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3 years ago

On the graph of the equation 2x + 5y = −30, what is the value of the y-intercept?

2 answers:

7 0

First we have to solve the equation for y

2x +5y=-30
-2x -2x

5y=-2x-30
-- -------------
5 5

y=-2/5x-6

now, the y-intercept is in the b position in y=mx+b so the y intercept is -6

Ksivusya [100]3 years ago

6 0

Y intercept is when the line crosses the y axis or when x=0
set x=0

2(0)+5y=-30
0+5y=-30
5y=-30
divide 5
y=-6

value of y intercept is -6 or (0,-6)

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Complete the standard form of the equation of a hyperbola that has vertices at (-10, -15) and (70, -15) and one of its foci at (

Elena L [17]

Answer:

$\frac{(x-30)^{2}}{40^{2}} - \frac{(y+15)^{2}}{3^{2}} = 1$

Step-by-step explanation:

The equation of the horizontal hyperbola in standard form is:

$\frac{(x-k)^{2}}{a^{2}} - \frac{(y-k)^{2}}{b^{2}} = 1$

The position of its center is:

$C(x,y) = \left(\frac{-10 + 70}{2}, -15 \right)$

$C(x, y) = (30,-15)$

The values for c and a are respectively:

$a = 70 - 30$

$a = 40$

$c = 30 - (-11)$

$c = 41$

The remaining variable is computed from the following Pythagorean identity:

$c ^{2} = a^{2} + b^{2}$

$b = \sqrt{c^{2}-a^{2}}$

$b = \sqrt{41^{2}-40^{2}}$

$b = 3$

Now, the equation of the hyperbola is:

$\frac{(x-30)^{2}}{40^{2}} - \frac{(y+15)^{2}}{3^{2}} = 1$

3 0

3 years ago

Read 2 more answers

A bag contains 150 marbles. Some are red and the rest are black. There are 14 red marbles for every black marble. How many red m

REY [17]

Answer:

114

Step-by-step explanation:

Ratio of red marbles to black marbles is 19:1. (Data from 3rd sentence)

19+1= 20

20 units= 120 (Data from 1st sentence)

1 unit= 120/20= 6

19 units= 120-6= 114 (Values solved in working above)

Ans: There are 114 red marbles.

i hope i cleared your doubt

8 0

3 years ago

Read 2 more answers

A bowling ball weighs 5.61 kg, and a bowling pin weighs 1.57 kg. About how many bowling pins would equal the weight of the bowli

nadezda [96]

3 bowling pins would be equal to the weight of the bowling ball.

You find the answer by dividing the amount that a bowling ball weighs (5.61 kg) by the amount that a bowling pin weighs (1.57 kg) which would give you 3 remainder 57 .. So it's 3.

4 0

3 years ago

The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of

Svetach [21]

Answer:

(a) P(1000 < X < 1500) = 0.0256

(b) P(X < 1025) = 0.0392

(c) P(X > 1200) = 0.6554

(d) Percentile rank of a bag that contains 1425 chocolate chips = 90.98%

Step-by-step explanation:

We are given that the number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 chips and standard deviation 129 chips.

Firstly, Let X = number of chocolate chips in a bag

The z score probability distribution for is given by;

Z = $\frac{ X - \mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = population mean = 1252 chips

$\sigma$ = standard deviation = 129 chips

(a) Probability that a randomly selected bag contains between 1000 and 1500 chocolate chips, inclusive is given by = P(1000 $\leq$ X $\leq$ 1500) = P(X $\leq$ 1500) - P(X < 1000)

P(X $\leq$ 1500) = P( $\frac{ X - \mu}{\sigma}$ $\leq$ $\frac{1500-1252}{129}$ ) = P(Z $\leq$ 1.92) = 0.9726

P(X < 1000) = P( $\frac{ X - \mu}{\sigma}$ < $\frac{1000-1252}{129}$ ) = P(Z < -1.95) = 1 - P(Z $\leq$ 1.95)

= 1 - 0.9744 = 0.0256

Therefore, P(1000 $\leq$ X $\leq$ 1500) = 0.9726 - 0.0256 = 0.947

(b) Probability that a randomly selected bag contains fewer than 1025 chocolate chips is given by = P(X < 1025)

P(X < 1025) = P( $\frac{ X - \mu}{\sigma}$ < $\frac{1025-1252}{129}$ ) = P(Z < -1.76) = 1 - P(Z $\leq$ 1.76)

= 1 - 0.9608 = 0.0392

P(X > 1025) = P( $\frac{ X - \mu}{\sigma}$ > $\frac{1200-1252}{129}$ ) = P(Z > -0.40) = P(Z < 0.40) = 0.6554

(d) Percentile rank of a bag that contains 1425 chocolate chips is given by;

Firstly we will calculate the z score of 1425 chocolate chips, i.e.;

Z = $\frac{1425-1252}{129}$ = 1.34

Now, we will check the area probability in z table which corresponds to this critical value of x;

The value which we get is 0.9098.

Therefore, 90.98% is the rank of bag that contains 1425 chocolate chips.

8 0

4 years ago

Which are partial products for 51 × 36?

12345 [234]

partial products for 51 × 36
50 x 30 = 1500
50 x 6 = 300
1 x 30 = 30
1 x 6 = 6

answer
A.1 x 6 = 6
B.1 x 30 = 30
C.50 x 6 = 300

hope it helps

8 0

4 years ago