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3 years ago

Write a paragraph proof.

Mathematics

1 answer:

Ivenika [448]3 years ago

6 0

RS Bisects QT means, it cuts QT in two equal halves, so QP would be equal to PT, as it is an isosceles triangle, one other side would be equal as well, so RP is equal to PS, Now, by ASA, we conclude the both mentioned triangles in the figure are congruent.

Hope this helps!

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If Isaac uses a coupon entitling him to a 25% discount off the purchase price before tax, how much will his bill be? Assume that

lions [1.4K]

Answer:

b) 25/100 x 79

= 19.75

= 79 - 19.75

= $59.25 (before tax)

7/100 x 59.25

= 414.75/100

= 4.15

= 59.25 + 4.15

= $63.4 (after adding tax)

First we have to take out the percentage of discount and minus it from the total cost . To find the discounted price with tax, we have to take out the percentage of the tax from the discounted amount and add it to the discounted amount to get the total cost.

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

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

ANSWER ASAP PLEASE RIGHT ANSWER GETS BRAINLIST

Natasha_Volkova [10]

Answer:

Step-by-step explanation:

We can set up equation for this one.

Let's say the number is X.

the sum of X and 14 can be expressed as : X+14

five times the sum of X and 14 can be expressed as 5(x+14)

and 5(X+14) = 80

$5(x+14) = 80\\x+14 = 80 \div 5 = 16\\x = 16-14 = 2$

The number is 2

8 0

3 years ago

Yan is climbing down a ladder. Each time he descends four rungs on the ladder, he stops to see how much farther he has to go

anastassius [24]

Question:

Yan is climbing down a ladder. Each time he descends 4 rungs on the ladder, he stopped to see how much farther he has to go. If Yan made eight stops with no extra steps, which expression best shows another way to write the product of the number of ladder rungs that Yan and climbed?

4+4+4+4

8+8+8+8

(-1)(4+4+4+4)

(-8) + (-8) + (-8) + (-8)

Answer:

$Total = (-8) +(-8) +(-8) +(-8)$