cost price of $2500 and was sold for $2895.

Based on the question,

We know that,

Cost Price = $2500

Selling Price = $2895

So, the profit is,

profit = $2895 - $2500

profit = $395

Now, the profit percentage is calculated by apply the values on the formula,

profit percentage (P%) = (395/2500) x 100

Therefore,

P% = 395/25

P% = 15.8%

Therefore, the profit percentage for the lawn owner is 15.8%.

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The mass m in terms of K and v is expressed as m= 2K/v^2

The subject of formula is a way of representing a variable in terms of other variables.

Given the equation below;

K = 1/2mv^2

Make m the subject of the formula

2K = mv^2

2K/v^2 = mv^2/v^2

2K/v^2 = m

Swap

m= 2K/v^2

Hence the mass m in terms of K and v is expressed as m= 2K/v^2

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Answer: 4.631*10^5

Step-by-step explanation:

463,100=

400,000+63,100=

4*100,000+(63,100/100,000)*100,000=

4*10^5+(631/1000)*10^5=

4*10^5+0.631*10^5=

(4+0.631)*10^5=4.631*10^5

Answer:

Step-by-step explanation:

1. -42

2. 6

3. -9

4. 545

5. 145

6. -183

7. -46

8. -15

9. -92

10. -111

Answer:

Corrected - didn't see the 10 to the negative 2 in the denominator at first - sorry)

8000

Step-by-step explanation:

Simplify

5.12 x 10 ^6/ 1.6 X 10 ^5 X (.4 X 10^-2)

Do the math

3.2 x 10/.04 x 1- ^-2)

Simplify

8 X 10^3

Simplify

8000

Answer:

x = 1 and x = -3.5

Step-by-step explanation:

y = -2x² -5x + 2

-2x² -5x + 2 = -5

which means y = -5

Draw the line on y = -5 like the green line in the attached file

and see where this line intersects with the graph

the values are:

x = 1 and x = -3.5

Answer:

Draw a line at y = -5.

x ≈ -3.5

x ≈ 1

Step-by-step explanation:

Given equation:

[tex]y = -2x^2 - 5x + 2[/tex]

This is the equation of the graphed parabola.

To solve the equation  [tex]-2x^2 - 5x + 2 = -5[/tex]  draw a line at y = -5 and find the points of intersection of the two graphed equations.

From inspection of the graph, the x-values of the points of intersection are:

Solving algebraically

Add 5 to both sides of the equation:

[tex]\implies -2x^2-5x+2+5=-5+5[/tex]

[tex]\implies -2x^2-5x+7=0[/tex]

Factor out -1 from the left side:

[tex]\implies -1(2x^2+5x-7)=0[/tex]

Divide both sides by -1:

[tex]\implies 2x^2+5x-7=0[/tex]

Find two numbers that multiply to -14 and sum to 5:  7 and -2

Rewrite b as the sum of these two numbers:

[tex]\implies 2x^2+7x-2x-7=0[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(2x+7)-1(2x+7)=0[/tex]

Factor out the common term (2x + 7):

[tex]\implies (x-1)(2x+7)=0[/tex]

Apply the zero-product property:

[tex](x-1)=0 \implies x=1[/tex]

[tex](2x+7)=0 \implies x=-\dfrac{7}{2}=-3.5[/tex]

Answer:

168

Step-by-step explanation:

You'd plug 6 in for x

f(x) = 24x + 24

f(6) = 24(6) + 24

f(6) = 144 + 24

f(6) = 168

Answer:

pqr²−p²r−q²r+pq

Step-by-step explanation:

Let's simplify step-by-step.

pq(r²+1)−r(p²+q²)

Distribute:

=(pq)(r²)+(pq)(1)+−p²r+−q²r

=pqr²+pq+−p²r+−q²r

=pqr²−p²r−q²r+pq

Answer:4.12

Step-by-step explanation:

Lambert calls the difference between the angle-sum of a triangle and 180 degrees the defect.

Therefore, Lambert calls the difference between the angle-sum of a triangle and 180 degrees the defect.

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The inequality for Leila claim is (0.75 × x) > (0.50 × y) and the support claim is x = 100 and y = 10 and that refutes the claim is x = 1 and y = 200

Inequality:

Inequality are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Given,

Leila says that 75% of a number will always be greater than 50% of any other number.

Here we need to find the inequality and we also need to find one that supports Leila's claim and one to show that she is incorrect.

Let x and y be two numbers.

Leila says that 75% of a number will always be greater than 50% of any other number.

This means that the inequality is,

=> (0.75 × x) > (0.50 × y)

We know that,

75% of x = 0.75 × x

and

50% of y = 0.50 × y

So,

Numbers that support Leila's claim.

Let x = 100 and b = 10

=> 0.75 × x

=> 0.75 × 100 = 75

and

=> 0.50 × 10 = 5

As we know that, based in on the inequality,

=> 75 > 5

Hence, x = 100 and y = 10 support Leila's claim.

Similarly,

Numbers that refutes her claim.

Let x = 1 and y = 200

=> 0.75 × x

=> 0.75 × 1 = 0.75

and

=> 0.50 × 200 = 100

As we know that,

=> 0.75 < 100

Hence, x = 1 and y = 200 refutes Leila's claim.

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Answer:   False

The correct expression is -4(x-1)^3+2

====================================================

Work Shown:

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

So the error is with the stuff in the parenthesis. Instead of (x^3-1) it should be (x-1)^3

Side note:  (x-1)^3 expands to x^3-3x^2+3x-1

The purpose why these concepts are present in the pictures is to develop imagination power among students.

As you imagine more, your mind becomes stronger and you have greater mental control. Innovation requires a strong imagination. If you succeed in what you set out to do, the same individuals who now accuse you of daydreaming will begin to aspire to be like you. Keep your aspirations high and your imagination expanding.

Imagination is a potent brain stimulant because it forces you to think differently than most people do. Your imagination can help you come up with scenarios that most effectively handle difficulties, even though your brain might classify them as being unexpected.

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Answer:

Step-by-step explanation:

So the nearest perfect square to 3793 is 3721. Hence, the least number that must be subtracted from 3793 to get a perfect square = 3793 - 3721 = 72.

Answer:

ABBCBAAHSHSHDHEEHDHSHHH74737477382

The area of a triangle is 4 square units.

Given that, the coordinates of the triangle ABC are A(4, 3), B(5, 1) and C(1, 1).

We need to find the area of a triangle ABC.

The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.

The base of the triangle = |5-1|=4

From vertices, A(4, 3) to the base the distance is 2 units at the vertice (4, 1)

So, the height of the triangle = 2 units

Now, the area of a triangle ABC = 1/2 × 4 × 2 = 4 square units.

In the given solution the height of a triangle is wrongly calculated.

Therefore, the area of a triangle is 4 square units.

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Answer:

Step-by-step explanation:

Let x represent the number of weeks a population of the bacteria increases. Then, we have the number of bacteria is molded by the expression of 900*3^x. By, the given expression and when we assigned a value of x=2. Then we have 900*3² .

Answer:

here is my answer........

Step-by-step explanation:

(3-x)^2 = 9 - 3x - 3x + X2

= X2 - 6x +9

The scale of the drawing is in the ratio of 1 millimeter : 3 meter

In this, we need to find the ratio that is 1millimeter:x meter where x is the original scaling of the plot.

We have been given that

                   24 millimeters = 72 meters

Now we have to find how many meters is equal to 1 millimeter which will find out by the unitary method.

Thus,   24 millimeters = 72 meters

               1 millimeter = 72/24 meter

               1 millimeter = 3 meter

Hence the scale of the drawing is 1 millimeter : 3 meter

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