Find the length of the minor axis of the ellipse described by the equation:x squared over 12 plus y squared over 13 equals 1

First,we will find the slope of the line

Using 8x - 6y = 5

we will have to re-arrange the equation above to be in the slope-intercept form.

That is; it should be in the form y = mx + b

8x - 6y = 5

6y = 8x -5

y = 8/6 x - 5/6

slope = 8/6 = 4/3

In a parellel equation the slope are the same, hence the slope of our new equation is 4/3

Next, we find the intercept of the new equation;

Using the point (-9, 1) and slope(m) = 4/3

we will substitute into the equation below and then solve for b, where b is the slope of our new equation

y = mx + b

1 = 4/3 (-9) + b

1 = 4(-3) + b

1 = - 12 + b

add 12 to both-side of the equation

1+ 12 = b

13 = b

b= 13

Substituting m = 4/3 and b = 13 into the formula; y = mx+ b

y = 4/3 x + 13

Answer:tiny bit confused what the question is asking

length=350

Step-by-step explanation:

perimeter =(length+width )x2

perimeter/2

1000/2=(length+width )

500=(length+width)

500-150=350length

The mass of the backpack is 1.02 kilograms.

On earth, the weight of an object of mass M is given by:

W = M*g

Where g is the gravitational acceleration:

g = 9.8m/s^2

In this case, the weight is 10N, then we can write:

10N = M*9.8m/s^2

Solving this for M we get:

10N/(9.8m/s^2) = M = 1.02 kg

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Answer:

102.06

Step-by-step explanation:

Absolute values are always positive

Answer:

Step-by-step explanation:

102.06

Absolute value is just the positive of any value.

Hope this helps! Have a nice day!

The solution to equation x+ 1/2x+2/3x+4= 30 and has one solution x = 12 which is the correct answer would be an option (D).

The no. of chocolates given to Sarah = 1/2 of x = x/2

Then Lily has two-thirds of what he has given David. Following the distribution of the chocolates,

The number of chocolates provided to Lily is equal to two-thirds of the number of chocolates given to David.

The number of chocolates given to Lily Equals 2/3 of x = 2x/3

Now, the total number of chocolates delivered to David, Sarah, and Lily

= x+x/2+2x/3

Here LCM of 2 and 3 is 6

The Total no. of chocolates given to David, Sarah, and lily

= (6x + 3x+ 4x)/6

The total number of chocolates distributed to David, Sarah, and Lily is 13x/6.

Jonathan had four chocolates left after giving them out.

The number of chocolates left with Jonathan equals the total number of chocolates given to David, Sarah, and Lily.

⇒ 4 = 30 - 13x/6

⇒ 4 + 13x/6  = 30

⇒ 13x/6 = 30-4 = 26

⇒ x = 26×6/13 = 2×6

⇒ x = 12

Hence, the equation which represents the given situation is 30 - 13x/6 =4

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We have to relate the angles of the trapezoid in order to find the measure of BAD.

Given:

Then

The angles are congruent because if AD and BC are congruent, and the lines are parallel, they sides will form the same angles.

Also, as the segment AD is "cut" by two parallel lines, the angles BAD and ADC are consecutive interior angles and are, therefore, supplementary.

Then, we can write:

Now, with the value of x, we can calculate the measure of BAD as:

Answer: the measure of BAD is 74°.

The equivalent composite function is expressed as  -9x + 5

Composite functions are also known as function of a function.

Given the following functions:

a(x) = 3x+2 and

b(x) = -3x + 1

Determine the value of a(b(x))

a(b(x)) = a(-3x+1)

a(b(x)) = 3(-3x+1) + 2

a(b(x)) = -9x + 3 + 2

a(b(x)) = -9x + 5

This gives the equivalent composite function.

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(a) Leila's car, 2 gallons

(b) 300, Raina's car

(a) Leila's car, 2 gallons At 150 miles, Raina's car has 9 gallons of gas and Leila's car had 11 gallons of gas.

(b) 300, Raina's car The amount of gas remaining is when the graphs intersect.

(a) At 150 miles, Raina's car has 9 gallons of gas and Leila's car had 11 gallons of gas. This can be seen by looking at the graph of the two cars' gas levels. The graph for Leila's car is higher than the graph for Raina's car at this point, so Leila's car has more gas.

(b) The amount of gas remaining is when the graphs intersect. This happens at 300 miles. Since the graph for Leila's car is higher than the graph for Raina's car before 300 miles, Raina's car will have less gas at this point.

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Looking at the inequalities, it involves the 'less than or equal to' symbol. This means that the lines of both inequalities must be solid. In options B, C and D, one or two of the lines is broken. This is an indication that they don't represent the given inequality. We would check option A

Optiona

Question 1

[tex]-14=-4(9x-1)\\\\-14=-36x+4\\\\-18=-36x\\\\x=\frac{1}{2}[/tex]

Question 2

Multiplying both sides by 12,

[tex]4x-7x=8\\\\-3x=8\\\\x=-\frac{8}{3}[/tex]

Formula to calculate Principal with clompound interest:

For the given situation:

A= 60,000

r= 7% =7/100= 0.07

n= 12 (as it is compounded monthly and a year has 12 months)

t= 10 years

Then, they must deposit approximately $29,855.75

A1 = 7

An = 3A(n-1) + 4. According to this, A2 would be= 3*7 + 4 =25

A1 = 7, A2 = 25, then the difference is d = 18

The general formula for an aritmethic progression is An = A1 + (n -1)d

For A4 = 7 + (4-1)*18 = 61

Answer:

=82

Step-by-step explanation:

the value of

x + y²

putting x=1,y=9

we get,

1+(9)^²

=1+81

=82

Answer:

a) 0.0187

b) 0.0943

c) 0.2959

Step-by-step explanation:

a) 9/31 * 8/30 * 7/29 = 0.0187

b) 10/31 * 9/30 * 8/29 + 12/31 * 11/30 * 10/29 + 9/31 * 8/30 * 7/29 = 0.0943

c) 21/31 * 20/30 * 19/29 = 0.2959

Answer:

[tex]260 \: {cm}^{2} [/tex]

Step-by-step explanation:

hope it helped, have a nice day!: )

For 3 yards, it costs, 1.50.

So for one yard,

Therefore for 5 yards,

On (-∞, -2) ∪ (3,∞) f(x) is positive, On (-∞, -0.5) it is negative, On (0.5, ∞) it is increasing, in none of the intervals it is having positive concavity, On (-∞, ∞) it has negative concavity.

Seeing as how f (x) = 0 there. A function’s “positive regions” are those times when it is above the x-axis. Y-values that are positive are where it is (not zero).

The portions of a function that are below the x-axis are known as its negative regions.

You must first take the derivative, then make it equal to 0, and then determine which zero values the function is positive between in order to determine when a function is rising. In order to determine when the function is positive and, thus, rising, test values on all sides of these.

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Answer:

m=35

Explanation:

Given the equation:

We solve for the value of m by adding 15 to both sides.

The value of m is 35.

ANSWER

EXPLANATION

The Principal is $5200;

Increase rate is; 6.5%

The increase in dollar is;

Hence, the amount in the account at the end of the year;

Therefore, the increase in dollar is $338 while the amount in the account at the end of the year is $5538

Answer:

6

Step-by-step explanation:

when you change h[×] to h[-2] , -2x +2 change to -2[-2]+2

Answer:

SAS= Side, Angle, Side

Step-by-step explanation:

According to the image, GB congruent to XP, and LB congruent to PF. So, it means that both triangle have the same angle since they both have two congruent side.

g(x)= x^4 √(1+x)

g(-x) = (-x)^4 √1-x

g (-x) = x^4 √1-x

Since the obtained function is not the same or the opposite it is neither.

The Simplification of the expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths is "negative 43 over 24 times j plus negative 1 over 12". option D

The expression which is equivalent to 3(−4.5b − 2.1) − (6b + 0.6) is −19.5b − 6.9. option c

negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths

= -1/8j + 2/3 - (5/3j + 9/12)

= -1/8j + 2/3 - 5/3j - 9/12

= -1/8j - 5/3j + (2/3 - 9/12)

= (-3j-40j / 24 + (8-9) / 12

= -43/24j + (-1)/12

The expression equivalent to 3(−4.5b − 2.1) − (6b + 0.6)

= -13.5b - 6.3 - 6b - 0.6

= -13.5b - 6b - 6.3 - 0.6

= - 19.5b - 6.9

So therefore, the equivalent expression to 3(−4.5b − 2.1) − (6b + 0.6) is - 19.5b - 6.9

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A probability is the number of outcomes divided by the number of total outcomes.

An odd is given by a:b, in which a is the number of successes and b is the number of failures.

From the question, the probability of 5 cars will pass over a small bridge is 0.16

That means the total outcomes is 100 and the outcomes of successes are 16

Then to find the failures subtract 16 from 100

The failures = 100 - 16 = 84

Successes = 16

a = 16

Failures = 84

b = 84

Odds = a: b

Odds = 16: 84

Divide each term by 4 to simplify

Odds = (16/4): (84/4)

Odds = 4: 21

The answer is 4: 21

Based on the given situation, if x is number of kilograms of lobster, you can write the following expressions:

51 + 5x cost in the first restaurant

33 + 8x cost in the second restaurant

In order to determine the value of x which makes the cost the same in both restaurants, equal the previous expressions and solve for x:

51 + 5x = 33 + 8x subtract 33 both sides and 5x subtract both sides

51 - 33 = 8x - 5x simplify

18 = 3x divide by 3 both sides

18/3 = x

6 = x

x = 6

Hence, the weight of the lobster is 6 kg.

The cost of the dinner is:

51 + 5(6) = 51 + 30 = 81

Hence, the cost of the dinner is $81

Using the law of cosines to find m∠B:

Since B is the largest angle (because it's opposite to the longer side), then angles A and C are smaller. In consequence, the three angles are smaller than 90°, which means that the triangle is acute

Answer:

See below

Step-by-step explanation:

Point (4,-8)  slope form would be

( y - -8) = -2 ( x -4)          

y+8 = -2x + 8       re-arrange to y = mx + b form

y = - 2x        

Answer:

4.5

Step-by-step explanation:

4.5 + 4.5 + 4.5 + 4.5 = 18

You write it like this in the number line:

4.5, 9, 13.5, 18

Answer:

y=0.75x+2

Step-by-step explanation: Slope as k and constant as b two points that showed by the graph: (0,2) (4,5)

so we can get 2=0*k+b b=2

5=4k+b

4k=5-2

4k=3

k=3/4

k=.75