Eliminate y to solve for x. Plug in x into the second equation to solve for y

Let

[tex]a=2\ in\\b=4\ in\\c=5\ in[/tex]

we know that

If [tex]c^{2} =a^{2}+b^{2}[/tex] -----> is a right triangle

If [tex]c^{2} > a^{2}+b^{2}[/tex] -----> is an obtuse triangle

If [tex]c^{2} < a^{2}+b^{2}[/tex] -----> is an acute triangle

so

substitute the values

[tex]5^{2} > 2^{2}+4^{2}[/tex] ------> is an obtuse triangle

therefore

the answer is

The triangle is not acute because [tex] 2^{2}+4^{2}< 5^{2}[/tex]

Answer:  The correct option is

(C)  The triangle is not acute because 2² + 4² < 5².

Step-by-step explanation:  We are to select the statement that best explains the type of the triangle having lengths of three sides as 2 inch, 5 inch and 4 inch.

We know that a triangle with side lengths a, b and c (c > a, b)is

(i) an acute-angled if a² + b² > c², and

(ii) an obtuse-angled if a² + b² < c².

For the given triangle,

a = 2 inch, b = 4 inch  and  c = 5 inch.

So, we have

[tex]a^2+b^2=2^2+4^2=4+16=20,\\\\c^2=5^2=25.[/tex]

Since,

[tex]20<25\\\\\Rightarrow a^2+b^2<c^2,[/tex]

so the given triangle is not acute, but obtuse.

Thus, the triangle is not acute because 2² + 4² < 5².

Option (C) is correct.

B) 25, 650 ft^2

If the ratio is 1:15, then the measurements of each side of the actual gym are 15 times greater than the scale's. So the areas would have a ratio of 1:225. 114 times 225 is equal to 25, 650

well in her first travel (when she goes to the anther city)

v1= 50mph

d1=100 m

t1=?

t=d/v=100/50=2h

that's meat that she will take 2hours during the first travel 

and total travel time = 3h 

she wants to take only 1 h in her second travel 

v2=?

d2=100 m

t2= 1h

v2= d2 *t2 =100mph 

total travel time is 3 hours and 40 minutes so i belive the correct answer is 60mph

To solve for b in the equation A = (a + b + c) / 3, multiply both sides by 3 and then subtract a and c from both sides. The correct answer is A) 3A - a - c = b.

To solve for b in the equation A = (a + b + c) / 3, you need to isolate the variable b.

First, multiply both sides of the equation by 3 to eliminate the denominator:

3A = a + b + c

Then, subtract a and c from both sides to get b by itself:

3A - a - c = b

So, the correct answer is:

A) 3A - a - c = b

To determine the side length of a Rubik's cube with a volume of 384 cubic centimeters, take the cube root of 384 to find that each side is approximately 7.24 centimeters long.

To find the length of one side of a cube when given the volume, you can use the formula for the volume of a cube, which is V = L³, where V is the volume and L is the length of a side of the cube.

In this case, the volume is 384 cubic centimeters, so we need to find the cube root of 384 to find the length of one side.

The calculation is as follows:

Therefore, each side of the Rubik's cube is approximately 7.24 centimeters long.

Answer:

90 mph

Step-by-step explanation:

Let speed of  both train=x mph

Time taken by train A to reach station A=[tex]2\frac{1}{2}[/tex] hr=\frac{5]{2} h[/tex]

Time taken by train B to reach station B=4 h

Distance between two trains=585 miles

We know that

Distance=[tex] speed\times time[/tex]

Distance covered by train A=[tex]\frac{5}{2} x[/tex]

Distance covered by train B=[tex]4x[/tex]

When two trains travel in opposite direction then total distance

[tex]\frac{5}{2}x+4x=585[/tex]

[tex]\frac{5x+8x}{2}=585[/tex]

[tex]\frac{13}{2}x=585[/tex]

[tex]x=585\times \frac{2}{13}=90 mph[/tex]

Hence, the rate of both trains=90 mph

Answer:

Option (c) is correct.

The system is Inconsistent.

Step-by-step explanation:

Given : A pair of lines.

We have to identify the system by type.

Consider the given system of pairs of lines.

Since, the graph shows two parallel lines.

1) Consistent :  A system of linear equation is said to be consistent if the graph of equation either intersect at a single point or two lines overlap each other.

that is a unique solution or infinite many solution.

2) equivalent :  When two system of equations have same solution then the two system are said to be equivalent.

3) Inconsistent : A system of linear equation is said to be inconsistent if the graph of equation are parallel to each other.

Thus, the given graph shows parallel lines,

Hence, The system is Inconsistent

A

first option is correct

Answer:

Option B is correct

The average rate of change of d(t) between 2 second and 4 second is; 90 ft/s

and it represents the average speed of the object between 2 seconds and 4 seconds.

Step-by-step explanation:

Average rate of change of function is defined as the ratio of the difference in the function f(x) as it changes from a to b to the difference between a and b. Then, the average rate of change is denoted as A(x).

[tex]A(x) =\frac{f(b)-f(a)}{b-a}[/tex]

As per the given statement, the distance d(t) is in feet and t is the time in second.

To find the average rate of change of d(t) between 2 seconds and 4 seconds.

From the table we have;

at t = 2 , d(2) = 60

and

at t =4 , d(4) = 240.

Then, by the definition of average rate of change ;

[tex]A(t) = \frac{d(4)-d(2)}{4-2}[/tex] = [tex]\frac{240-60}{4-2} =\frac{180}{2}[/tex]

Simplify:

[tex]A(t) = 90 ft/s[/tex]

therefore, the average rate of change of d(t) between 2 second and 4 second is; 90 ft/s and it represents the average speed of the object between 2 seconds and 4 seconds.

Answer:

Hence, Option: C is correct.

The term that does not describe polygon A'B'C'D' is:

Pre-image.

Step-by-step explanation:

Clearly we could observe that the polygon A'B'C'D' is the image that is obtained by the applying some transformation to the polygon ABCD.

The transformation that is applied to ABCD to obtain A'B'C'D' is:

Rotating the figure anticlockwise 90° and then translating it 7 units to the  left and 1 unit downward.

Hence, Polygon A'B'C'D' is not a pre-image.

Since it is an image which is formed or obtained by applying required transformation to the pre-image ABCD.

The correct option is C) preimage. Polygon [tex]\(A'B'C'D'\)[/tex] is the image of the transformation, not the preimage.

To determine which term does not describe polygon [tex]\(A'B'C'D'\)[/tex], we need to understand the definitions of each term in the context of transformations in geometry:

Rotation : This is a type of transformation that turns a figure around a fixed point at a certain angle. Polygon [tex]\(A'B'C'D'\)[/tex] could be a result of rotating polygon [tex]\(ABCD\)[/tex]  

Image : The image is the result of applying a transformation to a figure. [tex]A'B'C'D'\)[/tex] is the image of [tex]\(ABCD\)[/tex] after some transformation.

Preimage : The preimage is the original figure before a transformation is applied. In this context, [tex]\(ABCD\)[/tex] is the preimage, not [tex]\(A'B'C'D'\)[/tex]

Transformation : This is a general term that refers to any operation that moves or changes a figure in some way to produce a new figure. The process that produced [tex]\(A'B'C'D'\)[/tex] from [tex]\(ABCD\)[/tex] is a transformation.

From these definitions, the term that does not describe polygon [tex]\(A'B'C'D'\)[/tex] is preimage.

F = 32,000 (1+ 0.061*10)

F = 51,520

That makes the total interest equal 51,520 -32,000 = 19, 520.