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yarga [219]
3 years ago
14

Solve the system of equations by the substitution method.

Mathematics
1 answer:
xeze [42]3 years ago
6 0
We can substitute the second into the first, this gives:

x -5x = -24 =>
-4x = -24
x = 6

fill in this x value in the second equation:

y = -5*6 = -30

So the solution is x=6, y=-30
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Given the right triangle shown below.if Cos A =15/17 and tan A=8/15 which of the following represents the length of BC
otez555 [7]

Answer:

The Figure for Right triangle is below,

Therefore , 15 unit length represents BC.

Step-by-step explanation:

Given:

Consider a right triangle ABC, Such that

\cos A=\dfrac{15}{17}\\\\\tan A=\dfrac{8}{15}

To Find:

BC = ?

Solution:

In Right Angle Triangle ABC, Cosine and Tangent identity

\cos A = \dfrac{\textrm{side adjacent to angle C}}{Hypotenuse}\\

\tan A= \dfrac{\textrm{side opposite to angle A}}{\textrm{side adjacent to angle A}}

BUT,

\cos A=\dfrac{15}{17}\\\\\tan A=\dfrac{8}{15} ....Given

On Comparing,

Adjacent side to angle A = AB = 15

Opposite side to angle A = BC = 8

Hypotenuse = AC =17

Also Pythagoras theorem is Satisfies,

(\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}

(\textrm{Hypotenuse})^{2} = 17^{2}=289

(\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}=15^{2}+8^{2}=289

The Figure for Right triangle is below,

Therefore , 15 unit length represents BC.

7 0
3 years ago
Ms.Lamberson got a new puppy abd weighed it in September and October in September the Puppy Weighed9 and one Fourth pounds In Oc
ddd [48]

Answer: The puppy was 2.25\ lb havier in October that it was in September.

Step-by-step explanation:

You need to make the conversion from mixed numbers to decimal numbers. To do it, divide the numerator of the fraction by the denominator add the result to whole part number:

9\frac{1}{4}=9+0.25=9.25\\\\11\frac{1}{2}=11+0.5=11.5

The weight of the puppy in September was:

w_1=9.25\ lb

And its weight in October was:

w_2=11.5\ lb

Subtract its weight in September from its weight in October in order to find how much heavier the puppy was in October than it was in September:

w_2-w_1=11.5\ lb-9.25\ lb=2.25\ lb

8 0
3 years ago
Find the area of the triangle.<br> 7 yd<br> 24 yd
tino4ka555 [31]

Answer:

A=84 square yards

Step-by-step explanation:

A=1/2bh

A=1/2(7x24)

A=1/2(168)

A=84

6 0
2 years ago
Read 2 more answers
Factor x^6 - y^6 completely. Show your work
adell [148]

the answer is(x - y) ^6

3 0
3 years ago
Find the coordinates of the midpoint of a segment with the endpoints (12,2) and (7,9)
olga55 [171]

Answer:

(9\frac{1}{2}, 5\frac{1}{2}) or (9 1/2, 5 1/2)   (same things, just typed two different ways)

Step-by-step explanation

  I can't remember the midpoint formula so I'll use a different method to get the midpoint.  


    since the ratio of a midpoint is 1:1 and that as a fraction is 1/2, we can take these coordinates and designate which one is first and which one is second (12, 2) will be my second and (7,9) will be my first. The formula I will use will be \frac{m}{m+n} (second X, - first X) + first x, so 1/2( 12 - 7) +7. now distribute the 1/2 to both the numbers  \frac{1x12}{2}  -\frac{1x7}{2} + 7  \\ \\ 12/2 -7/2 = 5/2 + 7 = 9.5  or 9\frac{1}{2}. The same works with the Y values, which would equal up to 5.5 or 5 \frac{1}{2}

5 0
1 year ago
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