What is the rate of change in the y-values with respect to the x-values?

Answer: They are away for [tex]2\dfrac{3}{4}\ hours[/tex] from home.

Step-by-step explanation:

Since we have given that

Time to get there = [tex]\dfrac{1}{4}[/tex]

Time to get back = [tex]\dfrac{1}{4}[/tex]

Number of soccer games = 3

Time for each soccer games = [tex]\dfrac{3}{4}[/tex]

So, total time for 3 games would be

[tex]3\times \dfrac{3}{4}=\dfrac{9}{4}[/tex]

So, the time for which they will be away from home is given by

[tex]\dfrac{1}{4}+\dfrac{9}{4}+\dfrac{1}4}=\dfrac{1+9+1}{4}=\dfrac{11}{4}=2\dfrac{3}{4}\ hours[/tex]

Hence, they are away for [tex]2\dfrac{3}{4}\ hours[/tex] from home.

Caleb and his family will be away from home for a total of 2 3/4 hours.

To find out how long Caleb and his family will be away from home, we need to calculate the total time for the trip to and from the soccer games, as well as the duration of the games.

Adding it all together:

Total driving time: 1/4 hour + 1/4 hour = 1/2 hour

Total game time: 2 1/4 hours

Total time away from home: 1/2 hour + 2 1/4 hours = 2 3/4 hours

Therefore, Caleb and his family will be away from home for a total of 2 3/4 hours.

Answer:

85%

Step-by-step explanation:

The probability of finding our satisfactory service in the three visits in a row would be the multiplication of the probability of each event.

The event is always the same. 95% of the service will be satisfactory. That is a probability of 95/100

Then the final probability would be:

(95/100) * (95/100) * (95/100) = 0.85

In other words, the probability that a customer who visits three times will find our service satisfactory is 85%

Answer:

The answer to your question is   Momentum  = [tex]\frac{(x + 2)^{2}}{x - 3}[/tex]

Step-by-step explanation:

Data

mass = [tex]\frac{x^{2}+ 4x + 4 }{x^{2}- 9}[/tex]

velocity = [tex]\frac{x^{2}+ 5x + 6}{x + 2}[/tex]

Formula

Momentum = mass x velocity

Substitution

    Momentum = [tex]\frac{x^{2}+ 4x + 4}{x^{2}- 9} \frac{x^{2} + 5x + 6}{x + 2}[/tex]

Factor    The first numerator is a perfect square trinomial and the second one is a trinomial of the form x² + bx + c.

    Momentum = [tex]\frac{(x + 2)^{2}}{(x - 3)(x + 3)} \frac{(x + 2)(x + 3)}{x + 2}[/tex]

Simplify and result

   Momentum  = [tex]\frac{(x + 2)^{2}}{x - 3}[/tex] or [tex]\frac{x^{2} + 4x + 4}{x - 3}[/tex]

Answer:

C option is correct 5/8.

Step-by-step explanation:

Ela ate chocolate on Tuesday = 1/8

Remaining chocolate = 1 - 1/8

                                    = 7/8

Ela ate chocolate on Wednesday = 7/8

Chocolate left = 7/8 - 2/8

                        = 5/8

Answer:

u => 4,028

Step-by-step explanation:

To find the answer, we have the following formula:

u => m - t (alpha, n-1) * [sd / (n) ^ (1/2)]

where m is the mean.

where sd is the standard deviation.

where n is the sample size.

t is a parameter that depends on the confidence interval and the sample size.

alpha = 1 - ci

ci = 90% = 0.9

Therefore, alpha = 1 - 0.9 = 0.1.

n - 1 = 25 - 1 = 24

So it would come being t (0.1, 24), if we look in the table, which I will attach the value of t is equal to 1.318.

We know the rest of the values, m = 4.05; sd = 0.08; n = 25

u => 4.05 - 1,318 * [0.08 / (25) ^ (1/2)]

u => 4.028

Which means that the interval with a 90% confidence of the wall thickness measurement is:

u => 4.028

Answer:

Step-by-step explanation:

it has no solution (8,2)

just took the test

Answer:

[tex]x<120[/tex]

Step-by-step explanation:

We have been given an inequality [tex]-30<\frac{x}{-4}[/tex]. We are asked to solve the given inequality.

To solve for x, we will multiply both sides of inequality by negative 4. When we multiply or divide both sides of an inequality, the inequality sign reverses.

[tex]-30\cdot (-4)>\frac{x}{-4}\cdot (-4)[/tex]

[tex]120>x[/tex]

This means that 120 is greater than x or x is less than 120.

[tex]x<120[/tex]

Therefore, our required inequality would be [tex]x<120[/tex].

Final answer:

The solution to the inequality -30 < x / -4 is found by multiplying both sides by -4, which reverses the inequality sign, resulting in the solution x < 120. This demonstrates the manipulation of inequalities, particularly when involving negative multipliers.

Explanation:

The correct interpretation of this question is solving the inequality -30 < x / -4. To solve this inequality, we firstly multiply both sides by -4, remembering that multiplying or dividing by a negative number reverses the inequality sign. Thus, the inequality becomes 120 > x, which means x must be less than 120 for the inequality to hold true.

Therefore, the solution to the given inequality is x < 120. This highlights the importance of carefully handling inequalities, especially when multiplying or dividing by negative numbers, as it requires reversing the inequality sign to maintain the accurate relationship between both sides.

Answer:

View Image

Step-by-step explanation:

To identify if it's a polynomial, look at the x and its exponent.

x CANNOT be:

1. In the denominator: [tex]\frac{1}{x}[/tex] NOT polynomial

2. In the exponent: [tex]2^x[/tex]  NOT polynomial

3. In a root: [tex]\sqrt{x}[/tex] NOT polynomial

The exponent on the x must be a positive integer, therefore,

exponent:

1.) Cannot be a fraction:  [tex]x^{1/2}[/tex] NOT polynomial

2.) Cannot be negative: [tex]x^{-2}[/tex]  NOT polynomial

Answer:

Hi, the correct answer to this would be  B, INCONSISTENT.

I researched this and my cite is www.quizlet.com. It is this answer because it is not consistent Nor C,D.

Step-by-step explanation:

I answered this before but someone deleted every single question I ever answered. Hahaha

Hope this helps :)

Answer:

The answer is CONSISTENT AND DEPENDENT

Step-by-step explanation:

USA Test Prep

Answer:

$ 1.05

Step-by-step explanation:

To solve the problem it is necessary to pose some equations, which are the following:

Debt DVD = New Balance - Old Balance

With this we will calculate the net value that only has to do with the debt of the DVD:

Debt DVD: 7.75 - 2.50 = 5.25

Now, the other equation is the value per day that generates a delay.

Debt DVD / # days

Replacing

5.25 / 5 = 1.05

Then the daily fine for a overdueDVD is $ 1.05

Answer:

The answer to your question is Positive

Step-by-step explanation:

Function

                  g(x) = x⁴ - 8x³ + x² + 42x

To know if the function is positive or negative in the interval (0, 3), look for two numbers between this interval and evaluate the function.

The numbers I chose were 1 and 2

-  g(1) = (1)⁴ - 8(1)³ + (1)² + 42(1)

         = 1 - 8 - 1 + 42

        = + 36    positive

-  g(2) = (2)⁴ - 8(2)³ + (2)² + 42(2)

          = 16 - 64 + 4 + 84

          = + 40

Conclusion

The function is positive in the interval (0, 3)  

Answer:

system of equations i think

Step-by-step explanation:

A group of equations that have a common intersection point is called: system of equations.

A system of equations can be defined as an algebraic equation of the first order with two (2) variables and each of its term having an exponent of one (1).

Generally, a system of equations in two (2) variables must have at least two (2) solution.

This ultimately implies that, a system of equations must have a common intersection point.

In Mathematics, an example of a system of equations include the following:

Additionally, the above system of equations can easily be solved by using an elimination method.

In conclusion, a solution of the group of equations is an ordered pair that satisfies all the equations in a system of equations.

Read more: https://brainly.com/question/24085666

Answer:

  17 cm

Step-by-step explanation:

The formula for the area of a parallelogram is ...

  A = bh

The base (b) is given as (5 cm +15 cm) = 20 cm. The area is given as 340 cm^2. Filling in the give numbers, we have ...

  340 cm^2 = (20 cm)h

Dividing by the coefficient of h gives ...

  (340 cm^2)/(20 cm) = h = 17 cm

The height of the parallelogram is 17 cm.

_____

Comment on the geometry

The triangles at either end of the figure will be 5-12-13 right triangles, meaning the height of the figure is 12 cm. Using that height, we find the area to be (12 cm)(20 cm) = 240 cm^2 (not 340 cm^2). This leads us to believe there is a typo in the problem statement.

As the problem is given, the geometry is impossible. The height of the parallelogram cannot be greater than the length of the slanted side.

As the problem is written, it is a "one-step" problem. (Divide the area by the base length.) If the area were not given, then the Pythagorean theorem would be required to find the height. That is a 2-step problem:

  13^2 = 5^2 + h^2

  h^2 = 169 -25 = 144 . . . . solve for h²

  h = √144 = 12 . . . . . . . . . take the square root

It is not at all clear what 3 steps you're supposed to show in your work.

The equivalent equation is [tex](x+5)(x+12)=0[/tex]

The solution are [tex]x=-5, x=-12[/tex]

Explanation:

Given that the equation is [tex]-7 x-60=x^2+10 x[/tex]

Simplifying the equation, we get,

[tex]0=x^2+10 x+7x+60[/tex]

Switch sides, we have,

[tex]x^2+17 x+60=0[/tex]

Equivalent equation:

Let us factor the quadratic equation.

Thus, we have,

[tex]x^{2} +5x+12x+60=0[/tex]

Grouping the terms, we get,

[tex]x(x+5)+12(x+5)=0[/tex]

Factoring out (x+5), we get,

[tex](x+5)(x+12)=0[/tex]

Thus, the equivalent equation is [tex](x+5)(x+12)=0[/tex]

Solution:

Solving the equation [tex](x+5)(x+12)=0[/tex], we get,

[tex]x+5=0[/tex]  and   [tex]x+12=0[/tex]

  [tex]x=-5[/tex]   and       [tex]x=-12[/tex]

Thus, the solutions are  [tex]x=-5[/tex] and [tex]x=-12[/tex]

Answer:

A. 5

B. 12

C. -12 or -5

Step-by-step explanation:

(x + 5)(x + 12) = 0

What are the solutions of –7x – 60 = x2 + 10x?

x = -12 or -5

Answer:

Perimeter ΔRON = 18.66 units

Step-by-step explanation:

Complete Question has these information given as well:

Now, we draw an image according to the information given. THe image drawn is attached.

Looking at the figure, we can say the perimeter of triangle RON would be:

RON = OR + ON + RN

We know according to tangent theorem, QN = QR

RN is equal to that as well and RN = [tex]5\sqrt{3}[/tex]

Now,

OR and ON is the radius, which is "5"

Perimeter of RON = 5 + 5 + [tex]5\sqrt{3}[/tex] = 10 + [tex]5\sqrt{3}[/tex] = 18.66 units

Perimeter ΔRON = 18.66 units

Answer:

18.7 units

Step-by-step explanation:

Answer:

P [  1689  ≤   X  ≤  2267 ]  = 54,88 %

Step-by-step explanation:

Normal Distribution

Mean        μ₀  =  1730

Standard Deviation      σ  = 257

We need to calculate  z scores for the values   1689     and      2267

We apply formula for z scores

z =  ( X -  μ₀ ) /σ

X = 1689     then

z = (1689 - 1730)/ 257      ⇒ z = - 41 / 257

z  = -  0.1595

And from z table we get  for  z =  - 0,1595

We have to interpolate

        - 0,15          0,4364

        - 0,16          0,4325

Δ  =   0.01           0.0039

0,1595  -  0,15  =  0.0095

By rule of three

0,01                  0,0039

0,0095                 x ??      x  =  0.0037

And    0,4364  -  0.0037  = 0,4327

Then    P [ X ≤ 1689 ]  =  0.4327     or    P [ X ≤ 1689 ]  = 43,27 %

And for the upper limit  2267  z  score will be

z  =  ( X - 1730 ) / 257       ⇒  z =  537 / 257

z  =  2.0894

Now from z table   we find  for score   2.0894

We interpolate and assume  0.9815

P [ X ≤ 2267 ]  =  0,9815

Ths vale already contains th value of   P [ X ≤ 1689 ]  =  0.4327

Then we subtract  to get    0,9815  -  0,4327   = 0,5488

Finally

P [ 1689  ≤   X  ≤  2267 ]  =  0,5488  or  P [  1689  ≤   X  ≤  2267 ]  = 54,88 %

Answer: the solutions of the equation are

x = - 1

x = 8

x = 9

Step-by-step explanation:

The given cubic equation is expressed as

x³ - 16x² + 55x + 72 = 0

The first step is to test for any value of x that satisfies the equation when

x³ - 16x² + 55x + 72 = 0

Assuming x = - 1, then

- 1³ - 16(-1)³ + 55(-1) + 72 = 0

- 1 - 16 - 55 + 72 = 0

0 = 0

It means that x + 1 is a factor.

To determine the other factors, we would apply the long division method. The steps are shown in the attached photo. Looking at the photo, we would factorize the quadratic equation which is expressed as

x² - 17x + 72 = 0

x² - 9x - 8x + 72 = 0

x(x - 9) - 8(x - 9) = 0

(x - 9)(x - 8) = 0

Answer:

[tex]\left(3+x\right)^4:\quad x^4+12x^3+54x^2+108x+81[/tex]

Step-by-step explanation:

Considering the expression

[tex]\left(3+x\right)^4[/tex]

Lets determine the expansion of the expression

[tex]\left(3+x\right)^4[/tex]

[tex]\mathrm{Apply\:binomial\:theorem}:\quad \left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i[/tex]

[tex]a=3,\:\:b=x[/tex]

[tex]=\sum _{i=0}^4\binom{4}{i}\cdot \:3^{\left(4-i\right)}x^i[/tex]

Expanding summation

[tex]\binom{n}{i}=\frac{n!}{i!\left(n-i\right)!}[/tex]

[tex]i=0\quad :\quad \frac{4!}{0!\left(4-0\right)!}3^4x^0[/tex]

[tex]i=1\quad :\quad \frac{4!}{1!\left(4-1\right)!}3^3x^1[/tex]

[tex]i=2\quad :\quad \frac{4!}{2!\left(4-2\right)!}3^2x^2[/tex]

[tex]i=3\quad :\quad \frac{4!}{3!\left(4-3\right)!}3^1x^3[/tex]

[tex]i=4\quad :\quad \frac{4!}{4!\left(4-4\right)!}3^0x^4[/tex]

[tex]=\frac{4!}{0!\left(4-0\right)!}\cdot \:3^4x^0+\frac{4!}{1!\left(4-1\right)!}\cdot \:3^3x^1+\frac{4!}{2!\left(4-2\right)!}\cdot \:3^2x^2+\frac{4!}{3!\left(4-3\right)!}\cdot \:3^1x^3+\frac{4!}{4!\left(4-4\right)!}\cdot \:3^0x^4[/tex]

[tex]=\frac{4!}{0!\left(4-0\right)!}\cdot \:3^4x^0+\frac{4!}{1!\left(4-1\right)!}\cdot \:3^3x^1+\frac{4!}{2!\left(4-2\right)!}\cdot \:3^2x^2+\frac{4!}{3!\left(4-3\right)!}\cdot \:3^1x^3+\frac{4!}{4!\left(4-4\right)!}\cdot \:3^0x^4[/tex]

as

[tex]\frac{4!}{0!\left(4-0\right)!}\cdot \:\:3^4x^0:\:\:\:\:\:\:81[/tex]

[tex]\frac{4!}{1!\left(4-1\right)!}\cdot \:3^3x^1:\quad 108x[/tex]

[tex]\frac{4!}{2!\left(4-2\right)!}\cdot \:3^2x^2:\quad 54x^2[/tex]

[tex]\frac{4!}{3!\left(4-3\right)!}\cdot \:3^1x^3:\quad 12x^3[/tex]

[tex]\frac{4!}{4!\left(4-4\right)!}\cdot \:3^0x^4:\quad x^4[/tex]

so equation becomes

[tex]=81+108x+54x^2+12x^3+x^4[/tex]

[tex]=x^4+12x^3+54x^2+108x+81[/tex]

Therefore,

Answer:

  y = -9

Step-by-step explanation:

Standard form of the equation of a line is ...

  ax + by = c

When that line is a horizontal line, this can be reduced to ...

  y = c

The value of c must be the same as the y-coordinate of the point you want this line to go through.

  y = -9 . . . . . . horizontal line through (3, -9)

The simplified expressions for the area and perimeter of the rectangle are 16x and 4x, respectively.

To simplify the expressions for the area and perimeter of the rectangle, we can extract common factors:

Area: [tex]\(8(x + x) = 8 \times 2x = 16x\)[/tex]

Perimeter: [tex]\(2(x + x) = 2 \times 2x = 4x\)[/tex]

Therefore, the simplified expressions are:

Area: 16x

Perimeter: 4x

Answer:

Step-by-step explanation:

From the given right angle triangle,

The unknown side represents the hypotenuse of the right angle triangle.

With m∠40 as the reference angle,

x represents the adjacent side of the right angle triangle.

4 represents the opposite side of the right angle triangle.

To determine x, we would apply

the Tangent trigonometric ratio.

Sin θ = opposite side/hypotenuse. Therefore,

Tan 40 = 4/x

x = 4/Tan 40 = 4/0.839

x = 4.8

Question 1) Function defining the table:

From the table the x-intercepts are -2 and 1. This means the factors are:

(x+2) and (x-1)

Let

[tex]h(x) = a(x + 2)(x - 1)[/tex]

The point (-1,-1) satisfy this function since it is from the same table.

[tex] - 1 = a( - 1 + 2)( - 1 - 1) \\ - 1 = - 2a \\ a = \frac{1}{2} [/tex]

Therefore the function is

[tex]h(x) = \frac{1}{2} (x + 2)(x - 1)[/tex]

We expand to get:

[tex]h(x) = \frac{1}{2} ( {x}^{2} + x - 2)[/tex]

The standard form is:

[tex]h(x) = \frac{ {x}^{2} }{2} + \frac{x}{2} - 1[/tex]

Question 3) Parabola opening up

The x-intercepts are x=3 and x=7

The factors are (x-3), (x-7)

The factored from is

[tex]y = a(x - 3)(x - 7)[/tex]

The curve passes through (5,-4)

[tex] - 4= a( 5- 3)( 5 - 7) \\ - 4= - 4a \\ a = 1[/tex]

The equation is:

[tex]y = (x - 3)(x + 7)[/tex]

Expand:

[tex]y = {x}^{2} + 7x - 3x - 21[/tex]

[tex]y = {x}^{2} + 4x - 21[/tex]

This is the standard form:

Question 3) Parabola opening down:

The x-intercepts are x=-5 and x=1

The factors are (x+5), (x-1)

The factored form is

[tex]y = - (x + 5)(x - 1)[/tex]

We expand to get:

[tex]y = - ( {x}^{2} - x + 5x - 5)[/tex]

[tex]y = - {x}^{2} - 4x + 5[/tex]

This is the standard form.

Answer:

1/4 or 25%

Step-by-step explanation:

The set of new shoes is composed by all pairs bought by either Harry or Kate.

Harry bought a pair of rain boots and a pair of tennis shoes while Kate got a pair of tennis shoes and sandals, totaling 4 pairs. Out of those 4 pairs, only 1 pair are rain boots, the fraction corresponding to rain boots is:

[tex]f = \frac{1}{4}=25\%[/tex]

Rain boots are 1/4 of the set of new shoes.

Answer:

x - ( 16 , 0 ) , ( -16 , 0 )

y - ( 0 ,  4√7 ) , ( 0 , -4√7)

Step-by-step explanation:

Solution:

- The sum of the distances from a point on the ellipse to its foci is constant. You have both foci and a point, so you can find the sum of the distances.

-Then you can find the vertices since they are points on the ellipse on the x-axis whose sum of distances to the foci are that value.

- The 7 in y coordinate of (12,7) is the length of semi-latus rectum. Also c is 12:

                                     c^2 = a^2 + b^2

Where, a: x-intercept

            b: y-intercept

- The length of semi-latus rectum is given by:

                                     b^2 = 7*a

- Substitute latus rectum expression in the first one we get:

                                    c^2 = a^2 + 7a

                                    a^2 + 7a - 144 = 0

                                    ( a - 16 ) * ( a - 9 ) = 0

                                    a = +/- ( 16 )

- The y-intercept we will use latus rectum expression again:

                                    b = +/- √(7*16)

                                    b = +/- 4√7

- The intercepts are:

                                    x - ( 16 , 0 ) , ( -16 , 0 )

                                    y - ( 0 ,  4√7 ) , ( 0 , -4√7)  

Final answer:

An ellipse is a closed curve where the sum of the distances from any point on the curve to the two foci is constant. To find where this particular ellipse intersects the coordinate axes, we can set y = 0 to find the points of intersection with the x-axis and set x = 0 to find the points of intersection with the y-axis.

Explanation:

An ellipse is a closed curve where the sum of the distances from any point on the curve to the two foci is constant. The focal points of this ellipse are (12, 0) and (-12, 0). We know that the point (12, 7) lies on the ellipse. To find where this curve intersects the coordinate axes, we need to find the points where the ellipse intersects the x-axis and y-axis.

Intersecting the x-axis:

To find the points where the ellipse intersects the x-axis, we set y = 0 and solve for x. In this case, the coordinates of the intersection points will be (x, 0).

Plugging in y = 0 into the equation of the ellipse:

(x - 12)^2 / a^2 + (0 - 0)^2 / b^2 = 1

Simplifying this equation:

(x - 12)^2 / a^2 = 1

Since the ellipse is symmetric about the y-axis, the x-coordinates of the intersection points will have the same absolute value but opposite signs. So, we can solve for a single value of x and then take its negative to find the other intersection point.

(x - 12)^2 / a^2 = 1

x - 12 = a

x = a + 12

The coordinates of the intersection points on the x-axis are (a + 12, 0) and (-a - 12, 0).

Intersecting the y-axis:

To find the points where the ellipse intersects the y-axis, we set x = 0 and solve for y. In this case, the coordinates of the intersection points will be (0, y).

Plugging in x = 0 into the equation of the ellipse:

(0 - 12)^2 / a^2 + (y - 0)^2 / b^2 = 1

Simplifying this equation:

144 / a^2 + y^2 / b^2 = 1

Solving for y:

y^2 / b^2 = 1 - 144 / a^2

y^2 / b^2 = (a^2 - 144) / a^2

y^2 = b^2 * (a^2 - 144) / a^2

y = ± sqrt(b^2 * (a^2 - 144) / a^2)

The coordinates of the intersection points on the y-axis are (0, ± sqrt(b^2 * (a^2 - 144) / a^2)).

Answer:

[tex]8181.23 \ cm^3[/tex]

Step-by-step explanation:

-A standard basketball has a spherical shape.

-Given the ball has a diameter of 25cm.

-The space available for air is equivalent to the ball's volume and is calculated as:

[tex]V=\frac{4}{3}\pi r^3, D=25\\\\=\frac{4}{3}\pi (D/2)^3\\\\\frac{4}{3}\pi (25/2)^3\\\\=8181.23\ cm^3[/tex]

Hence, the space available for air is [tex]8181.23 \ cm^3[/tex]

Answer: There are 45 miles that she have to travel to get to the next down.

Step-by-step explanation:

Since we have given that

1 inch = 15 miles

If there are given 3 inches.

We need to find the number of miles she have to travel to get to travel to get to the next town.

So, it becomes,

[tex]\dfrac{1}{15}=\dfrac{3}{x}\\\\x=15\times 3\\\\x=45\ miles[/tex]

Hence, there are 45 miles that she have to travel to get to the next down.

Answer: he invested $5300 at 11% and $1000 at 6%

Step-by-step explanation:

Let x represent the amount which he invested in the first account paying 11% interest.

Let y represent the amount which he invested in the second account paying 6% interest.

He Invest $6,300 in two different accounts the first account paid 11% the second account paid 6% in interest. This means that

x + y = 6300

The formula for determining simple interest is expressed as

I = PRT/100

Considering the first account paying 11% interest,

P = $x

T = 1 year

R = 11℅

I = (x × 11 × 1)/100 = 0.11x

Considering the second account paying 6% interest,

P = $y

T = 1 year

R = 6℅

I = (y × 6 × 1)/100 = 0.06y

At the end of the year, he had earned $643 in interest , it means that

0.11x + 0.06y = 643 - - - - - - - - - -1

Substituting x = 6300 - y into equation 1, it becomes

0.11(6300 - y) + 0.06y = 643

693 - 0.11y + 0.06y = 643

- 0.11y + 0.06y = 643 - 693

- 0.05y = - 50

y = - 50/ - 0.05

y = 1000

x = 6300 - y = 6300 - 1000

x = 5300

The length of MK is 9

Explanation:

The length of the sides are [tex]J K=36[/tex] , [tex]\mathrm{JL}=48[/tex] , [tex]J N=60[/tex]

We need to determine the length of MK

From the figure, we can see that JMN is a triangle and KL is parallel to MN.

Then, by side - splitter theorem, we have,

[tex]\frac{JK}{KM} =\frac{JL}{LN}[/tex]

where [tex]J K=36[/tex] , [tex]\mathrm{JL}=48[/tex]

The length of LN can be determined by subtracting JN and JL.

Thus, we have,

[tex]LN=JN-JL[/tex]

[tex]LN=60-48=12[/tex]

The length of LN is [tex]LN=12[/tex]

Substituting the values [tex]J K=36[/tex] , [tex]\mathrm{JL}=48[/tex] and [tex]LN=12[/tex] in [tex]\frac{JK}{KM} =\frac{JL}{LN}[/tex], we have,

[tex]\frac{36}{KM} =\frac{48}{12}[/tex]

Multiplying both sides by 12, we have,

[tex]\frac{36\times 12}{KM} =48[/tex]

 [tex]\frac{432}{KM} =48[/tex]

  [tex]\frac{432}{48} =KM[/tex]

     [tex]9=KM[/tex]

Thus, the length of MK is 9

Answer:

The tank would hold 40 gallons of water when full.

Step-by-step explanation:

The tank is already 3/4 full of water

If Henry added 5 gallons, it will be 7/8 full.

Therefore the fraction added by Henry =7/8-3/4=1/8

It means that 1/8 of the total=5 gallons of water

Let the total capacity of the tank=x

[tex]\frac{1}{8}Xx=5 gallons\\ x=8X5=40 gallons[/tex]

The tank would hold 40 gallons of water when full.

Answer:

the answer is a

Step-by-step explanation:

Answer:

x = 13

Step-by-step explanation:

One of the THEOREM for triangles states that, A LINE DRAWN PARALLEL TO ONE SIDE OF THE TRIANGLE DIVIDES THE OTHER TWO SIDES IN THESAME RATIO.

From the figure above:

VW is parallel to SU.

VW divides ST and TU in thesame ration.

Hence:

TV / SV = TW / UW

14 / 6 = 21 / (x - 4)

Cross Multiplying gives:

14( x - 4) = 6 * 21

14x - 56 = 126

14x = 126 + 56

14x = 182

Divide through by 14.

x = 182/14

x = 13