What is the length of JM in the given figure?

Hey there! I'm happy to help!

Let's set this up a proportion (two equal ratios) to find out how many miles Wina can drive on 12 gallons gas.

[tex]\frac{miles}{gallons} =\frac{282}{10} =\frac{m}{12}[/tex]

What do we multiply the bottom 10 by to get to 12? Well, to find out, we can divide 12 by 10 below.

12÷10=1.2

This means that we multiply the numbers in the first fraction by 1.2 to have the same numerator and denominator as the second fraction.

If we multiplied our 10 b y 1.2 to get the denominator in the second fraction, we should be able to multiply 282 by 1.2 to get the numerator in the second fraction!

282×1.2=338.4

If you use 338.4 in this proportion, the ratios will be equal.

Therefore, Wina could drive 338.4 miles on 12 miles of gas at this same rate.

Have a wonderful day!

Answer:

Step-by-step explanation:

To find the value of x we use sine

sin ∅ = opposite / hypotenuse

From the question

29 is the hypotenuse

9 is the opposite

sin x = 9/29

x = sin-¹ 9/29

x = 18.08°

Hope this helps you

Answer:

Angle=71.9°

using the trig inverse formula sec(angle)= hypotenuse/adjacent

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{12}}}}}[/tex]

Step-by-step explanation:

hypotenuse ( h ) = x

Peendicular ( p ) = 10

base ( b ) = 22

Using the Pythagoras theorem

[tex] \boxed{ \sf{ {h}^{2} = {p}^{2} + {b}^{2} }}[/tex]

[tex] \dashrightarrow{ \sf{ {x}^{2} = {10 }^{2} + {22}^{2} }}[/tex]

[tex] \dashrightarrow{ \sf{ {x}^{2} = 100 + 44}}[/tex]

[tex] \dashrightarrow{ \sf{ {x}^{2} = 144}}[/tex]

[tex] \dashrightarrow{ \sf{ \sqrt{ {x}^{2} } = \sqrt{144}}} [/tex]

[tex] \dashrightarrow{ \sf{x = 12}}[/tex]

Hope I helped!

Best regards! :D

Answer: 77 degrees

Step-by-step explanation:

interior angles on the same side of transversal are supplementary.  Thus,

103+x=180

x = 77

Hope it helps <3

Answer:

Hey there!

This is a parallelogram, and we have the angles next to each  other add to 180 degrees. Angle ABC+Angle BCD=180

103+x=180

x=77

BCD=77 degrees.

Let me know if this helps :)

Answer:

d)

Step-by-step explanation:

the general form is ax + by = c

Answer:

x=3

Step-by-step explanation:

Use the Pythagorean Theorem to write an equation.

x^2+y^2=z^2

Substitute values from the problem.

x^2 + 6^2 = 9^2

Solve for what you know.

x^2 + 36 = 81

Square root it.

x+6=9

Subtract 6 from both sides.

x=3

In the future, if you see a right triangle with an unknown side, and the other two sides are either 3, 6, or 9, you know that the other one is the missing value out of 3/6/9. This is called a 3/6/9 triangle.

Answer:

Step-by-step explanation:

Hypotenuse (h) = 9

base (b) = X

Perpendicular (p) = 6

Now,

Using Pythagoras theorem:

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

[tex] {b}^{2} = {h}^{2} - {p}^{2} [/tex]

[tex] {b}^{2} = {(9)}^{2} - {(6)}^{2} [/tex]

[tex] {b}^{2} = 81 - 36[/tex]

[tex] {b}^{2} = 45[/tex]

[tex]b = \sqrt{45} [/tex]

[tex]b = 6.7[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

68 degrees

Step-by-step explanation:

Y=56,

56+56=112

180-112=68

Hope this helps, if you have any other questions, feel free to ask me to explain more

Have a good day! :)

Answer:

[tex]\large \boxed{\bf \sf \ \ \ 7x-9 = 3(x+2) \ \ \ }[/tex]

Step-by-step explanation:

Hello,

x represents this number and we know that

the difference between seven times this number and 9

   7*x - 9

is equal to three times the sum of this number and 2

   3(x+2)

So we can write

[tex]7x-9 =3(x+2) \\\\7x-9 =3x+6 \ \ \text{distributive law} \\\\7x-9-3x=3x+6-3x =6 \ \ \text{subtract 3x} \\\\4x-9+9=6+9 \ \text{add 9} \\\\4x=15 \ \ \text{divide by 4} \\\\ \boxed{x=\dfrac{15}{4}}\\[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

The system has exactly one solution where x = 0 and y = -3.

Step-by-step explanation:

-6x + y = -3

7x - y = 3

(7x - 6x) + (y - y) = 3 - 3

x + 0 = 0

x = 0

7(0) - y = 3

0 - y = 3

-y = 3

y = -3

-6(0) + y = -3

0 + y = -3

y = -3

So, the system has exactly one solution where x = 0 and y = -3.

Hope this helps!

Answer:

the expected area of the resulting circular region is 616.38 m²

Step-by-step explanation:

Given that:

[tex]f(r) = \left \{ {{\dfrac{3}{4}(1-(14-r)^2)} \atop {0 }} \right. \ \ 13 \leq r \leq 15[/tex] otherwise

The expected area of the resulting circular region  is:

= [tex]E(\pi r^2)[/tex]

= [tex]\pi E (r^2)[/tex]

To calculate [tex]E(r^2)[/tex]

[tex]E(r^2) = \int\limits^{15}_{13} {r^2} \ f(r) \ dr[/tex]

[tex]E(r^2) = \int\limits^{15}_{13} \ \dfrac{3r^2}{4}(1-(14-r)^2)dr[/tex]

[tex]E(r^2) = \dfrac{3}{4} \int\limits^{15}_{13} \ r^2 (1-196-r^2+28r) dr[/tex]

[tex]E(r^2) = \dfrac{3}{4} \int\limits^{15}_{13} \ r^2 (28r^3-r^4-195r^2)dr[/tex]

[tex]E(r^2) = \dfrac{3}{4}[\dfrac{28 r^4}{4}-\dfrac{r^5}{5}-\dfrac{195r^3}{3}]^{^{15}}}__{13}[/tex]

[tex]E(r^2) = \dfrac{3}{4} [ \dfrac{28 \times 50625}{4} - \dfrac{759375}{5} - \dfrac{195 \times 3375}{3} ]-[ \dfrac{28 \times 28561}{4} - \dfrac{371293}{5} - \dfrac{195 \times 2197}{3} ][/tex]

[tex]E(r^2) = \dfrac{3}{4} [ 354375-151875-219375-199927+74258.6+142805][/tex]

[tex]E(r^2) = \dfrac{3}{4} [261.6][/tex]

[tex]E(r^2) = 196.2[/tex]

Recall:

The expected area of the resulting circular region  is:

= [tex]E(\pi r^2)[/tex]

= [tex]\pi E (r^2)[/tex]

where;

[tex]E(r^2) = 196.2[/tex]

Then

The expected area of the resulting circular region  is:

= [tex]\pi \times 196.2[/tex]

= 616.38 m²

Answer:

23 dimes; 32 nickel

Step-by-step explanation:

Let n = number of nickels.

Let d = number of dimes.

A nickel is worth $0.05; n nickels are worth 0.05n.

A dime is worth $0.10; d dimes are worth 0.1d.

Number of coins:

d + n = 55

Value of the coins:

0.1d + 0.05n = 3.9

Solve d + n = 55 for d:

d = 55 - n

Substitute 55 - n for d in second equation.

0.1(55 - n) + 0.05n = 3.9

5.5 - 0.1n + 0.05n = 3.9

-0.05n = -1.6

n = 32

Substitute 32 for n in d + n = 55 and solve for d.

d + 32 = 55

d = 23

Answer: 23 dimes; 32 nickel

Answer:

4/ 100000

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Answer:

x = 25

Step-by-step explanation:

The sum of the angles of a quadrilateral are 360 degrees

3x+x+10 + 4x+6x = 360

Combine like terms

14x+10 = 360

Subtract 10 from each side

14x +10-10 = 360-10

14x = 350

Divide each side by 14

14x/14 = 350/14

x = 25

Answer

2x-y <or =-6

2x<or=-6+y

divide both sides by 2

x<or=1/2y+3

5(1/2y+3)+4y>or=20

5/2y+15+4y>or=20

5/2y+4y>or=20-15

13/2y>or=5

divide both sides by 2/13

y>or=10/13

2x-10/13<or=-6

2x<or=-6+10/13

2x<or=-68/13

divide both sides by 2

x< or =-34/13

Answer:

8 classmates

Step-by-step explanation:

[tex]9/1\frac{1}{8}=\\9/\frac{9}{8}=\\9*\frac{8}{9}=\\\frac{72}{9}=\\8[/tex]

Answer:

O B. Positive integers only

Step-by-step explanation:

You have that the temperature of a plate is measured respect to the number of hours that the plate has been left in the sun.

In this case you have that the independent variable is the number of hours and the dependent variable is the temperature.

Due to James would like to know how is changing the temperature of the plate, per hour, the best domain for the function, that is, the best available values for the time on which the temperature of the plate is measured, are the positive integers only.

O B. Positive integers only

Answer:

If you have    

[tex]f(x) = x^2[/tex]

The point  (2,4)   would be transformed to (1,1)

Step-by-step explanation:

If your compression is horizontal then the transformation you are making is the following

[tex]g(x) = f(x/2)[/tex]

Therefore, if you have    

[tex]f(x) = x^2[/tex]

The point  (2,4)   would be transformed to (1,1)

Answer:

The upper confidence bound for population mean escape time is: 379.27

The upper prediction bound for the escape time of a single additional worker  is 413.64

Step-by-step explanation:

Given that :

sample size n = 26

sample mean [tex]\bar x[/tex] =  371.08

standard deviation [tex]\sigma[/tex] = 24.45

The objective is to calculate an upper confidence bound for population mean escape time using a confidence level of 95%

We need to determine the standard error of these given data first;

So,

Standard Error S.E = [tex]\dfrac{\sigma }{\sqrt{n}}[/tex]

Standard Error S.E = [tex]\dfrac{24.45 }{\sqrt{26}}[/tex]

Standard Error S.E = [tex]\dfrac{24.45 }{4.898979486}[/tex]

Standard Error S.E = 4.7950

However;

Degree of freedom df= n - 1

Degree of freedom df= 26 - 1

Degree of freedom df= 25

At confidence level of 95% and Degree of freedom df of  25 ;

t-value = 1.7080

Similarly;

The Margin of error = t-value × S.E

The Margin of error = 1.7080 × 4.7950

The Margin of error = 8.18986

The upper confidence bound for population mean escape time is = Sample Mean + Margin   of  Error

The upper confidence bound for population mean escape time is =  371.08 +  8.18986

The upper confidence bound for population mean escape time is = 379.26986  [tex]\approx[/tex] 379.27

The upper confidence bound for population mean escape time is: 379.27

b.  Calculate an upper prediction bound for the escape time of a single additional worker using a prediction level of 95%.

The standard error of the mean = [tex]\sigma \times \sqrt{1+ \dfrac{1}{n}}[/tex]

The standard error of the mean = [tex]24.45 \times \sqrt{1+ \dfrac{1}{26}}[/tex]

The standard error of the mean = [tex]24.45 \times \sqrt{1+0.03846153846}[/tex]

The standard error of the mean = [tex]24.45 \times \sqrt{1.03846153846}[/tex]

The standard error of the mean = [tex]24.45 \times 1.019049331[/tex]

The standard error of the mean = 24.91575614

Recall that : At confidence level of 95% and Degree of freedom df of  25 ;

t-value = 1.7080

∴

The Margin of error = t-value × S.E

The Margin of error = 1.7080 × 24.91575614

The Margin of error = 42.55611149

The upper prediction bound for the escape time of a single additional worker  is calculate by the addition of

Sample Mean + Margin of Error

= 371.08 + 42.55611149

= 413.6361115

[tex]\approx[/tex] 413.64

The upper prediction bound for the escape time of a single additional worker  is 413.64

Answer:

168 mm²

Step-by-step explanation:

Let A be the area of this shape

the kite is made of two triangles

Let A' and A" be the areas of the triangles

let's calculate A' and A" :

The area of a triangle is the product of the base and the height over 2

Let's calculate A

Answer:

Step-by-step explanation:

The mean value theorem for integrals for the function f(c) over a given interval [a, b] is expressed as g prime(c) = g(b) - g(a)/b-a. The idea is that there is a value c in between the interval [a, b] for the function given.

Given the function g(x) = 5√x within the interval [4,9]

g prime (c) = g(9) - g(4)/9-4

g(9) = 5√9

g(9) = 5*3 = 15

g(4) = 5√4

g(4) = 5*2 = 10

g prime c) = 15-10/9-4

g prime (c) = 5/5

g prime(c) = 1

So we are to find the number for which g prime (x) = g prime(c)

If g(x) = 5√x = [tex]5x^{1/2}[/tex]

g prime (x) = [tex]5/2 \ x^{-1/2}[/tex]

g prime (x) = 5/2√x

Since g prime (c) = 1 then;

5/2√x = 1

5 = 2√x

√x = 5/2

x = (5/2)²

x = 25/4

The value of c guaranteed by the mid value theorem is 25/4

The possible value of c for [tex]\mathbf{f(x) = 5\sqrt x\ [4,9]}[/tex] is 6.25

The function is given as:

[tex]\mathbf{f(x) = 5\sqrt x\ [4,9]}[/tex]

Calculate f(4) and f(9)

[tex]\mathbf{f(4) = 5\sqrt 4 = 10}[/tex]

[tex]\mathbf{f(9) = 5\sqrt 9 = 15}[/tex]

Substitute c for x in f(x)

[tex]\mathbf{f(c) = 5\sqrt c }[/tex]

Calculate f'(c)

[tex]\mathbf{f'(c) = \frac{f(b) - f(a)}{b - a}}[/tex]

So, we have:

[tex]\mathbf{f'(c) = \frac{f(9) - f(4)}{9 - 4}}[/tex]

[tex]\mathbf{f'(c) = \frac{f(9) - f(4)}{5}}[/tex]

This gives

[tex]\mathbf{f'(c) = \frac{15 -10 }{5}}[/tex]

[tex]\mathbf{f'(c) = \frac{5 }{5}}[/tex]

[tex]\mathbf{f'(c) = 1}[/tex]

Also, we have:

[tex]\mathbf{f'(x) = \frac 52x^{-1/2}}[/tex]

Substitute c for x

[tex]\mathbf{f'(c) = \frac 52c^{-1/2}}[/tex]

Substitute 1 for f'(c)

[tex]\mathbf{\frac 52c^{-1/2} = 1}[/tex]

Multiply through by 2/5

[tex]\mathbf{c^{-1/2} = \frac 25}[/tex]

This gives

[tex]\mathbf{c^{1/2} = \frac 52}[/tex]

Square both sides

[tex]\mathbf{c = \frac{25}4}[/tex]

[tex]\mathbf{c = 6.25}[/tex]

Hence, the possible value of c is 6.25

Read more about mean value theorem at:

https://brainly.com/question/3957181

Answer:

I=0.24ampere

Step-by-step explanation:

Assuming that the voltage is the same:

I=V/R (V- voltage, I-current, R-resistance)

1/6ampere=V/3240ohms

V=1/6*3240

= 5400v

Voltage across =V=5400v

Since the voltage is the same when the resistance is 22500ohms

I=V/R

=5400/22500

=6/25

=0.24ampere

Answer:

b.  y = |x+4| - 10

Step-by-step explanation:

When you see a v-shaped graph, it could very well relate to an absolute-value function.

The value of the absolute value function has the vertex at x= -4, meaning that it has a minimum value when x=-4, which means that the absolute value function is of the form |x+4|  giving a zero when x= -4.

Also, the minimum of the function occurs at y = -10, meaning that the function has been translated by -10.

Therefore the function is

y = |x+4| - 10

Answer:

B

Step-by-step explanation:

EDGE unit review

Hi there! Hopefully this helps!

--------------------------------------------------------------------------------------------------             The frequency is ~7.5*1014 Hz

Since visible light has a wavelength spectrum of ~400 nm to ~700 nm, Violet light has a wavelength of ~400 nm and a frequency of ~7.5*1014 Hz.

Step-by-step explanation:

Speed = wavelength × frequency

3×10⁸ m/s = (400×10⁻⁹ m) f

f = 7.5×10¹⁴

Answer:

yyy = xxx + 151515

Step-by-step explanation:

Since you want to swim 151515 minutes longer one day at practice (note this time is actually 105 days), you simply need to swim the same amount of time as your friend, plus the extra time. Hence, your time will be equal to your friends time plus the extra time you plan to swim.

Answer:

108 degrees

Step-by-step explanation:

angle CDE is 108 degrees, which is supplementary to angle EDH, so EDH must be 72 degrees

then put it into an equation

90+90+72+x=360

solve

x=108

Answer:

The answer is 108

Answer:  see below

Step-by-step explanation:

1) The equation of a circle is: (x - h)² + (y - k)² = r²    where

2) If you are given a point on the circle and the center (h, k)

you can input those points into the equation of a circle to find r².

Then input (h, k) and r² to identify the equation of that particular circle.

3) If you divide each term in the equation of a circle by r², you will get:

[tex]\dfrac{(x-h)^2}{r^2}+\dfrac{(y-k)^2}{r^2}=1[/tex]

The difference between a circle and an ellipse is that an ellipse is in the shape of an oval.  In other words, the x-radius and y-radius are different.

The equation of an ellipse is:

[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]

Answer: The speed of Ina in still water is 5mph

Step-by-step explanation:

If the speed of Ina on still water is x, and the speed of the river is y:

The total speed of Ina when she goes along with the current is:

S = x + y

when she goes against the current we have:

St = x - y.

Now we can use the relation:

speed = time/velocity.

along with the current, we have:

x + y = 12mi/2h = 6mi/h

against the current we have:

x - y = 12mi/3h = 4mi/h

So we have the equations

x + y = 6mi/h

x - y = 4mi/h

in the first equation we can isolate x

x = 6mi/h - y

now we replace this in the second equation:

(6mi/h - y) - y = 4mi/h

6mi/h - 2y = 4mi/h

-2*y = 4mi/h - 6mi/h = -2mi/h

y = 1mi/h

now we replace this in the first equation:

x + 1mi/h = 6mi/h

x = 5mi/h.

The speed of Ina in still water is 5mph

There is only one distinct triangle possible, with m N= 33º. Therefore, option B is the correct answer.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

Given that, in ΔMNO, m = 20, n = 14, and m∠M = 51°.

Now, sin51°/20=sinN/14

0.7771/20=sinN/14

0.038855=sinN/14

sinN=14×0.038855

sinN=0.54397

N=33°

Therefore, option B is the correct answer.

Learn more about the sine rule here:

https://brainly.com/question/22288720.

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Explanation:

The directrix is horizontal, so the axis of symmetry is vertical. We'll have an x^2 term. The vertical distance from y = 4 to y = 8 is 4 units. Cut this in half to get 2, which is the focal distance p = 2.

The point (2,4) is directly below (2,8), and the point is on the directrix. The midpoint between (2,4) and (2,8) is (2,6). This is the vertex.

(h,k) = (2,6)

4p(y-k) = (x-h)^2

4*2(y-6) = (x-2)^2

8(y-6) = (x-2)^2

Answer:

700

Step-by-step explanation:

500+10*20=700

it's f(n) = 500+10n