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2 years ago

Lena's guest house is 15 m long and 12 m wide. How long is the diagonal of the house?

2 answers:

8 0

Imagine the diagonal of a rectangle being the split between two triangles. you are trying to find the longest side of the triangle, which is the "diagonal" of the rectangle.

to find the length of a side of a triangle, use the Pythagorean theorem. it is : a^2 + b^2 = c^2

so... plug in your data like this...

15^2 + 12^2= c^2.

225 + 144 = the square root of 369.

that is rounded to 19.2

this is just how I would solve this problem, if I helped you out please just let me know by voting me brainliest! :)

Nezavi [6.7K]2 years ago

5 0

Assuming that the legnths given ae th sides o the room and th room is a recagnel

the diagonal makes 2 right triangles
pythagorean theorem
a^2+b^2=c^2
a and b are legs
c=hypotonuse

in this case
legnth and width are te legs and the diagonal is the hyptonuse

15^2+12^2=c^2
225+144=c^2
369=c^2
square root both sides
3√41ft=c

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Answer: 4/5

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2 years ago

Using Synthetic Division Use synthetic division to find the expression for the area of the base of a rectangular prism with heig

SOVA2 [1]

The answer is x2 – 2x – 9 and that is option C

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3 years ago

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WHY CAN'T ANYONE HELP ME? :( Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and

devlian [24]

Answer:

Children: $13

Adults: $18

Step-by-step explanation:

Well for both sets we can set up the following system of equations,

$\left \{ {{3a + 4c = 106} \atop {2a + 3c = 75}} \right.$

So first we need to solve for a in the first equation.

3a + 4c = 106

-4c to both sides

3a = -4c + 106

Divide 3 by both sides

a = -4/3c + 35 1/3

Now we plug in that a for a in 2a + 3c = 75.

2(-4/3c + 35 1/3) + 3c = 75

-8/3c + 70 2/3 + 3c = 75

Combine like terms

1/3c + 70 2/3 = 75

-70 2/3 to both sides

1/3c = 4 1/3

Divide 1/3 to both sides

c = 13

Now we can plug in 13 for c in 3a + 4c = 106,

3a + 4(13) = 106

3a + 52 = 106

-52 to both sides

3a = 54

Divide 3 by both sides.

a = 18

Thus,

an adult ticket is $18 and a children's ticket is $13.

Hope this helps :)

5 0

3 years ago

Read 2 more answers

What is the radical form of the expression (2x^4y^5)^3/8

s344n2d4d5 [400]

We are given expression: $(2x^4y^5)^{3/8}$

Let us distribute 3/8 over exponents in parenthesis, we get

$(2^{3/8}x^{4\times 3/8}y^{5\times 3/8}) = (2^{3/8}x^{12/8}y^{15/8})$

$= (2^{3/8}x^{1\frac{4}{8}} y^{1\frac{7}{8}} )$

We can get x and y out of the radical because, we get whlole number 1 for x and y exponents for the mixed fractions.

So, we could write it as.

$(2^{3/8}x^{1\frac{4}{8}} y^{1\frac{7}{8}} ) = xy(2^{\frac{3}{8} }x^{\frac{4}{8}} y^{\frac{7}{8}} )$

Now, we could write inside expression of parenthesis in radical form.

$xy\sqrt[8]{2x^{3}x^4y^7}$

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3 years ago

Write the equation of a parabola whose focus is at (-7, 3) and whose directrix is the line x = -3.

Sav [38]

Check the picture below.

now, let's keep in mind that, the vertex is half-way between the focus point and the directrix, it's a "p" distance from each other.

since this horizontal parabola is opening to the left-hand-side, "p" is negative, notice in the picture, "p" is 2 units, and since it's negative, p = -2.

its vertex is half-way between those two guys, so that puts the vertex at (-5, 3)

$\bf \textit{parabola vertex form with focus point distance} \\\\ \begin{array}{llll} 4p(x- h)=(y- k)^2 \\\\ 4p(y- k)=(x- h)^2 \end{array} \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=-5\\ k=7\\ p=-2 \end{cases}\implies 4(-2)[x-(-5)]=[y-7]^2 \\\\\\ -8(x+5)=(y-7)^2\implies x+5=\cfrac{(y-7)^2}{-8}\implies \boxed{x=-\cfrac{1}{8}(y-7)^2-5}$

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3 years ago