What is 781,407 rounded to the nearest ten thousand What is 781,407 rounded to the nearest ten thousand?

Answer:

"Billy's age in 8 years", this refers to a future age, which implies adding 8 years to the present age. The expression would be:

[tex]B+8[/tex]

"In 8 years Billy will be 21 years", this expression, using the first one too, would be:

[tex]B+8=21[/tex]

How old is Billy now?

The answer to this question is the solution of the second equation:

[tex]B+8=21\\B=21-8=13[/tex]

Billy is 13 years old now.

A problem for the expression [tex]A-6=10[/tex] could be:

Six years ago Adam was 10 years old.

The six years in the past refers subtracting, and the age back then is the result of that difference.

Final answer:

To find two consecutive odd integers whose squares sum to 2594, a quadratic equation is set up and solved, revealing that the integers are 35 and 37.

Explanation:

To solve for two consecutive odd integers whose squares sum to 2594, we can set up equations based on the characteristics of odd integers. Let the smaller integer be n, then the next consecutive odd integer would be n + 2.

The equation based on the sum of the squares of the two numbers is then:

n2 + (n + 2)2 = 2594

Solving this equation:

Solving the quadratic equation we find that n = 35 and n + 2 = 37. Hence, the two consecutive odd integers are 35 and 37.

The sum of the squares of two sides is not equal to the square of the third side, the triangle PQR is not a right triangle.

According to Pythagoras Theorem, in a right angled triangle the square of the side opposite to the right angle is equal to the sum of squares of the other two sides.

Height² + Base² = Hypotenuse²

If a triangle is a right angle, then its sides should satisfy Pythagoras theorem.

The distance formula will be used to determine the length of the sides.

PQ² =  ( 3 - 0)² + (2-1)²

PQ² = 10

PQ = √10

RQ² =  ( 5 - 3)² + (-4-2)²

RQ² = 40

RQ = √40

RP² =  ( 5 - 0)² + (-4-1)²

RQ² =  25 + 36

RQ² =  61

Applying the Pythagoras's Theorem,

61 ≠ 40 + 10

Therefore, it is not a right angled triangle.

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30-24 = 6

6/2 = 3

24 + 3 = 27

 median width = 27

A coordinate plane is a graphical image that shows two number lines. These number lines have a y-axis and x-axis. The y-axis is the vertical number line and the x-axis is the horizontal number line.

The perimeter of the rectangle is 26.8 units

We would be applying Pythagoras Theorem to find the length and breadth of the rectangle.

Pythagoras Theorem states that:

c² = a² + b²

Note that c = The length or breadth of the rectangle

We have 4 units and 8 units.

a = 4 units

b = 8 units

Using the Pythagorean Theorem, you can calculate the length of the hypotenuse to be

c² = 4² + 8²

c² = 80

c = √ 80

c = 8.9 units

Applying this to the lower part,

We have 4 units and 2 units.

a = 2 units

b = 4 units

Using the Pythagorean Theorem, you can calculate the length of the hypotenuse to be

c² = 2² + 4²

c² = 20

c = √20

c = 4.5 units

Formula = 2L + 2B

Where

L = Length = 8.9 units

B = Breadth = 4.5 units

Hence:

8.9 x 2 + 4.5 x2 = 26.8 units

Therefore, the perimeter of the rectangle is 26.8 units

Option C is the correct answer

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Answer:

Point B will be 6

Step-by-step explanation:

We have point A= -24 and point B = 36, we want to know point B which is halfway between points A and C.

To find the middle between two points we have to add the two numbers and divide them by 2:

We would have:

(A+C)/2

We substitute the values of A and C:

B = (-24+36)/2

B = 12/2

B = 6.

We can also write this on a number line and get point B by counting how many numbers there are in between point A and C, and this result divides it by 2. This is in the attachment.

equation = g(x) = 2x-2

 when g(-3) replace x with -3

 so you get g(-3) = 2(-3)-2

2*-3 = -6-2 = -8

g(-3) = -8

That would be 32, 16 and 34.

Answer:

Option b - [tex]5w + 8 - w = 6w - 2( w - 4)[/tex]  

Step-by-step explanation:

To find : Which equation is an identity?    

Solution :

Option a - [tex]11- (2v + 3) = -2v - 8[/tex]          

If we open the parenthesis,

[tex]11- 2v -3 = -2v - 8[/tex]    

[tex]-2v+8\neq -2v - 8[/tex]    

No identity applied.

Option b - [tex]5w + 8 - w = 6w - 2( w - 4)[/tex]          

If we apply distributive property, [tex]a(b+c)=ab+ac[/tex]

[tex]5w + 8 - w = 6w - 2w+8[/tex]    

[tex]4w+8= 4w+8[/tex]    

Distributive identity is applied.

Option c - [tex]7m - 2 = 8m + 4 - m[/tex]          

Solve by subtracting in RHS

[tex]7m - 2 \neq 7m + 4[/tex]    

No identity applied.

Option d- [tex]8y + 9 = 8y - 3[/tex]          

This is not possible as [tex]8y + 9 \neq 8y - 3[/tex]

No identity applied.          

Therefore, Option b is correct.

The inequality y ≤ [tex]\frac{5}{2}[/tex] x+5 represents the given graph. Therefore, option D is the correct answer.

In mathematics, inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions.

From the graph the inequality intersect lines at (-2, 0) and (0, 5).

The graph is shaded below the line.

So, inequality y ≤ [tex]\frac{5}{2}[/tex] x+5.

The inequality y ≤ [tex]\frac{5}{2}[/tex] x+5 represents the given graph. Therefore, option D is the correct answer.

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The Answer Is B.2-1/3

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The expression −2/3(3-1/2)(-1) is equivalent to -5/3.

To simplify the expression −2/3(3-1/2)(-1), we can start by simplifying the expressions within the parentheses.

3-1/2 = 6/2 - 1/2 = 5/2

Next, we can multiply the expression −2/3(5/2)(-1).

−2/3(5/2)(-1) = -2/3 * 5/2 * -1 = -10/6 = -5/3

Therefore, the expression is equivalent to -5/3.

Answer:

1100 grams

Step-by-step explanation:

Answer:  The ratio of the volumes of two pyramids is 27 : 1331.

Step-by-step explanation:  Given that two two pyramids are similar and the ratio between the length of their edges is 3 : 11.

We are to find the ratio of the volumes of two pyramids.

Let a units and b units be the lengths of the edges of the two pyramids.

The, according to the given information, we have

[tex]a:b=3:11.[/tex]

We know that the ratio of the volumes of two similar pyramids is equal to the ratio of the cubes of the lengths of edges of the two pyramids.

Therefore, the ratio of the volumes of two pyramids will be

[tex]V:V'=\dfrac{V}{V'}=\dfrac{a^3}{b^3}=\left(\dfrac{a}{b}\right)^3=\left(\dfrac{3}{11}\right)^3=\dfrac{27}{1331}=27:1331\\\\\\\Rightarrow V:V'=27:1331.[/tex]

Thus, the ratio of the volumes of two pyramids is 27 : 1331.