The equation x + c = k has a solution of x = 2. Both cand k are rational numbers.
Select all the statements that must be true in all cases.
cis 2 greater than k.
cand k must be whole numbers.
The solution x = 2 is the only solution.
If c is a whole number, k is also a whole number.



I need help ASAP PLEASE

To prove the converse of the Pythagorean theorem, we can define a right triangle Δ DEF with sides a, b, and x.

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

ΔABC and ΔDEF

To prove the converse of the Pythagorean theorem, we can define a right triangle DEF with sides a, b, and x.

Thus,

ΔDEF is filled in the box.

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Answer:

range is y-coordinates so it should be 40

Step-by-step explanation:

domain is x-coordinates

Answer:

The answer is [tex]12\log{(x(x-2))}[/tex]

Step-by-step explanation:

Exponential property of logarithm:

We have that:

[tex]a \log{x} = \log{x^{a}}[/tex]

Sum of logarithms:

We have that:

[tex]\log{a} + \log{b} = \log{ab}[/tex]

Applying the exponential property:

[tex]3\log{x} = \log{x^3}[/tex]

[tex]4\log{(x-2)} = \log{(x-2)^4}[/tex]

So

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

Additive property

[tex]\log{x^3} + \log{(x-2)^4} = \log{x^3(x-2)^4} = \log{(x(x-2))^12}[/tex]

Exponential property:

[tex]\log{(x(x-2))^12} = 12\log{(x(x-2))}[/tex]

The answer is [tex]12\log{(x(x-2))}[/tex]

Answer:

1) 17.5×14×64

2) volume= 0.5×3.6×10×5=

3) d= 13, r=13/2= 6.5, h= 19

4) Base Area= a+b/2×h

5) L×W×H

6) v=πr²h

[tex]------------[/tex]

hope it helps...

have a great day!!

[tex] \huge \boxed{1}[/tex]

→17.5 × 14 × 6.4

→1568 in³

[tex] \huge \boxed{2}[/tex]

→0.5 × 3.6 × 10 × 5

→90 m³

[tex] \huge \boxed{3}[/tex]

→ Diameter = 13 mm

→ Radius = 13/2 = 6.5

→ Height = 19 mm

→Volume => πr²h

=> 22/7 × (6.5)² × 19

=> 2521.91 mm³

[tex] \huge \boxed{4}[/tex]

→ Base Area → a+b/2×h

→ (37+15)/2×25.7 cm²

→26×25.7 cm²

→ 668.2 cm²

(height= 20cm)

→volume => 668.2×20

→13364 cm²

[tex] \huge \boxed{5}[/tex]

→Area→ L × B × H

→ 25×7×18

→ 175×18

→ 3150 ft³

[tex] \huge \boxed{6}[/tex]

→Volume → πr²h

→ π(3.2²)(8)

→ 81.92π

→ 257.36 km²

[tex] \boxed{Extra-Information}[/tex]

[tex] \bold \green{TheExtraterrestrial}[/tex]

Answer:

2156000 J.

Bonus: 2 snickers bar

Step-by-step explanation:

Applying

P.E = mgh................. Equation 1

Where P.E = Gravitational potential energy, m = mass of the person, h = height of the mountain, g = acceleration due to gravity.

From the question,

Given: m = 55 kg, h = 4000 m

Constant: g = 9.8 m/s²

Substitute these values into equation 1

P.E = (55×4000×9.8)

P.E = 2156000 J.

If one snikers bar is 1100000 J of energy,

Then, (2156000/1100000) snickers bar would be enough to climb the mountain

Number of snickers bar =  (2156000/1100000)  = 1.96 ≈ 2

Answer:

32 mutipliy 20 and 5

Step-by-step explanation:

Answer:

78,799 children's tickets

Step-by-step explanation:

147,523 total tickets, 68,724 adult tickets

Subtract to find amount of children's tickets:

147,523-68,724 = 78,799

In a 30-60 right triangle the side opposite the 30 degree angle is half the length of the hypotenuse.

so RT= 10

I'm assuming x and y intercepts which would be (2.5,0) and (0,10)

Answer:

(507.05, 592.95)

Step-by-step explanation:

Given data:

sample mean = $550, sample standard deviation S = $60.05

95% confidence interval , n = 10

For 95% confidence interval for the mean

mean ± M.E.

where M.E. is margin of error = [tex]t_{n-1}, \alpha/2\times\frac{S}{\sqrt{n} }[/tex]

Substituting the values in above equation

[tex]=t_{10-1}, 0.05/2\times\frac{60.05}{\sqrt{10} }[/tex]

= 2.62×18.99

=42.955

= 550±42.95

=(507.05, 592.95)

Answer:38cm2

Step-by-step explanation:

The area of right angle triangle is 36 sq.cm. Whose base 9, Height 8 .

Base is 9 cm.

8 centimeters tall.

Triangle area equals 1/2 x base x height

Triangle's area is 1/2 x 9 x 8 = 36 square centimeters.

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.

The surface inside a flat figure is measured by its area. Squares are used to measure area. To obtain the square units, multiply the length by the width.

Learn more about Area

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Answer:

-7, 7

Step-by-step explanation:

Opposites are basically two numbers that are at different sides of the number line. For example, -2 and 2 are opposites because they are the same distance away from 0 on a number line making them opposites. To make an opposite just take a positive number, and then add a negative to it. (8, -8) Hope that helps :)

Answer:

[tex]\huge \fbox \pink {A}\huge \fbox \green {n}\huge \fbox \blue {s}\huge \fbox \red {w}\huge \fbox \purple {e}\huge \fbox \orange {r}[/tex]

[tex]5(x + 2) = 7(4 - x) \\ 5x + 10 = 28 - 7x \\ 5x + 7x = 28 - 10 \\ 12x = 18 \\ x = \frac{18}{12} \\ x = \frac{3}{2} \\ x = 1.5[/tex]

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

[tex] \huge\blue{ \mid{ \underline{ \overline{ \tt ꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐ }} \mid}}[/tex]

Answer: 1000 times less

Step-by-step explanation: multiply 0.054x1000

Answer:

1000 times

Step-by-step explanation:

To find how many times less 0.054 is than 54,

we can divide 54 by 0.054.

This gives us 54/0.054 = 1000

This means that 0.054 is 1000 times less than 54.

Answer:

<A=45°

Hope this helps you

Answer:

45

Step-by-step explanation:

Answer:

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

4 1/2% of 50 is 4.5% of 50 which is same as:

or substituting % with 1/100,

The matching choices are A and B.

Answer:

Below in bold.

Step-by-step explanation:

First find the height by use Pythagoras theorem on the right triangle:

h = sqrt (5^2 - 4^2)

= sqrt 9

= 3.

Volume of the prism = area of the triangle * length

= 1/2 * 3 * 4 * 10

= 1/2 * 12 * 10

= 60 cm^3.

Total area = area of 2 triangles + area 0f 3 rectangles

= 2 * 1/2 * 3 * 4 + 3 * 10 +  4 * 10 + 5 * 10

= 12 + 30 + 40 + 50

= 132 cm^2.

Answer:

-93

Step-by-step explanation:

Substitute by - 3 instead of X

Answer: D

Step-by-step explanation:

If the graph is shifted 5 units down, each output value should decrease by 5.

Answer:

Step-by-step explanation:

Let's assume that,

→ Length = 2x

→ Width = x

→ Perimeter = 30

Perimeter of rectangle formula,

→ P = 2(L + W)

Now the value of x will be,

→ P = 2(L + W)

→ 2(2x + x) = 30

→ 2 × 3x = 30

→ 6x = 30

→ x = 30/6

→ [ x = 5 ]

Then required dimensions are,

→ Length = 2x = 2 × 5 = 10

→ Width = x = 5

Hence, these are the dimensions.

Length = 10

width = 5

Given-

Perimeter =30

l=2b........................................................ i

so

P =2(l+b)

here

30 = 2(2b +b)... ... ..............         as l=2b from i

30 = 2*3b

30 = 6b

b= 5

which implies l= 2*5 --->10............................................ from i

so

Length = 10

width = 5

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Answer:

5/g

Step-by-step explanation:

Answer:

B. 8

Step-by-step explanation:

6, 15, 7, 5, 11, 11, 8

5, 6, 7, 8, 11, 11, 15

The middle number is 8.

Answer:

8

Step-by-step explanation:

Answer:

27/1

Step-by-step explanation:

3³=3·3·3=27

27=27/1

Answer:

here is the correct answer

The  slope of the table below? 3/8 15/12 9/10 0/7 is 23.8

Slope is defined as the rate of change of y with respect to x.  Invariably, it it the rise in y over the run  in x. put differently, slope is increase over increase in x

The slope of a line is defined

S= (increase in y)/(Increase in x) = Δy/Δx

Slope = (0/7 - 18/12) ÷ (9/10 -3/8)

Slope = 15/12 ÷ 42/80

Simplify the fractions to have

Slope = 15/12 * 80/42

The slope = 1200/504

Slope of the table is given as 23.4

Conclusively, the table gives us a slope approximately 23

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Answer:

x

)

=

2

x

4

−

3

x

+

3

f(x)=2x

4

−3x+3, then what is the remainder when

f

(

x

)

f(x) is divided by

x

−

1

x−1?