Will ran the diagonal distance across a square field measuring 40 yards on each side. James ran the diagonal distance across a rectangular field with a length of 25 yards and a width of 35 yards. Will ran a longer distance. How much longer did he run?

Answer:

C.g(x) = 5x²

Step-by-step explanation:

To find the equation for the function g(x), use the format for a quadratic equation. Without any up/down and left/right shifts, the form is y = ax².

Substituting "x" and "y" into the equation tells you if a point is on the graph.

"a" tells you the vertical stretch (greater than 1) or compression (greater than 0, less than 1).

In f(x) = x², a = 1 even though it's not written.

Use the point (1, 5) on g(x) and substitute it into the form for a quadratic function. Remember points are (x, y), so x = 1 and y = 5.

g(x) = ax²    

y = ax²       In function notation, g(x) replaces the "y". Switch it back to "y".

5 = a(1)²     Substitute x = 1 and y = 5

5 = a(1)     Solve the exponent first. (1)² = 1

5 = a         When you multiply "a" by 1, the answer is just "a".

a = 5         Solved for "a". Put variable on left side for standard formatting.

With the quadratic form, substitute "a" into g(x).

y = ax²

g(x) = 5x²

Answer:

The correct option is first one.

Therefore,

[tex]4(-1) = (-1)(4)[/tex] .. illustrates the associative property of multiplication.

Step-by-step explanation:

Associative property:

The associative property states that you can add or multiply regardless of how the numbers are grouped.

For example A x B = B x A

Therefore,

[tex]4(-1) = (-1)(4)[/tex] .. illustrates the associative property of multiplication.

Answer:

Option (-2-1)(8)=-2(1-8) is correct

The expression (-2-1)(8)=-2(1-8) represents the associative property of multiplication .

Step-by-step explanation:

Given expression is (-2-1)(8)=-2(1-8)

Associative property of multiplication is given by

(a+b)c=a(b+c)

Comparing the equations (-2-1)(8)=-2(1-8) and (a+b)c=a(b+c)  we get that the given expression is in the form of (a+b)c=a(b+c)

Therefore the given equation represents the associative property of multiplication .

Therefore option (-2-1)(8)=-2(1-8) is correct

The expression (-2-1)(8)=-2(1-8) represents the associative property of multiplication .

Answer: w = 4[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Let the unknown number be w , then

the product of w and 3 = 3w

Nine less than the product of 3 and the number = 3w - 9

completing the equation , we have

3w - 9 = 4

add 9 to both sides

3w = 13

w = 13/3

w = 4[tex]\frac{1}{3}[/tex]

The solution to the system of equations 10x - 2y = 24 and 6x + 2y = 8 is (2, -2).

To solve the system of equations 10x - 2y = 24 and 6x + 2y = 8, we can use the method of elimination.

Adding the two equations together, the 2y terms will cancel out:

[tex]\[ (10x - 2y) + (6x + 2y) = 24 + 8 \]\[ 10x - 2y + 6x + 2y = 32 \]\[ 16x = 32 \]\\[/tex]

Dividing both sides by 16:

x = 2

Now, we substitute x = 2 into one of the original equations to solve for y. Let's use the first equation:

[tex]\[ 10(2) - 2y = 24 \]\[ 20 - 2y = 24 \][/tex]

Subtracting 20 from both sides:

-2y = 4

Dividing both sides by -2:

y = -2

So, the solution to the system is (2, -2).

Option B

The first strain is [tex]2.182 \times 10^{-7}[/tex] mm larger than second strain

Solution:

Given that,

The length of one strain of the bacteria measures 0.000000242 mm

The length of the second strain measures 0.0000000238 mm

To find: Difference between the first strain and second strain

From given ,

Length of first strain = 0.000000242 mm

Length of second strain = 0.0000000238 mm

Let us convert them into scientific notation

Move the decimal point in your number until there is only one non-zero digit to the left of the decimal point. The resulting decimal number is a.

Count how many places you moved the decimal point. This number is b.

If you moved the decimal to the left b is positive.

If you moved the decimal to the right b is negative.

Write your scientific notation number as a x 10^b

Therefore,

[tex]0.000000242 = 2.42 \times 10^{-7}[/tex]

[ Here we moved the decimal point to right , we have moved 7 times. So exponent is -7 ]

[tex]0.0000000238 = 2.38 \times 10^{-8}[/tex]

[ Here we moved the decimal point to right , we have moved 8 times. So exponent is -8 ]

Now find the difference

[tex]Difference = length\ of\ first\ strain\ - length\ of\ second\ strain[/tex]

[tex]Difference = (2.42 \times 10^{-7}) - (2.38 \times 10^{-8})\\\\\text{Make the exponents same }\\\\Difference = (2.42 \times 10^{-7}) - (0.238 \times 10^{-7})\\\\\text{Take the common term out }\\\\Difference = 10^{-7}(2.42 - 0.238)\\\\Difference = 10^{-7} \times 2.182\\\\Difference = 2.182 \times 10^{-7}[/tex]

Thus first strain is [tex]2.182 \times 10^{-7}[/tex] mm larger than second

Answer:

why?

Step-by-step explanation:

Answer:

P=92 cm

Step-by-step explanation:

<B and <D are congruent so you now know that <D also equals 11.5

Add all the sides up then multiply by 2

You are multiplying by two because each point is at the radius (halfway)

11.5 + 11.5 +10.5+12.5 =46

46 x 2=92

Answer:

92 is the answer

Step-by-step explanation:

Notice the dots are only half way. You have the sides 11.5, 10.5, and 12.5. It says the side D and B are congrent which means they equal. So the side is 11.5. 11.5+11.5=23 Whihc is one side of the permiter. 10.5+10.5=21. 12.5+12.5=25. 11.5+11.5=23. When you add them up you get the answer 92. Hope this helps!

Answer:

3x+4=19 x is 5 3(5)=15+4=19

Step-by-step explanation:

Step-by-step explanation:

130.395 km^2 + 505.990 km^2 = 636.385 km^2

Answer:

This air travel distance is equal to 1,034 miles. The air travel (bird fly) shortest distance between Spain and United Kingdom is 1,664 km= 1,034 miles. If you travel with an airplane (which has average speed of 560 miles) from Spain to United Kingdom, It takes 1.85 hours to arrive.

Step-by-step explanation:

a. The solution set is (-3,2)

b. The solution set is (2,6)

c. The solution set is (1,1)

d. The solution set is (-0.5,1.5)

e. The solution set is (7.5, -4.5)

f. The solution set is (-2,7)

Step-by-step explanation:

a. x+2y=1   Eqn 1

   x=y-5      Eqn 2

Putting value of x from Eqn 2 in Eqn 1

[tex](y-5)+2y=1\\y-5+2y=1\\3y=1+5\\3y=6[/tex]

Dividing both sides by 3

[tex]\frac{3y}{3}=\frac{6}{3}\\y=2[/tex]

Putting y=2 in Eqn 2

[tex]x=2-5\\x=-3[/tex]

The solution set is (-3,2).

b. y-x=4    Eqn 1

   y=3x     Eqn 2

Putting value of y from Eqn 2 in Eqn 1

[tex]3x-x=4\\2x=4[/tex]

Dividing both sides by 2

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

Putting x=2 in Eqn 2

[tex]y=3(2)\\y=6[/tex]

The solution set is (2,6)

c. y = x     Eqn 1

  y = -x+2   Eqn 2

Putting value of y from Eqn 1 in Eqn 2

[tex]x=-x+2\\x+x=2\\2x=2[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2}=\frac{2}{2}\\x=1[/tex]

Putting x=1 in Eqn 1

[tex]y=1[/tex]

The solution set is (1,1)

d. y=5x+4    Eqn 1

   x+3y=4     Eqn 2

Putting value of y from Eqn 1 in Eqn 2

[tex]x+3(5x+4)=4\\x+15x+12=4\\16x=4-12\\16x=-8[/tex]

Dividing both sides by 16

[tex]\frac{16x}{16}=\frac{-8}{16}\\x=-0.5[/tex]

Putting x= -0.5 in Eqn 1

[tex]y=5(-0.5)+4\\y=-2.5+4\\y=1.5[/tex]

The solution set is (-0.5,1.5)

e. x-y=12   Eqn 1

   y = 3-x   Eqn 2

Putting value of y from Eqn 2 in Eqn 1

[tex]x-(3-x)=12\\x-3+x=12\\2x=12+3\\2x=15[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2}=\frac{15}{2}\\x=7.5[/tex]

Putting x=7.5 in Eqn 2

[tex]y=3-7.5\\y=-4.5[/tex]

The solution set is (7.5, -4.5)

f. 2x+y=3      Eqn 1

  x+y=5       Eqn 2

From Eqn 2;

y = 5-x

Putting in Eqn 1

[tex]2x+(5-x)=3\\2x+5-x=3\\x=3-5\\x=-2[/tex]

Putting x=-2 in Eqn 1

[tex]2(-2)+y=3\\-4+y=3\\y=3+4\\y=7[/tex]

The solution set is (-2,7).

Keywords: linear equation, substitution method

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Answer:

They both are the same.

Step-by-step explanation:

every day is 24 hours and that times three is 72

Answer: None of them is more. Both them are equal because 24 hours = 1 day.

1 day = 24 Hours

2 days = 48 hours

3 days = 72 hours

24 added to each one

Step-by-step explanation:

[tex]\bf \begin{cases} -2x+y=0\\ \boxed{y} = 2x\\[-0.5em] \hrulefill\\ 5x+3y=-11 \end{cases}\qquad \qquad \implies \stackrel{\textit{substituting on the 2nd equation}}{5x+3\left( \boxed{2x} \right)=-11} \\\\\\ 5x+6x=-11\implies 11x=-11\implies x = \cfrac{-11}{11}\implies \blacktriangleright x = -1 \blacktriangleleft \\\\\\ \stackrel{\textit{we know that}}{y = 2x}\implies \blacktriangleright y = -2 \blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (-1~~,~~-2)~\hfill[/tex]

Based on the , the counterexample to the statement "If two angles are congruent, then the angles are vertical angles" is:

B) Right Triangle with Two 45° Angles

Here's why:

The diagram shows a right triangle ABC.

Angles ∠ACB and ∠CAB are both 45 degrees, as indicated by the markings.

Therefore, ∠ACB and ∠CAB are congruent (they have the same measure).

However, these angles are not vertical angles. They are adjacent angles in the right triangle, sharing the vertex C but not formed by intersecting lines.

Therefore, diagram C provides a counterexample to the original statement. The other diagrams:

A) Doesn't show any congruent angles.

B) Shows vertical angles, but they are not marked as congruent.

D) Shows congruent corresponding angles in parallel lines, but not vertical angles.

Answer:

Step-by-step explanation:

Let's calculate the distance between the corresponding coordinates of points A and C.

[tex]A(1,\ -5),\ C(-5,\ 4)\\\\|AC|_x=|-5-1|=|-6|=6\\\\|AC|_y=|4-(-5)|=|4+5|=|9|=9[/tex]

We find such B that

[tex]|AB|=\dfrac{2}{3}|AC|=\dfrac{2|AC|}{3}[/tex]

Calculate the unit of division

[tex]a_x=\dfrac{6}{3}=2\\\\b_y=\dfrac{9}{3}=3[/tex]

Therefore the coordinateso f the point B are:

[tex]B(x+2,\ y-3)\\\\x+2=-5+2=-3\\\\y-3=4-3=1\\\\\boxed{B(-3,\ 1)}[/tex]

Answer:

x=14

Step-by-step explanation:

2x-7<21

+7=0

2×<21+7=28

2×/2=0

2/28

=14

Answer:

91

Step-by-step explanation:

Trust me, it's an Aops question, and I got mastery on it, or blue if you want.

Answer:

D. No solution.

Step-by-step explanation:

2x - 3 = 2x - 5

2x - 2x - 3 = 2x - 2x - 5

-3 = -5   which is absurd so there is No Solution.

Answer:

D no solution

Step-by-step explanation:

2x-3= 2x-5  means  : -3=-5   ...false

Answer:

c. 24 is a solution

Step-by-step explanation:

Given equation:

[tex]\frac{4}{3}=\frac{32}{d}[/tex]

To test the numbers 22, 23, 24, 25 for the solution.

Solution:

In order to test the given number for the solution, we will plugin each number in the unknown variable [tex]d[/tex] and see if it satisfies the equation.

1) [tex]d=22[/tex]

[tex]\frac{4}{3}=\frac{32}{22}[/tex]

Reducing fraction to simplest form by dividing the numerator and denominator by their G.C.F.

[tex]\frac{4}{3}=\frac{32\div 2}{22\div 2}[/tex]

[tex]\frac{4}{3}=\frac{16}{11}[/tex]

The above statement can never be true and hence 22 is not a solution.

2) [tex]d=23[/tex]

[tex]\frac{4}{3}=\frac{32}{23}[/tex]

The fractions can no further be reduced.

The statement can never be true and hence 23 is not a solution.

3) [tex]d=24[/tex]

[tex]\frac{4}{3}=\frac{32}{24}[/tex]

Reducing fraction to simplest form by dividing the numerator and denominator by their G.C.F.

[tex]\frac{4}{3}=\frac{32\div 8}{24\div 8}[/tex]

[tex]\frac{4}{3}=\frac{4}{3}[/tex]

The above statement is always true and hence 24 is a solution.

4) [tex]d=25[/tex]

[tex]\frac{4}{3}=\frac{32}{25}[/tex]

The fractions can no further be reduced.

The statement can never be true and hence 25 is not a solution.

Answer:

its c

Step-by-step explanation:

Answer:

-10y - 11x

Step-by-step explanation:

First you need to distribute -7 through the parentheses.

-7y - 14x - 3y + 3x

then you need to collect the like terms (terms with the same variable)

-10y - 11x

Answer:-10y - 11x

Step-by-step explanation:

Expanding , we have

-7y - 14x -3y  + 3x

collecting the like terms , we have

- 7y - 3y - 14x + 3x

Simplifying , we have

-10y - 11x

Answer:

Max

Step-by-step explanation:
what is this question

Answer:

The correct answer is C. 3 (-64 ÷ 8) + 25

Step-by-step explanation:

Let's solve the four expressions to find out the positive one, this way:

A. - 4 + (-5) (-6) ÷ (-3)

= -4 + 30 ÷ -3

= - 4 - 10 = - 14

B. 8 [10 ÷ (2) (-2)]

= 8 [10 ÷ -4]

= 8 * - 2.5 = -20

C. 3 ( -64 ÷ 8) + 25

= 3 ( -8) + 25

= - 24 + 25 = 1

D. -2 (-5) (-3) ÷ 10

= - 30 ÷ 10 = -3

As we can see, after solving the four expressions, the only with a positive result is C. 3 ( -64 ÷ 8) + 25

Answer:

The volume of the observatory is 497.43 [tex]feet^{3}[/tex]

Step-by-step explanation:

i) The diameter of the floor is 10 feet. The floor is circular and has a radius,          

    r =  [tex]\frac{10}{2}[/tex] = 5 feet.

   Therefore the area of the circular floor of the observatory

     = [tex]\pi r^{2}[/tex]      =   3.14159 × [tex]5^{2}[/tex]    =    78.54 [tex]feet^{2}[/tex]

ii) The observatory is made up of two parts

  a)  3 foot tall cylinder

      ∴ volume of cylinder = [tex]\pi r^{2}[/tex]   × h

                                         = 78.54 × 3

                                         = 235.62 [tex]feet^{3}[/tex]

   b)  hemisphere = [tex]\frac{1}{2}[/tex] × [tex]\frac{4}{3} \pi r^{3}[/tex] = 0.6667 × 78.54 × 5   =  261.81 [tex]feet^{3}[/tex]

    c) Therefore the total volume of the observatory is = a) + b)

         = 235.62 + 261.81 =   497.43 [tex]feet^{3}[/tex]

6x +2y

Solution:

Given expression is (6x + 4y) –2y.

To find the equivalent expression for the given expression.

⇒ (6x + 4y) –2y

⇒ 6x + 4y –2y

Combine like terms together.

⇒ 6x + (4y –2y)

⇒ 6x + 2y

6x +2y is equivalent to (6x + 4y) –2y.

Hence, the expression equivalent to (6x + 4y) –2y is 6x + 2y.

Answer:

a) the area of a square is in terms of x is

[tex](x+1)^2[/tex] centimeter square

b)The length of the rectangle is l = (x+1)

                                       l = 7+1 =8 cm

The width of the rectangle is w = [(x+1)-5]

                                     w = (7+1)-5 =3 cm

Step-by-step explanation:

a) the area of a square is in terms of x is

 area of square is [tex]l^{2} = (x+1)(x+1)[/tex]

                                 = [tex](x+1)^2[/tex]

b)  Given length is  l = (x+1) cm and

the width is 5 cm less than its length.

so we have take width is w = (x+1)-5 cm

Given area of triangle is  24 cm

Area of rectangle = length X width

24  =  (x+1)(x+1 -5 )

now simplification [tex]24 = (x+1)^2 - 5 (x+1)[/tex]

apply (a+b)^2 = a^2+2 a b+b^2

[tex]x^2+2 x+1-5 x-5 =24[/tex]

[tex]x^2 -3 x -4-24=0[/tex]

[tex]x^{2} -3 x -28 =0[/tex]

now find factors of 28  = 7 X 4 is  

[tex]x^{2} -7 x+4 x-28=0[/tex]

[tex]x(x-7)+4(x-7)=0[/tex]

[tex](x+4)(x-7)=0[/tex]

x = -4 and x=7

there fore you have to choose x = 7

The length of the rectangle is l = (x+1)

                                       l = 7+1 =8

The width of the rectangle is w = [(x+1)-5]

                                     w = (7+1)-5 = 3

Verification:-

Given area of rectangle  = 24 = 8 X 3

                                           24 =24

so we can not choose x=-4

we have to choose x =7 only

Answer: yes , it is possible

Step-by-step explanation:

Let the first number be x and the second number be y .Then , the sum of the two numbers will be x + y , and their difference will be x - y.

Combining the two , we have :

x + y = 1 ............................... equation 1

x - y = 8 ................................. equation 2

solving the system of linear equation by substitution method. From equation 1 , make x the subject of the formula ,

x = 1 - y ...................... equation 3

Substitute equation 3 into equation 2 ,

1 - y - y = 8

1 - 2y = 8

add 2y to both sides

1 = 8 + 2y

subtract 8 from both sides

1 - 8 = 2y

- 7 = 2y

divide through by 2

y = [tex]\frac{-7}{2}[/tex]

y = - 3.5

substitute y = -3.5 into equation 3 to find the value of x , we have

x = 1 - y

x = 1 - ( - 3.5 )

x = 1 + 3.5

x = 4.5

Let us check :

x + y will be

4.5 + (-3.5) = 1

Also ,

x - y will be

4.5 - (-3.5)

⇒ 4.5 + 3.5 = 8

Answer:

[tex]\frac{\pi }{4}[/tex] could be used as a reference angle for [tex]\frac{15\pi }{4}[/tex].

Step-by-step explanation:

Given the trigonometric expression

[tex]\frac{15\pi }{4}[/tex]

In order to find the reference angle for [tex]\frac{15\pi }{4}[/tex], find an angle that is positive, less than [tex]2\pi[/tex], and coterminal with

Subtract  [tex]2\pi[/tex] from  [tex]\frac{15\pi }{4}[/tex].

[tex]\frac{15\pi }{4} -2\pi[/tex]

The resulting angle of [tex]\frac{7\pi }{4}[/tex] is positive, less than [tex]2\pi[/tex], and coterminal with   [tex]\frac{15\pi }{4}[/tex].

[tex]\frac{7\pi }{4}[/tex]

Since the angle [tex]\frac{7\pi }{4}[/tex] is in the fourth quadrant, subtract

[tex]2\pi-\frac{7\pi }{4}=\frac{\pi }{4}[/tex]

Therefore, [tex]\frac{\pi }{4}[/tex] could be used as a reference angle for [tex]\frac{15\pi }{4}[/tex].

Keywords: reference angle

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The reference angle = [tex]\frac{\pi}{4}[/tex].

Note that     [tex]\frac{15\pi}{4}[/tex]  [tex]\frac{15\pi}{4}=3.75\pi[/tex] lies in the 4th quadrant and it is close to  [tex]4\pi[/tex].

To find the reference angle of  [tex]\frac{15\pi}{4}[/tex]  we will subtract it from [tex]4\pi[/tex].

So, the reference angle is:

[tex]4\pi-\frac{15\pi}{4}=\frac{\pi}{4}[/tex]

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Answer:

see work attached and shown

Answer:

[tex]FJ=18\ units[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

△FEG is similar with △FHJ -----> by AA Similarity Theorem

so

[tex]\frac{FE}{FH}=\frac{FG}{FJ}[/tex]

we have

[tex]FE=HF+EH=12+8=20\ units[/tex]

[tex]FH=HF=12\ units[/tex]

[tex]FG=30\ units[/tex]

substitute the given values

[tex]\frac{20}{12}=\frac{30}{FJ}[/tex]

[tex]FJ=12(30)/20\\FJ=18\ units[/tex]

Answer:

9.25

Step-by-step explanation:

An equation is formed of two equal expressions.The value of y in the equation 5x + 2y = 20, when x = 0.3 is 9.25. The correct option is C, 9.25.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The value of y in the equation 5x + 2y = 20, when x = 0.3 can be found by substituting the value in the equation.

5x + 2y = 20

Substitute the value of x,

5(0.3) + 2y = 20

1.5 + 2y = 20

Subtract 1.5 from both sides of the equation,

1.5 + 2y - 1.5 = 20 - 1.5

Divide both the sides of the equation by 2,

2y /2 = 18.5 /2

y = 9.25

Hence, the value of y in the equation 5x + 2y = 20, when x = 0.3 is 9.25.

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