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3 years ago

Does a triangle with side lengths 7, 80, and 31 from a right triangle?

Mathematics

2 answers:

Anarel [89]3 years ago

6 0

What is the square of the longest side?

What is the sum of the squares of the two shorter sides?

Is the triangle a right triangle?

Yes, the square of the longest side equals the sum of the squares of the shorter sides

zhannawk [14.2K]3 years ago

6 0

Answer:

What is the square of the longest side?

What is the sum of the squares of the two shorter sides?

Is the triangle a right triangle?

yes the square of the longest side equals the sum of the squares of the shorter sides.

Step-by-step explanation: i got it right on edg-enuity

You might be interested in

A rectangle has a perimeter of 24 inches and a width of 4 inches. What is the length?

Svetradugi [14.3K]

Answer: the length is 8

Step-by-step explanation:

3 0

2 years ago

a student walks 50m on a bearing 0.25 degrees and then 200m due east how far is she from her starting point.

Inessa05 [86]

Answer:

Step-by-step explanation:

I'm going to use Physics here for this concept of vectors. Here are some stipulations I have set for the problem (aka rules I set and then followed throughout the problem):

** I am counting the 50 m as 2 significant digits even though it is only 1, and I am counting 200 as 3 significant digits even though it is only 1. 1 sig dig doesn't really give us enough accuracy, in my opinion.

** A bearing of .25 degrees is measured from the North and goes clockwise; that means that measured from the x axis, the angle is 89.75 degrees. This is the angle that is used in place of the bearing of .25 degrees.

** Due east has an angle measure of 0 degrees

Now let's begin.

We need to find the x and y components of both of these vectors. I am going to call the first vector A and the second B, while the resultant vector will be C. Starting with the x components of A and B:

$A_x=50cos(89.75)$ so

$A_x=.22$

$B_x=200cos(0)$ so

$B_x=200$ and we need to add those results together. Due to the rules for adding significant digits properly, the answer is

$C_x=200$ (and remember I am counting that as 3 sig fig's even though it's only 1).

Now for the y components:

$A_y=50sin(89.75)$ so

$A_y=50$ (which I'm counting as 2 sig fig's)

$B_y=200sin(0)$ so

$B_y=0$ and we need to add those results together.

$C_y=50$

Now for the resultant magnitude:

$C_{mag}=\sqrt{(200)^2+(50)^2}$ and that gives us a final magnitude of

$C_{mag}=206$ m

Now for the angle:

Since both the x and y components of the resultant vector are in quadrant 1, we don't need to add anything to the angle to get it right, so

$tan^{-1}(\frac{50}{200})=14$

The girl is 206 meters from her starting point at an angle of 14 degrees

4 0

3 years ago

WILL GIVE 5 STAR IF CORRECT: Chasity purchased a pool for $9,270 using a six-month deferred payment plan with an interest rate o

Verdich [7]

Answer:

$297.41

Step-by-step explanation:

Given that:

Amount = 9270

Derferred period = 6 months = 0.5 yr

Rate = 17.95% = 0.1795

Amount = 9270(1 + 0.1795)^0.5

Amount = 9270(1.1795)^0.5

Amount = 10067.663

PV = 10067.663

Number of months, n = 48

Monthly amount to be paid :

rp = rate per period = 0.1795/12 = 0.0149583

(rp * PV) / 1 - (1 + rp)^-n

(0.0149583 * 10067.663) / 1 - (1 + 0.0149583)^-48

150.5951234529 / 0.5096723

= 295.47441

Closest option is $297.41

6 0

2 years ago

Please someone answer this please

gladu [14]

Option C:

$\frac{3 a^{2} b^{11}}{2 }$ is equivalent to the given expression.

Solution:

Given expression:

$$\frac{-18 a^{-2} b^{5}}{-12 a^{-4} b^{-6}}$

To find which expression is equivalent to the given expression.

$$\frac{-18 a^{-2} b^{5}}{-12 a^{-4} b^{-6}}$

Using exponent rule: $\frac{1}{a^m}=a^{-m}, \ \ \frac{1}{a^{-m}}=a^{m}$

$$=\frac{-18 a^{-2} b^{5}a^{4} b^{6}}{-12 }$

$$=\frac{-18 a^{-2} a^{4} b^{5} b^{6}}{-12 }$

Using exponent rule: ${a^m}\cdot{a^n}=a^{m+n}$

$$=\frac{-18 a^{(-2+4)} b^{(5+6)}}{-12 }$

$$=\frac{-18 a^{2} b^{11}}{-12 }$

Divide both numerator and denominator by the common factor –6.

$$=\frac{3 a^{2} b^{11}}{2 }$

$$\frac{-18 a^{-2} b^{5}}{-12 a^{-4} b^{-6}}=\frac{3 a^{2} b^{11}}{2 }$

Therefore, $\frac{3 a^{2} b^{11}}{2 }$ is equivalent to the given expression.

Hence Option C is the correct answer.

8 0

3 years ago

Y = – 2x² + 12x - 7

Vikentia [17]

Answer:

a) axis of symmetry: <em> </em><em>x</em> = <em>h</em>

b) Vertex: (3, 11).

c/d) Maximum point = vertex (3, 11).

Step-by-step explanation:

<em><u>Note:</u></em><em> </em>This post will only provide the answers for parts a through d, in accordance with Brainly's Guidelines.

Given the quadratic equation, y = – 2x² + 12x - 7, where a = -2, b = 12, and c = -7:

<h3> </h3><h3>a) What is equation of the axis of symmetry?</h3>

The <u>axis of symmetry</u> is an imaginary line that divides the graph of a parabola into two symmetrical parts. The axis of symmetry goes through the x-coordinate of the vertex, (<em>h</em>, k). Hence, the axis of symmetry is often represented by the following equation: x = h.

<h3 /><h3>b) What is the vertex?</h3>

We can find the x-coordinate of the vertex by using the following formula:

$\displaystyle\mathsf{x\:=\:\frac{-b}{2a}}$

Substitute the given values for a = -2, and b = 12 into the formula:

$\displaystyle\mathsf{x\:=\:\frac{-(12)}{2(-2)}\:=\:\frac{-12}{-4}\:=\:3}$

Hence, the x-coordinate of the vertex is 3.

Substitute x = 3 into the given quadratic equation to find its corresponding y-coordinate:

y = – 2x² + 12x – 7

y = – 2(3)² + 12(3) – 7

y = –2(9) + 36 – 7

y = – 18 + 36 – 7

y = 11

Therefore, the <u>vertex</u> of the given quadratic equation is (3, 11).

<h3 /><h3>c/d) Does the equation have a maximum or minimum? What is the maximum/minimum?</h3>

The value of the "<em>a</em>" coefficient in the quadratic equation, y = <u>a</u>x² + bx + c, determines whether a given parabola has either a minimum, or a maximum.

If <em>a</em> > 1, then it means that the graph of a parabola opens <u>upward</u>, and the vertex is its <u><em>minimum</em></u> point.

If <em>a</em> < 0, then the graph of a parabola opens downward, and the vertex is its <u><em>maximum</em></u> point.

Since the value of our given quadratic equation is a = -2, then it means that its graph opens <em>downward</em>, and that the <u>vertex is its maximum point</u>.

Attached is a screenshot of the graph, where it shows the vertex occurring at point (3, 11), for which the axis of symmetry goes through at x = 3.

5 0

2 years ago