Point K is on line segment \overline{JL} JL . Given JK=5x+7,JK=5x+7, JL=2x+8,JL=2x+8, and KL=4,KL=4, determine the numerical length of \overline{JL}. JL .

Answer:

3%

Step-by-step explanation:

Sorry I have no step by step explanation at this time.

Answer:

3=x or x=3

Step-by-step explanation:

2x+7=3x+4

-2x+2x7=-2x+3x+4

7=x+4

7-4=x+4-4

3=x or x=3

Answer:

5x + 3y = 95

8x + 6y = 170

x = 10 ; y = 15

Step-by-step explanation:

Let :

x = pack of juice boxes

y = pack of water bottles

Pack of juice box = $5

Pack of water bottles = $3

Amount of money spent :

5x + 3y = $95

Number of drinks purchased :

8x + 6y = 170

Using both equations ;

5x + 3y = 95 - - - (1)

8x + 6y = 170 - - - (2)

Multiply (1) by 6 and (2) by 3

30x + 18y = 570

24x + 18y = 510

Subtract :

6x = 60

x = 60 / 6

x = 10

Put x = 10 in (1)

5(10) + 3y = 95

50 + 3y = 95

3y = 95 - 50

3y = 45

y = 45 / 3

y = 15

x = 10 ; y = 15

The definition and explanation of an equation are given below with an example.

in mathematics, an equation is defined as an expression that expresses equality between 2 quantities or expressions. We use equations quite a lot in our daily lives whenever we have to equate two quantities and find out how they are equal. These are used in all branches of science because of the huge purpose they serve.

in simple words it tells what we have on the Left-Hand Side of the "=" sign is the same as what we have on the right-hand side of the statement. Some examples of equations are-

E²=m²c⁴+p²c²

x²+3x-1=0

70 oranges= 7 oranges × 10 oranges

Learn more about equations on

https://brainly.com/question/29657983?referrer=searchResults

#SPJ4

The exponential form of the regression, after an exponential transformation, is:ŷ = 9.68278 *\(e^(0.986 * x)\)None of the options provided match the correct exponential form.

In this case, the LSRL (Least Squares Regression Line) equation in logarithmic form is given as:

log ŷ = 0.986 + 3.149x

To convert this equation to exponential form, we need to take the exponential (base e) of both sides:

\(e^(log y) =\)\(e^(0.986 + 3.149x)\)

\(y= e^0.986 * e^(3.149x)\)

Simplifying further, we can write it as:

ŷ = 9.68278 * e^(3.149x)\(y = 9.68278 * e^(3.149x)\)

Therefore, the correct exponential form of the regression equation is ŷ = 9.68278 * \(e^(3.149x).\)

Learn more about exponents here:

https://brainly.com/question/30565877

#SPJ8

Answer:

2038 that's a answer po because hindi kasali ang 10

The exponent is represented as \(A=2*10^{4}\) where the resulting quotient has 10 raised to the power of 4.

Given data:

To perform the given division of  \(A=\frac{4*10^{2}}{2*10^{-2}}\) , we can use the properties of exponents and arithmetic operations.

When dividing numbers with the same base (in this case, 10), we subtract the exponent in the denominator from the exponent in the numerator:

So, the exponent is represented as A.

The exponential form of a number is a way of representing a number using exponents, where the base is typically a number greater than 1.

Now, the value of  \(A=\frac{4*10^{2}}{2*10^{-2}}\).

Now, simplify the exponent expression:

\(A=\frac{4*10^{2+2}}{2}\)

\(A=2*10^{4}\)

Hence, the exponential form is \(A=2*10^{4}\).

To learn more about exponential form, refer:

https://brainly.com/question/29337692

#SPJ3

Answer:

0.17 per ounce

Step-by-step explanation:

To find the price per ounce, divide the price by the number of ounces.

price/ number of ounces

A 2 pound bag costs $5.44. We need to find out how many ounces are in 2 pounds.

Each pound has 16 punches. Therefore, 2 pounds will have 32 ounces (16 ounces * 2 pounds=32 ounces).

Now we can find the price per ounce by dividing the price by the number of ounces.

price/ounces

We know the bag is 2 pounds, which is equal to 32 ounces. We also know the bag costs $5.44

price= $5.44

ounces= 32 ounces

$5.44/ 32 ounces

$0.17 / ounces

The asparagus costs 0.17 per ounce.

The difference quotient of the function f(x) = 4x² - 5x is 8x + 4h - 5.

The formula for difference quotient is expressed as:

\(\frac{f(x+h)-f(x)}{h}\)

Given the function in the question:

f(x) = 4x² - 5x

To solve for the difference quotient, we evaluate the function at x = x+h:

First;

f(x + h) = 4(x + h)² - 5(x + h)

Simplifying, we gt:

f(x + h) = 4x² + 8hx + 4h² - 5x - 5h

f(x + h) = 4h² + 8hx + 4x² - 5h - 5x

Next, plug in the components into the difference quotient formula:

\(\frac{f(x+h)-f(x)}{h}\\\\\frac{(4h^2 + 8hx + 4x^2 - 5h - 5x - (4x^2 - 5x)}{h}\\\\Simplify\\\\\frac{(4h^2 + 8hx + 4x^2 - 5h - 5x - 4x^2 + 5x)}{h}\\\\\frac{(4h^2 + 8hx - 5h)}{h}\\\\\frac{h(4h + 8x - 5)}{h}\\\\8x + 4h -5\)

Therefore, the difference quotient is 8x + 4h - 5.

Learn more about difference quotient here: https://brainly.com/question/6200731

#SPJ1

The statement ""what goes up must come down. the ball went up. it will come down." can be reached through a deductive reasoning.

The mental process of forming deductive deductions is known as deductive reasoning. An inference is deductively valid if its conclusion follows logically from its premises, i.e. if the premises cannot be true while the conclusion is false.

The primary distinction between inductive and deductive thinking is that inductive reasoning seeks to develop a hypothesis, whereas deductive reasoning seeks to test an existing theory. Inductive thinking proceeds from individual observations to broad generalizations, whereas deductive reasoning proceeds in the other direction.

In conclusion, the correct option based on the information is a deductive reasoning.

Learn more about deductive reasoning on:

https://brainly.com/question/7284582

#SPJ1

To solve the initial value problem y" + 4y = 4u_n(t), where y(0) = 0 and y'(0) = 1, we will follow these steps:

a. Find the Laplace transform of the solution y(t).

The Laplace transform of the given differential equation can be obtained using the properties of the Laplace transform. Taking the Laplace transform of both sides, we get:

s^2Y(s) - sy(0) - y'(0) + 4Y(s) = 4U_n(s),

where Y(s) represents the Laplace transform of y(t) and U_n(s) is the Laplace transform of the unit step function u_n(t).

Since y(0) = 0 and y'(0) = 1, the equation becomes:

s^2Y(s) - s(0) - 1 + 4Y(s) = 4U_n(s),

s^2Y(s) + 4Y(s) - 1 = 4U_n(s).

Taking the inverse Laplace transform of both sides, we obtain the solution in the time domain:

y''(t) + 4y(t) = 4u_n(t).

b. Find the solution y(t) by inverting the transform.

To find the solution y(t) in the time domain, we need to solve the differential equation y''(t) + 4y(t) = 4u_n(t) with the initial conditions y(0) = 0 and y'(0) = 1.

The homogeneous solution to the differential equation is obtained by setting the right-hand side to zero:

y''(t) + 4y(t) = 0.

The characteristic equation is r^2 + 4 = 0, which has complex roots: r = ±2i.

The homogeneous solution is given by:

y_h(t) = c1cos(2t) + c2sin(2t),

where c1 and c2 are constants to be determined.

Next, we find the particular solution for the given right-hand side:

For t < n, u_n(t) = 0, and for t ≥ n, u_n(t) = 1.

For t < n, the particular solution is zero: y_p(t) = 0.

For t ≥ n, we need to find the particular solution satisfying y''(t) + 4y(t) = 4.

Since the right-hand side is a constant, we assume a constant particular solution: y_p(t) = A.

Plugging this into the differential equation, we get:

0 + 4A = 4,

A = 1.

Therefore, for t ≥ n, the particular solution is: y_p(t) = 1.

The general solution for t ≥ n is given by the sum of the homogeneous and particular solutions:

y(t) = y_h(t) + y_p(t)

y(t) = c1cos(2t) + c2sin(2t) + 1.

Using the initial conditions y(0) = 0 and y'(0) = 1, we can determine the values of c1 and c2:

y(0) = c1cos(0) + c2sin(0) + 1 = c1 + 1 = 0,

c1 = -1.

y'(t) = -2c1sin(2t) + 2c2cos(2t),

y'(0) = -2c1sin(0) + 2c2cos(0) = 2c2 = 1,

c2 = 1/2.

To learn more about inverse : brainly.com/question/30339780

#SPJ11

Answer:

a) 1

b) 0

c) hundreths

d) .8

Step-by-step explanation:

The order, for this problem, is:

hundreds, tens, ones,

then after the decimal

tenths, hundredths, thousandths, ten thousandths, etc.

as for step d, imagine .08 as 8/100, and 8/10. Would you rather have 8 slices of pizza out of 100 slices, or 8 out of 10 slices of the whole?

I hope I helped!

Answer:

C. -36 3/10

Step-by-step explanation:

4 2/5 = 22/5

22/5 = 4.4

4.4(-8.25)

-36.3 = -36 3/10

Have a great day :3

Answer:

720 possible ways

Step-by-step explanation:

The gold is awarded to the first position, the silver is awarded to the second position while the bronze is awarded to the third position.

The first position can be taken by any of the 10 runners

Now, the second position can be taken by remaining 9 runners

while the third position can be taken by the renaming 8 runners.

Thus, the number of ways in which these medals can be awarded = 10 * 9 * 8 = 720 ways

Answer:

f

f

v

Step-by-step explanation:

In order for a function to be defined, the inputs must fall within the domain of the function. When working with functions with multiple inputs, the domain of the outside function depends on the inside functions.

In (a) g(t) = sin(e^−t), the inside function is e^−t, which is defined over all real numbers. Therefore, the outside function sin needs to include all real numbers as well in order to be defined, making the domain of g(t) all real numbers.

In (b) g(t) = √1 − 5^t, the inside function 5^t must be equal to or less than 1 in order for the outside function (square root) to be defined. Therefore, the domain for g(t) is all real numbers less than or equal to 0, or [-∞, 0).

To know more about domain click on below link :

https://brainly.com/question/29452843#

#SPJ11

A 95% confidence interval for the true population proportion of people who received flu vaccinations this year is  0.067 < p < 0.133.

To construct a 95% confidence interval for the true population proportion of people who received flu vaccinations, we can use the formula:

CI = p ± z√((p(1-p))/n)

where:

CI is the confidence interval

p is the sample proportion (33/300 = 0.11)

z is the z-score associated with a 95% confidence level, which is approximately 1.96

n is the sample size (300)

Substituting the values, we get:

CI = 0.11 ± 1.96√((0.11(1-0.11))/300)

CI = 0.11 ± 0.043

CI = (0.067, 0.133)

Therefore, the 95% confidence interval for the true population proportion of people who received flu vaccinations is 0.067 < p < 0.133.

Learn more about confidence interval at https://brainly.com/question/30328824

#SPJ11

Answer: circumcenter

Step-by-step explanation:

If you meant the point of intersection of the perpendicular bisectors, this should be your answer.

The constant of proportionality for x gallons water and y miles is k = 25

The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality.

Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.

A proportionate connection is simple to represent as a straight line on a coordinate plane. It is a straight line because it is directly proportional; the slope serves as the constant of proportionality.

The proportionate change along the x and y axes never varies, hence the slope or increase is constant.

According to the question,

x(gallons)     y(miles)

 1                       25

 2                      50

 3                      75

 4                      100

As we know, If y is proportional to x

=> y ∝ x

=> y = kx , where k is constant of proportionality

Using the table,

when x = 1 => y = 25

=> 25 = k(1)

=> k = 25

To know more about Constant of Proportionality here

https://brainly.com/question/29126727

#SPJ4

Using the given percentage, it is found that there is a 0.877 = 87.7% probability that it arrives on time.

In this question, over a large number of flights, 87.7% arrive on time in Atlanta. Hence, there is a 0.877 = 87.7% probability that it arrives on time.

For more on probabilities, you can check https://brainly.com/question/15536019

Answer:

see the attachment.

Answer:

C, -1.5

Step-by-step explanation:

edge

Answer: b. and c.

Step-by-step explanation:

\(\displaystyle\\Let\ arcsin\frac{-\sqrt{3} }{2} =x\ \ \ \ -\frac{\pi }{2} < x < \frac{\pi }{2}\\So,\\sin(arcsin\frac{-\sqrt{3} }{2} )=sin(x)\\\frac{-\sqrt{3} }{2}=sin(x )\\sin(x)=-\frac{\sqrt{3}}{2} \\\\x_1=\frac{4\pi }{3}+2\pi n\\\\ x_2=\frac{5\pi }{3} +2\pi n.\\\\ -\frac{\pi }{2} < x < \frac{\pi }{2},\\\\Hence,\\\\x_1=\frac{4\pi }{3} \\\\x_2=\frac{5\pi }{3} .\)

Answer:

equal to

Step-by-step:

Again, the mean reflects the slanted the most.

To summarize, generally if the distribution of data is slanted to the left, the mean is less than the median, which is often less than the mode. If the distribution of data is slanted to the right, the mode is often less than the median, which is less than the mean.

Answer:

Equal

Step-by-step explanation:

The median is the midmoint of all points (as many values below as above this value). The mean is the (sum of values) / (count of values). Since every value has the exact same count, the mean and median will be the same.

The farmer will purchase five bags of kind A and six bags of type B.

Per bag, Type A includes 9 pounds of oats and 3 pounds of maize.

Per bag, Type B includes 2 pounds of oats and 10 pounds of maize.

The farmer is looking for a blend that comprises at least 57 pounds of oats and 75 pounds of maize.

Allow the farmer to mix type A feed = x pounds.

and feed type B = y pounds

(9x + 2y) pounds of oats when blended

Corn amount when combined: (3x + 10y) pounds

Oats equation: 9x + 2y = 57 ———— (1)

Corn equation: 3x + 10y = 75 ————- (2)

Subtract equation (2) from equation (2) by multiplying it by three (1)

3(3x + 10y) - (9x + 2y) = 75×3 - 57

9x + 30y - 9x - 2y = 225 - 57

28y = 168

y = 6 bags

derived from the equation (1)

9x + 2×6 = 57

9x + 12 = 57

9x = 57 - 12

9x = 45

x = 5 bags

Because the business has 15 bags of each sort, each bag costs $4.

As a result, the cost of 5 bags of type A and 6 bags of type B is = (54) + (64)

= 20 + 24

= $44

The farmer intends to buy five bags of kind A and six bags of type B.

Learn more about mathematical expressions at

https://brainly.com/question/14070584

#SPJ1

The angle x of the triangle is 60 degrees.

A triangle is a polygon with three sides. The sum of angles in a triangle is equals to 180 degrees.

A triangle can be classified base on the sides and angles. For example equilateral triangle, scalene triangle and isosceles triangle.

Therefore, the angle x of the triangle can be found as follows:

x + x + x = 180

3x = 180°

divide both sides of the equation by 3

3x / 3 = 180 / 3

x = 180 / 3

x = 60 degrees.

learn more on triangle here: https://brainly.com/question/25950519

#SPJ1

Answer:

the person below or above me is the answer. Yeah

Step-by-step explanation:

Answer:

It is the right-angled triangle.

Step-by-step explanation:

According to the Pythagorean theorem, \(a^{2}+b^{2}=c^{2}\), which c is the longest side of the triangle.

So, \(27^{2}+36^{2}=45^{2}\) if the triangle is right angle.

\(LHS=27^{2} + 36^{2} = 2025\)

\(RHS=45^{2}=\)\(RHS=45^{2} = 2025\)

∵LHS=RHS

∴It is a right-angled triangle.

Answer:

The right angled triangle

x = 108

y = 36

z = 72

=============================================================

Explanation:

Check out the diagram below. I have added letters of x, y and z in places to help find the values of y and z. Note the triangle on top is isosceles (since a regular polygon has all sides equal; therefore the triangle on top has the top diagonal sides equal).

Before we find either y or z, let's find x.

For any regular polygon, the interior angles are all the same measure. They sum to 180(n-2). In this case, n = 5, so the angles sum to 180(5-2) = 540. Each individual interior angle is 540/n = 540/5 = 108 degrees

x = 108

Another way to find this interior angle is to first find the exterior angle. For any convex polygon (regular or not), the exterior angles always add to 360. When we talk about regular polygons, each individual exterior angle is 360/n. So in this case, we have 360/5 = 72 as one exterior angle. The adjacent interior angle is therefore x = 180-72 = 108. So there are two ways to find the measure of an interior angle.

--------

Referring to the diagram, specifically the isosceles triangle on top, we can see that it has angles of x, y and y. They add to x+y+y = x+2y. Set this equal to 180, plug in x = 108 and solve for y

x+2y = 180

108+2y = 180

2y = 180-108

2y = 72

y = 72/2

y = 36

--------

The bottom most triangle is a congruent copy of the triangle on top. We have another isosceles triangle with the same side lengths as before. This triangle also has x, y and y as mentioned above.

Notice the adjacent angles of y and z in the bottom left corner. They must add to 108 as this was the measure of the interior angle of a regular pentagon. So,

y+z = x

36+z = 108

z = 108-36

z = 72

Answer:

Step-by-step explanation:

w is the independent

b is the dependent

Think of it this way: the number of birdhouses depends on the amount of wood available.

The solution to the system of equations is (5, -3). To solve the system of equations 3x + 2y = 9 and 2x + 3y = 6, we can use the method of substitution.

We can solve one of the equations for one of the variables in terms of the other variable. For example, we can solve the second equation for x to get x = (6 - 3y)/2. Then, we can substitute this expression for x into the first equation and solve for y: 3(6 - 3y)/2 + 2y = 9

Simplifying this equation, we get: 9 - 9y + 4y = 18. Solving for y, we get: y = -3

Now that we have the value of y, we can substitute it into one of the original equations to solve for x. Using the first equation, we get: 3x + 2(-3) = 9

Simplifying this equation, we get: 3x = 15. Solving for x, we get: x = 5

Therefore, the solution to the system of equations is (5, -3).

To know more about substitution, refer here:

https://brainly.com/question/30284926#

#SPJ11

The equation: \(\frac{x^{2}}{6^{2}}={y^{2}+z^{2}\),  represents a circle with radius r = y = x/6, and the surface that results is a cone, as obtained with the help of surface of revolution.

Now,

If we consider the point (6y, y, 0) in the xy plane, it appears to be a circular path that is a cone when the curve is rotated about the x axis. The cone's equation takes the following form:

\(\frac{x^{2}}{c^{2}}=\frac{y^{2}}{a^{2}}+\frac{z^{2}}{b^{2}}\)

Given that x = 6y, we square x = 6y to give the equation the form shown above, which results in:

x² = (6y)²

x² = 36y²

Circular paths go parallel to the y-axis, hence the equation should be circular in nature. 36z² needs to be added, so:

x² = 36y² + 36z²

=> \(\frac{x^{2}}{6^{2}}={y^{2}+z^{2}\)

Hence, This equation represents a circle with radius r = y = x/6, and the surface that results is a cone, as obtained with the help of surface of revolution.

To learn more about Surface of revolution, refer to the link: https://brainly.com/question/14640419

#SPJ4