Prove triangle ABC is congruent to triangle DEC.

Answer:

[tex] \frac{289}{111} [/tex]

Step-by-step explanation:

[tex]2 + \frac{603}{1000 - 1} = 2 \frac{603}{999} = 2 \frac{67}{111} = \frac{289}{111} [/tex]

Answer:

Step-by-step explanation:

Solution by substitution method

3x+5y=7

and 4x-y=5

Suppose,

3x+5y=7→(1)

and 4x-y=5→(2)

Taking equation (2), we have

4x-y=5

⇒y=4x-5→(3)

Putting y=4x-5 in equation (1), we get

3x+5y=7

⇒3x+5(4x-5)=7

⇒3x+20x-25=7

⇒23x-25=7

⇒23x=7+25

⇒23x=32

⇒x=32/23

→(4)

Now, Putting x=32/23

in equation (3), we get

y=4x-5

⇒y=4(32/23)-5

⇒y=(128-115)/23

⇒y=13/23

∴y=13/23   and x=32/23

Answer: neither graph A nor graph B, because, even though both curves are above the horizontal axis, neither graph has an area of 1

Step-by-step explanation:

Areas under the graphs:

Graph A

[tex](1)(0.5)+(7-2)(0.2)=1.5\\\\[/tex]

Graph B

[tex]\frac{\pi}{2}(1^{2})=\frac{\pi}{2}[/tex]

As neither of these graphs have an area of 1, neither of them are density curves.

The statement - "neither graph A nor graph B, because, even though both curves are above the horizontal axis, neither graph has an area of 1" is true.

A few fundamental principles apply to density curves:

Neither curve of Graph A nor of Graph B has the area under the curve summed up as 1, though the curve is above the horizontal axis.

Hence, because neither graph has an area of 1, even if both curves are above the horizontal axis, the statement "neither graph A nor graph B, because, even though both curves are above the horizontal axis, neither graph has an area of 1" is true.

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Answer:

Let us assume that √2 is a rational number.

So it can be expressed in the form p/q where p, q are co-prime integers and q≠0

√2 = p/q

Here p and q are coprime numbers and q ≠ 0

Step-by-step explanation:

√2 = p/q

On squaring both the sides we get,

=>2 = (p/q)2

=> 2q2 = p2……………………………..(1)

p2/2 = q2

So 2 divides p and p is a multiple of 2.

⇒ p = 2m

⇒ p² = 4m² ………………………………..(2)

From equations (1) and (2), we get,

2q² = 4m²

⇒ q² = 2m²

⇒ q² is a multiple of 2

⇒ q is a multiple of 2

Hence, p, q have a common factor 2. This contradicts our assumption that they are co-primes. Therefore, p/q is not a rational number

√2 is an irrational number.

The short leg of a 90-45-45 triangle is 3 and the long leg is 7. The hypotenuse would be [tex]c = \sqrt{58}[/tex].

The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

The short leg of a 90-45-45 triangle is 3 and the long leg is 7.

Since this is a right triangle, we can use the Pythagoras theorem

a^2+b^2 = c^2  

where a and b are the legs and c is the hypotenuse

[tex]3^2 + 7^2 = c^2\\\\9 + 49 = c^2\\\\58 = c^2\\\\c = \sqrt{58}[/tex]

Hence, The hypotenuse would be [tex]c = \sqrt{58}[/tex].

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Answer:

3

Step-by-step explanation:

Cardinalities are the number of elements in a set.

(A∩B∩C) is the very middle part of the circle, and there are 3 elements there.

Answer:

A. 0.78

Step-by-step explanation:

A rational number is a number that you can express as [tex]\frac{x}{y}[/tex] where [tex]y\neq 0[/tex].

Answer:

Step-by-step explanation:

The answer would be "me" as the indirect object

David will be 10 and John will be 9

The total number of tea received in three years is 192.

The total number of coffee received in three years is 128.

The total number of biscuits received in three years is 64.

The total quantity of tea, coffee and biscuits received in the first year = (6 x 2) , (4 x 2) ,  (2 x 2) = 12, 8, 4 respectively

The total quantity of tea, coffee and biscuits distributed in the second year = (6 x 12) , (4 x 12) ,  (2 x 12) = 72, 48, 24 respectively

The total quantity of tea, coffee and biscuits distributed in the third year = (6 x 18) , (4 x 18) ,  (2 x 18) = 108, 72, 36 respectively

Total number of tea received in three years = 108 + 72 + 12 = 192

Total number of coffee received in three years = 8 + 48 + 72 = 128

Total number of biscuits received in three years = 4 + 24 + 36 = 64

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The average rate of change (slope) is 579.875 if, in 2009, there were 12,078 Burger King restaurants; in 2017, there were 16,717 Burger King restaurants.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have:

In 2009, there were 12,078 Burger King restaurants; in 2017, there were 16,717 Burger King restaurants.

The slope:

[tex]\rm m =\dfrac{16717-12078}{2017-2009}[/tex]

m = 4639/8

m = 579.875

Thus, the average rate of change (slope) is 579.875 if, in 2009, there were 12,078 Burger King restaurants; in 2017, there were 16,717 Burger King restaurants.

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The cash flow in year 1 is $15.

A growing perpetuity increases continuously and indefinitely.

Cash flow = present value x (rate of return - growth rate)

214 x (10% - 3%)

214 x 0.07 = $15

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Answer:

0.5km or 500m

Step-by-step explanation:

Given Distance = Speed x Time

In this case, we should use the difference in speed and time of the 2 scenarios.

Difference in Time = 20 mins(late) + 10 mins(early)

= 30 mins or 0.5 hour

Difference in Speed = 4km/h - 3km/h = 1km/h

Distance = 1km/h x 0.5 hr = 0.5km or 500m.

[tex]\huge\text{Hey there!}[/tex]

[tex]\text{4x = 19}\\\\\large\textbf{DIVIDE 4 to BOTH SIDES}\\\\\rm{\dfrac{4x}{4} = \dfrac{19}{4}}\\\\\large\textbf{SIMPLIFY IT!}\\\\\rm{x = \dfrac{19}{4}}\\\\\rm{x = 19 \div 4}\\\\\text{x = 4.75}\\\\\rm{x \approx 4.7500}\\\\\\\huge\text{Therefore, the answer should be: \boxed{\mathsf{4.7500}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

Step-by-step explanation:

4c + 11 = -25

4c = -25 - 11

4c = -36

c = -36 : 4

c = -9

or

4c + 11 + 25 = 0

4c + 36 = 0

c = (-36)/4

c = -9

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

check

4 *(-9) + 11 = -25

-36 + 11 = -25

-25 = -25

the answer is good

Answer:

c= -9

Step-by-step explanation:

1. 4c + 11 = -25

2. Put all like terms together and change the sign. In this case, the +11 will go to the right with the -25 and it will become -11.

Therefore:

4c= -25 -11

4c= -36

3. Make c the subject. Since 4 is being multiplied by c, when it goes to the right, it will divide.

Therefore:

c= -36/4

c= -9

Answer:

This is my answer↓:

Step-by-step explanation:

He school play sold $550 in tickets one night.

The number of $8 adult tickets was 10 less than twice the number of

$5 child tickets.

How many of each ticket were sold

Let say child ticket sold = x

Adult tickets was 10 less than twice the number of    child tickets.

=> Adult ticket sold = 2x - 10

Child ticket sold = x

$5 child tickets price

=> Revenue = 5x  $

Adult ticket sold = 2x - 10

$8 Adult tickets price

=> Revenue = 8(2x - 10) =16x - 80 $

5x + 16x - 80 = 550

=> 21x = 630

=> x = 30

Child ticket sold = 30

Adult ticket sold = 50

Total ticket sold = 80

Mark as brainlist, thanks me, and rate. Hope it helps!!!

The complete question is

"What is the value of this expression when c= -4 and d= 10?

1/4 (c^3+d²)

A.2

B.9

C.21

D.41"

The value of this expression when c = -4 and d = 10 will be option B 9.

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

The given expression is

[tex]1/4 (c^3+d^2)\\\\1/4 ((-4)^3+(10)^2)\\\\1/4 ( -64 + 100)\\\\1/4 (36)\\\\9[/tex]

Hence, the value of this expression when c = -4 and d = 10 will be option B 9.

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Therefore, we can write it as f(x) ≥ 0 over the interval [-1,1].

The given coordinates of the given table are (-3,15), (-2,-5), (-1,0), (0,5), and (1,0).

We need to write a valid prediction about the continuous function f(x).

In mathematics, a continuous function is a function such that a continuous variation of the argument induces a continuous variation of the value of the function.

Now, it is clear from the values of f(x) with respect to x, that the function reaches zero at x = -1, then goes up to 5 at x = 0 and then again reaches zero at x = 1.

So, the value of f(x) remains positive within the interval of [-1,1].

Therefore, we can write it as f(x) ≥ 0 over the interval [-1,1].

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Answer:

1/90

Step-by-step explanation:

Comment

To begin with, there are 10 tiles.. You draw one and don't replace it. Then you draw another tile from the 9 that remain.  The job is to figure out the probability of that happening.

You have a 1/10 chance of drawing the M.

But now there are only 9 tiles left and you have a 1 in 9 chance of drawing a T

Solution

P(M,T) = 1/10 * 1/9 = 1 / 90

You have a 1 in 90 chance of getting the two tiles in the order you have specified.

D.

[tex]m(x) = 0 \\ - 3x = 0 \\ x = 0[/tex]

E.

[tex]m(x) = \frac{ - 3}{25} [/tex]

[tex] \frac{ - 3x}{x {}^{2} + 2x - 24} = \frac{ - 3}{25} [/tex]

[tex] - 3(x {}^{2} + 2x - 24) = - 3(x)(25) \\ divide \: both \: sides \: by - 3[/tex]

[tex]x {}^{2} + 2x - 24 = 25x[/tex]

[tex]x {}^{2} - 23x - 24 = 0[/tex]

[tex](x - 24)(x + 1) = 0 [/tex]

[tex]x = 24 \\ x = - 1[/tex]

Answer:

D

x=0

Step-by-step explanation:

E)

[tex]\frac{-3x}{x^2+2x-24} =\frac{-3}{25} \\x^2+2x-24=25x\\x^2+2x-25x-24=0\\x^2-23 x-24=0\\x^2-24x+x-24=0\\x(x-24)+1(x-24)=0\\(x-24)(x+1)=0\\x=24,-1[/tex]

Answer:

b) angles 1 and 4 are congruent.

Hope it helps!

The correct answer is option B which is 3

Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.

Given data:-

4,3,2

The mean will be calculated as:-

Mean = (4 + 3 + 2) / 3

Mean =  9 / 3

Mean = 3

Therefore the correct answer is option B which is 3

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Answer: 8

Step-by-step explanation:

We are going from a smaller triangle to a larger triangle, so the scale factor is greater than 1.

We know scale factor = (image)/(preimage), so the scale factor is 32/4 = 8

The scale factor of dilation of the triangle is k = 8

Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent

The result of dilation is that the shapes and boundaries of objects in the input image are expanded or thickened. It is often used in conjunction with other morphological operations such as erosion, opening, and closing to manipulate and enhance images.

Given data ,

Let the first triangle be represented as ΔABC

Let the second triangle be represented as ΔDEF

where the measures of sides of ΔABC are

AB = 6 , BC = 6 and AC = 4

The measure of sides of triangle ΔDEF are

DE = 48 , EF = 48 and DF = 32

The scale factor of dilation k = measure of side DE / measure of side AB

k = 48 / 6

k = 8

Hence , the dilation factor is k =8

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Solving a quadratic equation, the age of the man with a blood pressure of 125 mmHg is of 27 years old.

A quadratic function is given according to the following rule:

[tex]y = ax^2 + bx + c[/tex]

The solutions are:

In which:

[tex]\Delta = b^2 - 4ac[/tex]

The pressure is given by:

P = 0.006A² - 0.02A + 120.

When the pressure is of 125 mmHg, we have that:

0.006A² - 0.02A + 120 = 125.

0.006A² - 0.02A - 5 = 0.

Hence the coefficients are a = 0.006, b = -0.02, c = -5, and the solutions, applying the formula are:

A = -30 and A = 27.

Age has to be positive, hence the man is 27 years old.

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[tex]\dfrac{x!-(x-3)!}{23}=1\\x!-(x-3)!=23\\(x-3)!((x-2)(x-1)x-1)=23\\(x-3)!((x^3-x^2-2x^2+2x)-1)=23\\(x-3)!((x^3-3x^2+2x)-1)=23[/tex]

23 is a prime number, therefore there are two possibilities:

[tex]\text{I.}\, (x-3)!=1 \wedge x^3-3x^2+2x-1=23[/tex]

or

[tex]\text{II.}\, (x-3)!=23 \wedge x^3-3x^2+2x-1=1[/tex]

[tex]\text{I.}\\(x-3)!=1\\x-3=0 \vee x-3=1\\x=3 \vee x=4[/tex]

Now, we check if any of these solutions is also a solution to the second equation:

[tex]3^3-3\cdot3^2+2\cdot3-1=23\\27-27+6-1-23=0\\ -18=0[/tex]

Therefore, 3 is not a solution.

[tex]4^3-3\cdot4^2+2\cdot4-1=23\\64-48+8-1-23=0\\0=0[/tex]

Therefore, 4 is a solution.

[tex]\text{II.}[/tex]

[tex](x-3)!=23[/tex]

We know that [tex]3!=6[/tex] and [tex]4!=24[/tex], therefore there isn't any [tex]n\in\mathbb{N}[/tex], for which [tex]n!=23[/tex], so there's no solution.

So, the only solution is [tex]x=4[/tex].

Answer:

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