2x²+3x²+3.(-1) =5x.x+5x .1

Answer:

[tex]\|a\| = 5\sqrt{13}[/tex].

[tex]\|b\| = 3\sqrt{29}[/tex].

Step-by-step explanation:

Let [tex]m[/tex],[tex]n[/tex], and [tex]k[/tex] be scalars such that:

[tex]\displaystyle a = m\, (2\, \vec{i} + 3\, \vec{j}) = m\, \begin{bmatrix}2 \\ 3\end{bmatrix}[/tex].

[tex]\displaystyle b = n\, (2\, \vec{i} + 5\, \vec{j}) = n\, \begin{bmatrix}2 \\ 5\end{bmatrix}[/tex].

[tex]\displaystyle (a + b) = k\, (8\, \vec{i} + 15\, \vec{j}) = k\, \begin{bmatrix}8 \\ 15\end{bmatrix}[/tex].

The question states that [tex]\| a + b \| = 34[/tex]. In other words:

[tex]k\, \sqrt{8^{2} + 15^{2}} = 34[/tex].

[tex]k^{2} \, (8^{2} + 15^{2}) = 34^{2}[/tex].

[tex]289\, k^{2} = 34^{2}[/tex].

Make use of the fact that [tex]289 = 17^{2}[/tex] whereas [tex]34 = 2 \times 17[/tex].

[tex]\begin{aligned}17^{2}\, k^{2} &= 34^{2}\\ &= (2 \times 17)^{2} \\ &= 2^{2} \times 17^{2} \end{aligned}[/tex].

[tex]k^{2} = 2^{2}[/tex].

The question also states that the scalar multiple here is positive. Hence, [tex]k = 2[/tex].

Therefore:

[tex]\begin{aligned} (a + b) &= k\, (8\, \vec{i} + 15\, \vec{j}) \\ &= 2\, (8\, \vec{i} + 15\, \vec{j}) \\ &= 16\, \vec{i} + 30\, \vec{j}\\ &= \begin{bmatrix}16 \\ 30 \end{bmatrix}\end{aligned}[/tex].

[tex](a + b)[/tex] could also be expressed in terms of [tex]m[/tex] and [tex]n[/tex]:

[tex]\begin{aligned} a + b &= m\, (2\, \vec{i} + 3\, \vec{j}) + n\, (2\, \vec{i} + 5\, \vec{j}) \\ &= (2\, m + 2\, n) \, \vec{i} + (3\, m + 5\, n) \, \vec{j} \end{aligned}[/tex].

[tex]\begin{aligned} a + b &= m\, \begin{bmatrix}2\\ 3 \end{bmatrix} + n\, \begin{bmatrix} 2\\ 5 \end{bmatrix} \\ &= \begin{bmatrix}2\, m + 2\, n \\ 3\, m + 5\, n\end{bmatrix}\end{aligned}[/tex].

Equate the two expressions and solve for [tex]m[/tex] and [tex]n[/tex]:

[tex]\begin{cases}2\, m + 2\, n = 16 \\ 3\, m + 5\, n = 30\end{cases}[/tex].

[tex]\begin{cases}m = 5 \\ n = 3\end{cases}[/tex].

Hence:

[tex]\begin{aligned} \| a \| &= \| m\, (2\, \vec{i} + 3\, \vec{j})\| \\ &= m\, \| (2\, \vec{i} + 3\, \vec{j}) \| \\ &= 5\, \sqrt{2^{2} + 3^{2}} = 5 \sqrt{13}\end{aligned}[/tex].

[tex]\begin{aligned} \| b \| &= \| n\, (2\, \vec{i} + 5\, \vec{j})\| \\ &= n\, \| (2\, \vec{i} + 5\, \vec{j}) \| \\ &= 3\, \sqrt{2^{2} + 5^{2}} = 3 \sqrt{29}\end{aligned}[/tex].

Answer:

W

Step-by-step explanation:

I done it before

Answer:

5

Step-by-step explanation:

It is 5 because you just have to count by using a jumping math tectechnique.

Answer:

hope it help ..........you

Answer:

True, they may not be congruent

Step-by-step explanation:

A figure cannot be determined as congruent from three angles alone. In order  for two shapes to be congruent, all corresponding parts must be congruent. This means all the sides and angles of the two shapes must be the same in order for the two shapes to be congruent. If we know all the angles are the same, the sides could still be different lengths, so this does not prove congruency.

The triangles shown below may not be congruent is True statement.

Two geometric figures are said to be congruent, or to be in the relationship of congruence, if one can be superimposed on the other and they correspond throughout.

In both Triangle we can see that

2 Angles measures 25.

2 Angles measures 100.

and, 2 angles measures 55.

As, we know there no Congruence rule for AAA.

Thus, both triangles are not Congruent.

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Based on the relationship between Mary's age and that of John, the representation of Mary's age is (X + 5).

Your question seems incomplete or not worded well so I'll give a more general response.

Mary is said to be older than John by 5 years. This means that however old John gets, Mary will always be older by 5 years.

If John is X years therefore, Mary's age will simply be:

= John's age + Age difference

= X + 5

For instance, if John is 20 years then Mary would be:

= 20 + 5

= 25 years

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Answer:

Answer is x=1 inthe sentences

Answer:

C. TRANSLATE 2 UNITS UP AND 4 UNITS DOWN

Step-by-step explanation:

The transformation that takes place with the following rule (x - 2, y + 4) is translates 2 units left AND 4 units up, the correct option is A.

The transformation of a function may involve any change.

Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming horizontal axis is input axis and vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units:

y=f(x+c) (same output, but c units earlier)

Right shift by c units:

y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = [tex]k \times f(x)[/tex]

Horizontal stretch by a factor k: y =[tex]f\left(\dfrac{x}{k}\right)[/tex]

We are given that;

The points (x - 2, y + 4)

Now,

The rule (x - 2, y + 4) means that every point (x,y) of the original figure is moved to a new point (x - 2, y + 4) by subtracting 2 from the x-coordinate and adding 4 to the y-coordinate.

The x-axis is horizontal and positive to the right. Subtracting from the x-coordinate means moving left and adding to the x-coordinate means moving right.

The y-axis is vertical and positive upwards. Subtracting from the y-coordinate means moving down and adding to the y-coordinate means moving up.

Subtracting 2 from the x-coordinate means moving 2 units left and adding 4 to the y-coordinate means moving 4 units up.

Therefore, by transforming functions the answer will be translates 2 units left AND 4 units up.

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Answer:

Less than 360 degree

Step-by-step explanation:

I think so

Answer:

Square both sides

√(2x+1)=2+√(x-3)

or, 2x+1=(2+√(x-3))²

solving it you'll get two values of x, which are,

x = 4 and x = 12

Answer:

Hello,

x=4 or x=12

Step-by-step explanation:

[tex]\sqrt{2x+1} =2+\sqrt{x-3} \\\\2x+1=4+4\sqrt{x-3} +(x-3)\\\\2x+1-x+3-4=4\sqrt{x-3} \\\\x=4\sqrt{x-3} \\\\ x^2-16x+48=0\\\\\Delta=16^2-4*48=64=8^2\\\\x=\dfrac{16-8}{2} \ or x=\dfrac{16+8}{2}\\\\x=4 \ or\ x=12\\\\Since \ we\ have \ squared \ we\ must\ verify\ the \ solutions\ found:\\\\x=4 \Longrightarrow \sqrt{2*4+1} =? 2+\sqrt{4-3} \Longrightarrow 3 =? 2+1 \\\\x=12 \Longrightarrow \sqrt{2*12+1} =? 2+\sqrt{12-3} \Longrightarrow 5 =? 2+3 \\\\[/tex]

Answer:

5.6m + n - 9.9

Step-by-step explanation:

-(-5.6m-n+9.9)

5.6m + n - 9.9

Answer:

The factors of 27 are 1,3,9,27.

The factors of 36 are 1,2,3,4,6,9,12,36.

HCF=1,3,9

Answer:

x + 6 / 8

Step-by-step explanation:

The sum of a number is the answer to addition. So that means an unknown number and 6 are being added together. Lets make this unknown number x.

x + 6

The sum of this is being divided by 8. Since we already know what division is, we can just add the line and 8.

x + 6 / 8

Answer:

A possible answer could be 2√2. It depends where points B and C would be. I guess this information was given in the parts A and B.

Step-by-step explanation:

See picture attached

Answer:

1000000000026

Step-by-step explanation:

i hope this helps!!!!!

Answer:

I believe it is A. 1,1150.6cm^3

Step-by-step explanation:

To solve for the volume of a cone:

[tex]V = \pi radius^{2} \frac{height}{3}[/tex]

========================================================

Explanation:

We'll need the slope first

m = slope

m = (y2-y1)/(x2-x1)

m = (0-(-4))/(-3-(-5))

m = (0+4)/(-3+5)

m = 4/2

m = 2

The slope is 2.

Next, pick either of the two given points to play the role of [tex](x_1,y_1)[/tex]

Let's say we picked on (-5,-4). The order doesn't matter so you could easily pick the other point as well.

We'll plug these items into the point slope equation below to solve for y.

[tex]y - y_1 = m(x - x_1)\\\\y - (-4) = 2(x - (-5))\\\\y + 4 = 2(x +5)\\\\y + 4 = 2x +10\\\\y = 2x +10-4\\\\y = 2x +6\\\\[/tex]

Or we could have picked on (-3,0). The m value stays the same (at m = 2)

[tex]y - y_1 = m(x - x_1)\\\\y - 0 = 2(x - (-3))\\\\y = 2(x +3)\\\\y = 2x+6\\\\[/tex]

This one takes a few less steps. Either way, we get to the same answer.

You only need to pick one of the points, but doing both of them helps show that the two points are on the same line. It helps confirm the answer.

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

Another way to check the answer is to plug the (x,y) coordinates into y = 2x+6 for each point.

So let's say we check (x,y) = (-5,-4)

y = 2x+6

-4 = 2(-5)+6 ... replace x with -5, replace y with -4

-4 = -10+6

-4 = -4

This confirms the first point. I'll let you check the second point.

Answer:

y = 2x+6

Step-by-step explanation:

Attached below is my graph

I graphed the two points, and formed a line

From the point (0,0), i counted the units till the first point the line touches on the y axis (6)

This is the y intercept

The slope-intercept form is written as y = mx+b

m = slope

b = y intercept

So so far we have y = mx + 6

The slope is the rise to the next point the line touches, over the run

You can see that as it rises 2, it runs 1

Rise / Run = 2/1 = 2

Slope = 2

Equation: y = 2x + 6

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

11.8

Step-by-step explanation:

Refer to the image attached.

Total boxes = 9

Total scarves in each box = s

ATQ

9s+(-9) = 36

9s -9 = 36

9s = 36+9

9s = 45

s = 45/9

s = 5

Value of s is 5

Must click thanks and mark brainliest

Answer:

s = 5

Step-by-step explanation:

9* number of scarves in each box after removing 1 scarf = 36

9 *(s -1) = 36

9s - 9 =  36   {Distributive property}

9s = 36+ 9     {add 9 to both sides}

9s = 45

s= 45/9  {Divide both sides by 9}

s = 5

Answer:

f(x)=y

5x+4=y

5x=y-4

x=y-4/5

inverse of x=(x-4)/5

Answer

1

[tex](a + b)^{2} = {a}^{2} + 2ab + {b}^{2} [/tex]

Therefore

Answer:

1

Step-by-step explanation:

SEE IMAGE FOR Solution ...

The net cost after discounts will be $ 2,450.

Given that Economy Hardware Store ordered items retailing for $ 2,500, and they received a chain discount of 5/20/2, the following calculation must be performed to find the net cost, knowing that the net cost is equal to the initial cost minus the discounts made about it:

First, the discount percentage must be calculated.

5/20/2 = X

4/2 = X

2 = X

Then, this percentage must be subtracted from the initial value.

2500 x (1-0.02) = X

2500 x 0.98 = X

2450 = X

Therefore, the net cost after discounts will be $ 2,450.

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Answer:

Behold.

Step-by-step explanation

The answer to the statement is 1)false 2) false 3) true 4) true and 5) false.

Given functions,f

1) For x ≤ -2: f(x) = -12 + 6x

2) For -2 < x < 1: f(x) = 41 - 15x

3) For x ≥ 1: f(x) = 31 - 4x

1) The graph crosses the y-axis at (0, -15).

This is false because if x = 0, the function value would be -12 + 6 * 0 = -12, not -15.

2) The graph has a point of discontinuity at x = 1.

This is false because the function is defined at x = 1 there is no space, so there is no point of discontinuity at x = 1.

3) The graph is increasing over the interval (4, ∞).

This is true because the coefficient of x in the function's expression is negative, showing that it is decreasing. Therefore, as x increases, the function values decrease.

4) The graph is decreasing over the interval (-12, -2).

This is true because the coefficient of x in the first piece of the function (-12 + 6x) is positive, showing an increasing trend. Therefore, as x decreases from -12 to -2, the function values increase.

Statement 5: The domain of the function is all real numbers.

This is false because the domain of the function is limited by the intervals in its definition. The function is defined differently for different intervals of x.

So, the answer to the statement is

1) false

2) false

3) true

4) true

5) false

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Answer:

Choice D.

Step-by-step explanation:

Hello! Me again, this is my explanation to my solution,

A stem-and-leaf plot shows the data shape and the densities of the different classes in a graphical form such that the information in the data such as the data characteristics are self displayed by the data numbers arranged in the stem-and-leaf plot. The stem-and-leaf plot keeps the raw numerical data, in the form they were obtained and by their arrangement, outliers are easily spotted.

Hope this helped! Let me know if you have further questions! :)

Answer:

0.86603 is the answer of the question

Answer:

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

Step-by-step explanation:

Using the rule of exponents

[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]

Given

64[tex]x^{\frac{1}{2} }[/tex] = 27[tex]x^{-\frac{5}{2} }[/tex] ( divide both sides by [tex]x^{-\frac{5}{2} }[/tex] )

64 × [tex]\frac{x^{\frac{1}{2} } }{x^{-\frac{5}{2} } }[/tex] = 27

64 × [tex]x^{\frac{1}{2}-(-\frac{5}{2}) }[/tex] = 27

64 × [tex]x^{\frac{1}{2}+\frac{5}{2} }[/tex] = 27

64 x³ = 27 ( divide both sides by 64 )

x³ = [tex]\frac{27}{64}[/tex] ( take the cube root of both sides )

x = [tex]\sqrt[3]{\frac{27}{64} }[/tex] = [tex]\frac{\sqrt[3]{27} }{\sqrt[3]{64} }[/tex] = [tex]\frac{3}{4}[/tex]

Answer:

W = 7 - x

Step-by-step explanation:

The perimeter is P= 2L + 2×W , where L is the length and W is the width.

If L = (x+2) , replacing L with the expression x+2 we have

P= 2×(X+2) + 2W ⇔ 18 = 2x + 4 + 2W ⇔ 2W =18 - 2x - 4 ⇔ 2W = 14 - 2x

⇔ W = 7 - x

Answer:

[tex] {6}^{3} = 216[/tex]

Answer:

let,

√x-5=ky

x=30 when y=2

√30-5=2k

or, k=(√30-5)/2

now, when y=8

√x-5=8×(√30-5)/2

or, √x-5=4√30-20

or, √x=4√30-15

or, x=(4√30-15)²

or, x=47.73..