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2 years ago

Please Help 6-10 or just one of them

Mathematics

1 answer:

Free_Kalibri [48]2 years ago

5 0

Answer:

6) 20

7) I think is 2.5 (im not sure)

8) 7

Step-by-step explanation:

6) (5x+9)+(3x+11)=180

8x+20=180

-20 -20

8x=160

Divide 8 on each side

x=20

7) (17x+1)=(20x-14)

17x+15 =20x

+17 +17

15 = 37x

divide 15 on each side

X=2.5

8) (3x+3)+(10-4)=90

(3x)+(10x-1)

13x-`1=90

+1 +1

13x=91

Divide 13 on each side

x=7

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Find the angle between u =the square root of 5i-8j and v =the square root of 5i+j.

fenix001 [56]

Answer:

The angle between vector $\vec{u} = 5\, \vec{i} - 8\, \vec{j}$ and $\vec{v} = 5\, \vec{i} + \, \vec{j}$ is approximately $1.21$ radians, which is equivalent to approximately $69.3^\circ$ .

Step-by-step explanation:

The angle between two vectors can be found from the ratio between:

their dot products, and
the product of their lengths.

To be precise, if $\theta$ denotes the angle between $\vec{u}$ and $\vec{v}$ (assume that $0^\circ \le \theta < 180^\circ$ or equivalently $0 \le \theta < \pi$ ,) then:

$\displaystyle \cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|}$ .

<h3>Dot product of the two vectors</h3>

The first component of $\vec{u}$ is $5$ and the first component of $\vec{v}$ is also

The second component of $\vec{u}$ is $(-8)$ while the second component of $\vec{v}$ is $1$ . The product of these two second components is $(-8) \times 1= (-8)$ .

The dot product of $\vec{u}$ and $\vec{v}$ will thus be:

$\begin{aligned} \vec{u} \cdot \vec{v} = 5 \times 5 + (-8) \times1 = 17 \end{aligned}$ .

<h3>Lengths of the two vectors</h3>

Apply the Pythagorean Theorem to both $\vec{u}$ and $\vec{v}$ :

$\| u \| = \sqrt{5^2 + (-8)^2} = \sqrt{89}$ .
$\| v \| = \sqrt{5^2 + 1^2} = \sqrt{26}$ .

<h3>Angle between the two vectors</h3>

Let $\theta$ represent the angle between $\vec{u}$ and $\vec{v}$ . Apply the formula $\displaystyle \cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|}$ to find the cosine of this angle:

$\begin{aligned} \cos(\theta)&= \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|} = \frac{17}{\sqrt{89}\cdot \sqrt{26}}\end{aligned}$ .

Since $\theta$ is the angle between two vectors, its value should be between $0\; \rm radians$ and $\pi \; \rm radians$ ( $0^\circ$ and $180^\circ$ .) That is: $0 \le \theta < \pi$ and $0^\circ \le \theta < 180^\circ$ . Apply the arccosine function (the inverse of the cosine function) to find the value of $\theta$ :

$\displaystyle \cos^{-1}\left(\frac{17}{\sqrt{89}\cdot \sqrt{26}}\right) \approx 1.21 \;\rm radians \approx 69.3^\circ$ .

3 0

3 years ago

If y varies jointly with x and z and y=40 when x=10 and z=9 find z when x =55 and y=105

Eduardwww [97]

Answer:

z = 189/44

Step-by-step explanation:

The "varies jointly" relationship can be expressed by ...

y = kxz

We can find k from the given values.

40 = k(10)(9)

40/90 = k = 4/9 . . . divide by the coefficient of k

Now we want to find z for given values of x and y. That can be found from ...

y = (4/9)xz

9y/(4x) = z . . . . . multiply by 9/(4x)

Filling in the new numbers, we have ...

z = 9·105/(4·55)

z = 4 13/44 = 189/44 ≈ 4.2954...(repeating 54)

4 0

3 years ago

At the local pet store, zebra fish cost $1.80 each and neon tetras cost $2.10 each. If Ernesto bought 16 fish for a total cost o

madreJ [45]

<span>zebra fish a then tetras fish (11 – a)
2.2a + 1.85(11 – a) = 22.80
2.2a + 20.35 – 1.85a = 22.80
0.35a = 2.45
a = 7 zebra and 11 – 7 = 4 neon fish

</span>

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3 years ago

Use a flowchart to prove if the triangles in each pair of similar. NO LINKS!!!<br>

vekshin1

Answer:

Step-by-step explanation:

Start

<F = <Q Given

<GPF = <RPQ Vertically opposite angles

<FGP = <QRP A triangle has 180 degrees. 2 equal angles means the third pair must be equal

Triangle GPF ~ Triangle RPQ AAA

end

I don't see any way to make these triangles similar except by stating the statement and why it is so. There really are no yes / no choices. If you get another answer, choose it.

JL/LE = 90/27 Given

KL /LD = 90/27 Given

<JLK = <DLK Vertically opposite

Are the ratios equal Yes Then is the angle included Yes

Then the triangles are similar.

Are the ratios not equal No then the triangles cannot be similar

Is the angle not included Then similarity cannot be proved.

ΔJLK ≈ ΔDLK Equal Ratios and included angle === similarity

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Gelneren [198K]

Answer:

quadrilateral, parallelogram, rhombus

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