Timmy uses 1 1/2 cups of sugar for every 2 gallons of lemonade he makes.

Which measures are accurate regarding triangle JKL? Check all that apply.

mixas84 [53]

Answer:

Option (1), (3) and (6) is correct.

m∠K = 84° , k ≈ 3.7 units and KL ≈ 3.2 units.

Step-by-step explanation:

Given : ∠J = 58° , ∠L = 38° and length of side JK = 2.3 units.

We need to check all the options and choose that follows.

First we find the measure of ∠K

Using angle sum property , Sum of angles of a triangle is 180°

⇒ ∠J + ∠k + ∠L = 180°

⇒ 58° + ∠k + 38° = 180°

⇒ ∠k + 96° = 180°

⇒ ∠k = 180° - 96°

⇒ ∠k = 84°

Also using sine rule on ΔJKL , we get,

$\frac{KL}{\sin J}=\frac{JL}{\sin K}=\frac{JK}{\sin L}$

Substitute the values, we get,

$\frac{KL}{\sin 58^{\circ}}=\frac{k}{\sin 84^{\circ}}=\frac{2.3}{\sin 38^{\circ}}$

Consider the last two ratios, we have,

$\frac{k}{\sin 84^{\circ}}=\frac{2.3}{\sin 38^{\circ}}$

${k}=\frac{2.3}{\sin 38^{\circ}}\times {\sin 84^{\circ}}$

On solving we get,

${k}=3.71$

Also, now consider the first and last ratio, we get,

$\frac{KL}{\sin 58^{\circ}}=\frac{2.3}{\sin 38^{\circ}}$

${KL}=\frac{2.3}{\sin 38^{\circ}}\times {\sin 58^{\circ}$

${KL}=3.16$

Thus, k ≈ 3.7 units and KL ≈ 3.2 units.

Option (1), (3) and (6) is correct.

5 0

4 years ago

Read 2 more answers

Suppose that the population P(t) of a country satisfies the differential equation dP/dt = kP (600 - P) with k constant. Its pop

jeka94

Answer:

The country's population for the year 2030 is 368.8 million.

Step-by-step explanation:

The differential equation is:

$\frac{dP}{dt}=kP(600 - P)\\\frac{dP}{P(600 - P)} =kdt$

Integrate the differential equation to determine the equation of P in terms of t as follows:

$\int\limits {\frac{1}{P(600-P)} } \, dP =k\int\limits {1} \, dt \\(\frac{1}{600} )[(\int\limits {\frac{1}{P} } \, dP) - (\int\limits {\frac{}{600-P} } \, dP)]=k\int\limits {1} \, dt\\\ln P-\ln (600-P)=600kt+C\\\ln (\frac{P}{600-P} )=600kt+C\\\frac{P}{600-P} = Ce^{600kt}$

At t = 0 the value of P is 300 million.

Determine the value of constant C as follows:

$\frac{P}{600-P} = Ce^{600kt}\\\frac{300}{600-300}=Ce^{600\times0\times k}\\\frac{1}{300} =C\times1\\C=\frac{1}{300}$

It is provided that the population growth rate is 1 million per year.

Then for the year 1961, the population is: P (1) = 301

Then $\frac{dP}{dt}=1$ .

Determine k as follows:

$\frac{dP}{dt}=kP(600 - P)\\1=k\times300(600-300)\\k=\frac{1}{90000}$

For the year 2030, P (2030) = P (70).

Determine the value of P (70) as follows:

$\frac{P(70)}{600-P(70)} = \frac{1}{300} e^{\frac{600\times 70}{90000}}\\\frac{P(70)}{600-P(70)} =1.595\\P(70)=957-1.595P(70)\\2.595P(70)=957\\P(70)=368.786$

Thus, the country's population for the year 2030 is 368.8 million.

3 0

3 years ago

5x+7y=3914. I'm not quite sure how to write the x and y! First answer will get Brainliest, thanks!

Stolb23 [73]

Answer:

hanges made to your input should not affect the solution:

(1): Dot was discarded near "4.".

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

5*x+7*y-(3914)=0

STEP

1

:

Equation of a Straight Line

1.1 Solve 5x+7y-3914 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 5x+7y-3914 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 3914/7 so this line "cuts" the y axis at y=559.14286

y-intercept = 3914/7 = 559.14286

Calculate the X-Intercept :

When y = 0 the value of x is 3914/5 Our line therefore "cuts" the x axis at x=782.80000

x-intercept = 3914/5 = 782.80000

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 559.143 and for x=2.000, the value of y is 557.714. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 557.714 - 559.143 = -1.429 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = -1.429/2.000 = -0.714

Geometric figure: Straight Line

Slope = -1.429/2.000 = -0.714

x-intercept = 3914/5 = 782.80000

y-intercept = 3914/7 = 559.14286

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

The coordinate plane below shows a triangular region at sea between three islands. Each unit on the coordinate plane represents

statuscvo [17]

Answer:

Step-by-step explanation:

A point in geometry is a location. It has no size i.e. no width, no length and no depth. A point is shown by a dot. A line is defined as a line of points that extends infinitely in two directions. ... A plane extends infinitely in two dimensions

4 0

3 years ago

3y+6(3y-2) = 2(y-1)-7 solve for y , reduce answer to integer or fraction.

Alexxandr [17]

=3y+18y-12=2y-2-7
=21y-12=2y-9
=21y-2y=-9+12
=19y=3
Y=0,16

4 0

3 years ago

Read 2 more answers