Which equation has roots of 3 ± √2?

Answer:

Tim is 8 years old.

Explanation:

8 is the cube number of 2, as 2 × 2 × 2 = 8. Additionally, 8 is double 4, which is the square number of 2, and half of 16, which is the square number of 4.

Tim who goes to school is 8 years old.

Good numerical ability describes your ability to think and conclude logical thoughts in your daily life also in your working role how you handle data in form of numbers, graphs, statements etc.

According to the given question Tim goes to school.

His age is a cube number let that number be x therefore age of Tim would be x³.

His age can also be defined as double of 1 square number which is 2x² and half of a different square of a numbers.

Let us equate x³ = 2x² and by hit and trial we get to know that x = 2 satisfies this condition.

So, Age of Tim could be 8 years,Now lets check our third statement half a different square number 16 is square of 4 so half of 16 is also 8.

Thus Tim is 8 years old.

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Answer:

The rank of a matrix is the number of nonzero rows in the reduced matrix, so the rank is 3. option (C)

Step-by-step explanation:

Echelon Form : it is used to find the rank of matrix by reducing rows into zeros then the number of non zero rows is the rank of the matrix

[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\2&-2&-2&5&1\\1&0&-12&9&-3\\-1&1&7&-7&1\end{array}\right][/tex]

apply row operations:

R₂= R₂ - 2 R₁

[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\0&0&-12&9&-3\\1&0&-12&9&-3\\-1&1&7&-7&1\end{array}\right][/tex]

R₃= R₃ -  R₁

[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\0&0&-12&9&-3\\0&0&-17&11 &-5\\-1&1&7&-7&1\end{array}\right][/tex]

R₄ = R₄ +R₁

[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\0&0&-12&9&-3\\0&0&-17&11 &-5\\0&0&12&-9 &3\end{array}\right][/tex]

R₄ = R₄ +R₃

[tex]\left[\begin{array}{ccccc}1&-1&5&-2&2\\0&0&-12&9&-3\\0&0&-17&11 &-5\\0&0&0&0 &0\end{array}\right][/tex]

we can clearly see that after performing row operations there are 3 non zero rows,

therefore the Rank of the given matrix is 3

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Answer:

x=12

Step-by-step explanation:

Given that there is only one expression given in each triangle, if we only use the information in a single triangle, there is no way to set up an equation that we could solve to find the expression.  (For this situation, at best we could use the triangle sum theorem to say that the three angles in one triangle added to 180°, but since we don't know the other two angles, that's 3 unknowns with only 1 equation... that's not solvable)

The only way to solve this problem is to make a relationship of some sort between the two triangles.

Proving a relationship between triangles - option 1

You may have a theorem about the Third angles of two triangles... "Given two arbitrary triangles, [tex]\triangle ABC[/tex] and [tex]\triangle D E F[/tex], if [tex]\angle A \cong \angle D[/tex] and [tex]\angle B \cong \angle E[/tex],  then [tex]\angle C \cong \angle F[/tex] "

If you have this, then the third angles are congruent.

In a more general situation of a similar problem (one in which you don't know two of the angles to begin with), it might be easier to prove triangle congruence, or triangle similarity.

Other Relationships between triangles

There are two main relationships between triangles: similarity and congruence.

Most people learn about congruence first.

In the situation for this problem, the two triangles happen to be congruent (we'll prove it shortly), which implies that all corresponding angles between shapes are congruent (and all corresponding sides between shapes are congruent).

For the purpose of solving for things related to angles, proving that the two triangles are similar is enough to know that angles between triangles are congruent (sides wouldn't necessarily be equal, but would be proportional, and since we're not solving for anything related to side lengths, proving that the triangles are similar would be enough).

Proving a relationship between triangles - option 2 - congruence

Notice that the triangle on top has two angles with markings (a single mark, and a double mark), and one side with a marking (a single tick).  These three pieces are in a configuration of ASA (the side is between the two angles).

Looking at the bottom triangle, it also has angles and sides with corresponding markings, and they are also in an ASA configuration.

Thus, by ASA congruence, these triangles are congruent triangles.

Knowing the triangles are congruent (even though we only used 3 parts), the rest of the corresponding parts (including the third angles) are also congruent.

Proving a relationship between triangles - option 3 - Similarity

For similarity, the process is similar to proving congruence, however the theorems we have for proving similarity are different.

SSS, SAS, or AA similarity.

Since the triangles in our problem do have two angles that are congruent, by AA similarity, the triangles are "similar".

Knowing the triangles are similar (even though we only used 2 parts), the last set of corresponding angles are also congruent.

Building our equation

Since the third angle of each triangle is congruent, by definition of congruent angles, the measures of each of those two angles are equal, and so we can build an equation knowing that the two expressions are equal to each other:

[tex]3x-7=2x+5[/tex]

Solving for x

From there, we need some algebraic properties equality to solve for x.

Subtract 2x from both sides...

[tex](3x-7)-2x=(2x+5)-2x\\x-7=5[/tex]

add 7 to both sides...

[tex](x-7)+7=(5)+7\\x=12[/tex]

Extension

Knowing the value for x, we could solve for the measure of the angles, if that had been requested.  Simply substitute 12 back into the expressions for the angle measure (the results should be the same for both angles, since they were congruent angles)

[tex]3(12)-7\\36-7\\29[/tex]         [tex]2(12)+5\\24+5\\29[/tex]

So, if we had been asked, the measure of the angle is 29°

Answer:

a) Cat

b) 4 (unless there is a key that says otherwise)

c) 3 more people

Step-by-step explanation:

a) It has the least number of shapes (only 5)

b) Cat has 1 small square which stands for 1 person and 4 small squares put together make a big square so a big square is 4 people. Unless a key says that a small square is more or less 1, then it should be 4.

c) If one big square is 4 people, then there are 10 people for giraffes and 7 people for dogs. 10 - 7 = 3 more people.

Answer:

550g

Step-by-step explanation:

total g in 1 kg is 1000

so 1000 - 550 =450

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Answer:  [tex]7.21[/tex]

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Given:  [tex]\textsf{(2, -3) and (-4, -7)}[/tex]

Find: [tex]\textsf{Find the distance between the two points}[/tex]

Solution:  Use the distance formula and the two points that were provided to determine the distance.

Plug in the values

Simplify and expand

If we are using square root we use the square root of 52 but if we simplify it to a decimal point we would use 7.21

Answer:

I iitiriririrrifjjrjr idiocy jdkthink 179.86

The conversion ratio that can be illustrated will be converting 2030m to kilometers.

The unit conversion that can be illustrated based on the information can be convert 2030m to kilometers.

It should be noted that 1000 meters makes 1 kilometer. Therefore, rounding up 2030m mentally will be 2000m and the conversion to kilometers will be:

= 2000/1000

= 2 km

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The ship is 88.8 miles far from the port at 4 pm.

Given,

The displacement from 1 to 3 in the afternoon.

D1 = 30 miles/hr × 2 hr

     = 60 miles to the north

The displacement from 3 till 4 in the afternoon.The ship changes its course 20 degrees eastward at 3 o'clock.

Therefore, D2 = 30 miles/hr × 1 hr

                       = 30 miles to the 20° north eastward

By combining two vectors, the resulting displacement:

D = √((D1 ₊ D2 × cos(20°))² ₊ (D2 × sin(20°))²

D = √((60 ₊ 30 × cos (20°))² ₊ (30 × sin(20°))²

D = 88.8 miles

Hence the ship is 88.8 miles far away from the port at 4 pm.

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Answer:

[tex]\huge\boxed{\sf x =5 \ \ \ OR \ \ \ x = 1}[/tex]

Step-by-step explanation:

[tex]x^2-6x+5=0[/tex]

[tex]x^2-5x-x+5=0\\\\Take \ common\\\\x(x-5)-1(x-5)=0\\\\Take \ (x-5) \ common\\\\(x-5)(x-1)=0[/tex]

Either,

x - 5 = 0         OR         x - 1 = 0

[tex]\rule[225]{225}{2}[/tex]

The amount in the new checking account is 600 dollars

The operation (5 α 3) + (7 α 5) is 46.

She had 1000 dollars in her checking account. she had a loan of 800 dollars to pay.

After paying her loan form her checking account the balance of the loan reduce to half.

Therefore, she paid 800 / 2 = 400 dollars for her loan

Hence,

Her new checking account = 1000 - 400 = 600 dollars

a α b = ab - a + b

Therefore,

(5 α 3) + (7 α 5)

(5 α 3) = 5(3) - 5 + 3 = 13

(7 α 5) = 7(5) - 7 + 5 = 33

Therefore,

(5 α 3) + (7 α 5) = 13 + 33 = 46

Note: I can't use the at symbol because it is a swear word.

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Answer: Right iscoleces triangle

Step-by-step explanation: The square on the left bottom side means it is a right angle. The lines means that a side is congruent to the other side. By definition, iscoleces triangles have two congruent sides, so this must be it.

Answer:

right isosceles

Step-by-step explanation:

the right angle and the two sides that are equal make the triangle a right isosceles

The maximum profit will be 956 birrs for both cows and sheep.

The amount of money earned by any seller on the cost price is called the profit.

Given that:-

From the given data we can see that the total number of animals cows and sheep is 16.

C + S = 16

To raise a cow need 2 Br

To raise Sheep need 5 Br

The number of sheep is 12 and cows 4.

So the amount required to raise sheep and cows is:-

Sheeps = 12 x 2 = 24 Br

Cows = 4 x 5 = 20 Br

Total = 44 Br

The selling price of cows and sheep are 100 and 50 Br.

Cows = 100 x 4 = 400Br

Sheeps = 50 x 12 = 600 Br

Total = 1000 Br

So the profit will be calculated as follows:-

P = 1000 - 44 = 956 Br

Therefore the maximum profit will be 956 birrs for both cows and sheep.

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Step-by-step explanation:

Can you attach the questions please? Thanks

Answer:

f(x) = -3x + 5

Step-by-step explanation:

The slope of the function is -3 as the outputs decrease by three for each iteration.

The constant is 5 and can be determined if you plug in 1 as an x value and solve for c in an equation like this: -3(1) + c = 2

The solution will be x= -10

Simplifying the given expression

[tex]1.8(1.1x - 1.3) - 1.88 = - 24.02[/tex]

Step1: Convert decimal to fraction

[tex]1.8( \frac{11x}{10} - 1.3) - 1.88 = - 24.02[/tex]

[tex]1.8( \frac{11x}{10} - \frac{13}{10} ) - 1.88 = - 24.02[/tex]

[tex]\frac{18}{10} ( \frac{11x}{10} - \frac{13}{10} ) - 1.88 = - 24.02[/tex]

Step2: Make denominator common

[tex]\frac{18}{10} ( \frac{11x - 13}{10}) - 1.88 = - 24.02[/tex]

Step3: Simplifying the fraction

[tex]\frac{9}{5} ( \frac{11x - 13}{10}) - 1.88 = - 24.02[/tex]

Step4: Make denominator common

[tex] \frac{9(11x - 13)}{5 \times 10} - \frac{1.88 \times 50}{50} = - 24.02[/tex]

[tex] \frac{9(11x - 13)}{50} - \frac{94}{50} = - 24.02[/tex]

[tex] \frac{9(11x - 13 - 94)}{50} = - 24.02[/tex]

[tex] \frac{99x - 117 - 94}{50} = - 24.02[/tex]

Step5: Simplifying

[tex] \frac{99x - 211}{50} = - 24.02[/tex]

[tex] 99x - 211 = - 24.02 \times 50[/tex]

[tex] 99x - 211 = - 1201[/tex]

[tex] 99x = - 1201 + 211[/tex]

[tex] 99x = - 990[/tex]

[tex] x = \frac{ - 990}{99} [/tex]

[tex]x = - 10[/tex]

Hence, the solution x=-10

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The match is shown in the picture for the function of a parabola and the graph of a parabola.

It is defined as the graph of a quadratic function that has something bowl-shaped.

As we know the standard form of the parabola is:

y = a(x - h)² + k

If a > 0 (parabola opens upwards)

If a < 0 (parabola opens downwards)

or

x = a(y - h)² + k

If a > 0 (parabola opens right side)

If a < 0 (parabola opens left side)

Here (h, k) is the vertex of the parabola and a is the leading term.

Thus, the match is shown in the picture for the function of a parabola and the graph of a parabola.

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Answer:

Step-by-step explanation:

sin θ=1/4,tan θ>0

so θ lies in first quadrant.

cos θ=√(1-sin²θ)=√(1-(1/4)²)=√(1-1/16)=√(15/16)=√15/4

[tex]2cos^2 \frac{\theta}{2} =1+cos \theta[/tex]

[tex]2~cos^2\frac{\theta}{2} =1+\frac{\sqrt{15} }{4} =\frac{4+\sqrt{15}}{4} \\cos~\frac{\theta}{2} =\sqrt{\frac{4+\sqrt{15} }{4 \times 2} } \\cos\frac{\theta}{2} =\frac{\sqrt{8+2\sqrt{15}} }{4}[/tex]

Answer:

60200 cm^2

Step-by-step explanation:

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Using it's concept, it is found that the probability that the button is either pink or blue is:

[tex]p = \frac{26}{29}[/tex]

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, we have that:

There are six times as many pink buttons as yellow books, hence:

z = 6x.

Considering the ratio of yellow buttons to blue buttons, we have that:

[tex]\frac{x}{y} = \frac{3}{8}[/tex]

3y = 8x

[tex]y = \frac{8x}{3}[/tex]

The total number of buttons is given by:

[tex]T = x + \frac{8x}{3} + 6x[/tex]

[tex]T = \frac{29x}{3}[/tex]

The number of pink or blue is given by:

[tex]y + z = \frac{8x}{3} + 6x = \frac{26x}{3}[/tex]

Hence the probability is given by:

[tex]p = \frac{\frac{26x}{3}}{\frac{29x}{3}} = \frac{26}{29}[/tex]

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Answer:

The equation of a parallel line is y = x

Step-by-step explanation:

Parallel lines have the same slope

hence the new lines slope is = 1

The equation of the line is written in the slope-intercept form,

y = mx + b

where m represents the slope

          b represents the y-intercept

where the format of a point is (x, y)

Given:

we need to find b, y = 1x + b

we can plug in the point (2, 2)

2 = 1(2) + b

2 = 2 + b

0 = b

Hence, the equation of the line through point

(2, 2) and parallel to y = x+4 is y = x

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The difference of two squares expression is (d) 25a^2-36b^6

The difference of two squares is represented as:

x^2 - y^2

Where x and y are perfect square expressions.

From the list of options, we have:

25a^2-36b^6

The terms of the above expression are perfect squares

i.e.

25a^2 = (5a)^2

36b^6 = (6b^3)^2

Hence, the difference of two squares expression is (d) 25a^2-36b^6

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The values of f(3.52)=26.61 and f(-8.77)=257.05

An assignment of an element from set Y to each element of set X constitutes a function from set X to set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

The notation f: X→Y denotes a function, its domain, and its codomain. The value of a function at an element x of X, denoted by the symbol f(x), is referred to as the image of x under f or the value of f applied to the argument x.

The given function is f(x) = 3x²-3x =3x(x-1)

f(3.52)=3*(3.52)(3.52-1)

=26.61

f(-8.77)=3*(-8.77)(-8.77-1)

=257.05

Therefore, the values of f(3.52)=26.61 and f(-8.77)=257.05

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Answer:

2nd option

Step-by-step explanation:

the mean is calculated as

mean = [tex]\frac{sum}{count}[/tex]

         = [tex]\frac{4x+5+7x-6-8x+2}{3}[/tex]

         = [tex]\frac{3x+1}{3}[/tex]

         = [tex]\frac{3x}{3}[/tex] + [tex]\frac{1}{3}[/tex]

        = x + [tex]\frac{1}{3}[/tex]

Answer:

-3 is a zero of the function  False

-1 is a zero of the function  True

1 is a zero of the function   False

2 is a zero of the function  True

4 is a zero of the function   False

The distance between B and C is 26.926 units.

The distance between coordinate P(x1 , y1) and coordinate Q(x2 , y2) is calculated using the distance formula: d = √[(x2 - x1)² + (y2 - y1)²]

The zip-line course distance from platform A to platform F are given

Coordinates of B = (-25, -20)

coordinates of C = (-15, 5)

Now, the distance between B and C is

= `√(5-(-20))² +((-15)-(-25))²

=√25² + 10²

= √725

= 26.926 units.

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Answer:

1/a+ 1/b = 1/2

Adding the fractions we get

b+a/ab=1/2

cross Multiplying the denominator we get,

b+a=ab/2

a= ab/2 -b

Answer:

a = 1/(1/2 + 1/b)

Step-by-step explanation:

1/a + 1/b = 1/2

1/a = 1/2 - 1/b

1 = a(1/2 - 1/b)

1/(1/2 + 1/b) = a