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3 years ago

15

How many solutions does the system have? ? y = -27 -4 y = 3x +3

1 answer:

Alisiya [41]3 years ago

6 0

Answer:

-27-4=3x+3

-30-3=3x

X=-11

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Determine if the two triangles are congruent. If they are, state how you know.

Leto [7]

Answer:

By SSS Test

Step-by-step explanation:

Since the sides of both the triangle are equal

By SSS test, we can say that the both the triangles are congruent

6 0

3 years ago

Brad sells each cup of lemonade for $0.50. He wrote the equation y = 0.50x to figure out the amount y he will get for selling cu

Dvinal [7]

(X,Y) is (20,10) so that mean he made 10 bucks and sold 20 cups

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4 years ago

The center of an ellipse is (-9,3). one focus is (-7,3). The major axis is 24 units long. What is the equation of the ellipse in

CaHeK987 [17]

Answer:

$\frac{(x+9)^2}{144}+\frac{(y-3)^2}{140}=1$

Step-by-step explanation:

The standard equation of the ellipse is

$\frac{(x-\alpha)^2}{a^2}+\frac{(y-\beta)^2}{b^2}=1\;\cdots(i)$

where, $(\alpha, \beta)$ is the center and a,b are semi axes of the ellipse along x-axis and y-axis respectively.

Given that, $(\alpha, \beta)=(-9,3)$ and major axis, $2a=24$ .

So, semi major axis, $a=24/2=12$ .

Now, focus of the ellipse is (-7,3).

Let $e$ be the eccentricity of the ellipse,

So, $e=\frac c a$

where $c$ is the distance between the center and focus of the ellipse.

By using the distance formula,

$c=\sqrt{(-9-(-7))^2+(3-3)^2}=2$

$\Rightarrow e=\frac {2}{12}=\frac{1}{6}\;\cdots(ii)$

Again, the relationship among $a,b$ and $e$ is

$e=\sqrt{1-\frac{b^2}{a^2}$

$\Rightarrow \frac{1}{6}=\sqrt{1-\frac{b^2}{(12)^2}$ [from equation (ii)]

$\Rightarrow \frac{1}{36}=\sqrt{1-\frac{b^2}{144}$ [squaring on both the sides]

$\Rightarrow \frac{b^2}{144}=1-\frac{1}{36}$

$\Rightarrow b^2=\frac{35}{36}\times144=140$

So, the value of square of semi-minir axis, $b^2=140$ .

Hence, from equation (i), the equation of required ellipse is standard form is

$\frac{(x-(-9))^2}{144}+\frac{(y-3)^2}{140}=1$

$\Rightarrow \frac{(x+9)^2}{144}+\frac{(y-3)^2}{140}=1$

8 0

3 years ago

Solve a triangle when A=15° B=113° and b=7?

JulsSmile [24]

Let us draw a triangle ABC with A=15° ,B=113° and b=7.

Please see the attached image.

We know that the sum of interior angles of a triangle is 180 degrees. Thus, we have

$A+B+C=180\\
\\
15+113+C= 180\\
\\
C=62^{\circ}$

Apply Sine rule in the triangle ABC, we get

$\frac{a}{\sin 15}= \frac{7}{\sin 113}\\
\\
a=\frac{7 \sin 15}{\sin 113}\\
\\
a=1.97\\
\\
\text{Again apply sine rule, we get}\\
\\
\frac{c}{\sin 62}= \frac{7}{\sin 113}\\
\\
c=\frac{7 \sin 62}{\sin 113}\\
\\
c=6.71$

Therefore, we have

$a=1.97\\
c=6.71\\
C=62^{\circ}$

4 0

4 years ago

World population at a particular time was 7,11,36,02,566. Can you write it in words in the international numeration system ?

stellarik [79]

Answer:

Seven billion , one hundred thirteen million, six hundred and two thousand , five hundred and sixty six.

Step-by-step explanation:

B, HM TM, M Hth, TTh Th , H T O

7, 1 1, 3 6, 0 2, 5 6 6

Seven billion , one hundred thirteen million, six lac, two thousand , five hundred and sixty six.

Where

B= billion

HM = hundred million

TM = ten million

M = million

HTh = Hundred Thousand

TTh = Ten thousand

Th = thousand

H = hundred

T = tens

O= ones or units

In system international each category in further divided into units, hundreds and thousands.

We see that we have thousand, ten and then hundred thousand .

Similarly we have million, ten and hundred million.

This continues for billions and so on.

6 0

3 years ago