Use the interactive number line to find the difference. 4.7 - 2.3 = 4.7 + (-2.3) =

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:

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:

[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:

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:  A.   A=(1000-2w)*w      B. 250 feet

C.  125 000 square feet

Step-by-step explanation:

The area of rectangular is A=l*w    (1)

From another hand the length of the fence is 2*w+l=1000        (2)

L is not multiplied by 2, because the opposite side of the l is the barn,- we don't need in fence on that side.

Express l from (2):

l=1000-2w

Substitude l in (1) by 1000-2w

A=(1000-2w)*w        (3)   ( Part A. is done !)

Part B.

To find the width w  (Wmax) that corresponds to max of area A   we have to dind the roots of equation (1000-2w)w=0  ( we get it from (3))

w1=0  1000-2*w2=0

w2=500

Wmax= (w1+w2)/2=(0+500)/2=250 feet

The width that maximize area A is Wmax=250 feet

Part C.   Using (3) and the value of Wmax=250 we can write the following:

A(Wmax)=250*(1000-2*250)=250*500=125 000 square feets

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:

[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:  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:-95 1/7 feet

Step-by-step explanation:

-120 4/7+25 3/7=-95 1/7 feet

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:

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:

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

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

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:

a)d = 180,91 m

b)t = 11,76 seg

Step-by-step explanation:

Para el lanzamiento de proyectil, la ecuación que nos da la velocidad en V(y) es:

V(y)  = Voy - g*t

en donde Voy = Vo * senα    ( donde Vo es la velocidad inicial, α el angulo del disparo.

Si en esta ecuación hacemos V(y) = 0 estamos en el punto donde el componente en el eje y de la velocidad del proyectil es cero, ese punto es el punto medio del recorrido.

0 =  Vo*sen 60⁰     - g*t

g*t  =  Vo* √3/2

t  = { 32 [m/s] * √3 }2*9,8 [m/s²]

t = 16*√3  / 9,8

t = 2,8278 seg

El tiempo total del primer recorrido es entonces por simetría

t₁ = 2 * 2,8278           t₁  = 5,6556 seg

La distancia del primer impacto al suelo es:

x = Vox * t₁                        ( Vox es constante   Vx = Vo*cos 60⁰ )

x  =  32 * (1/2) * 5,6556

x₁  =  90,49 m

Aplicando los mismos criterios ahora para el segundo bote

Ahora Vo = 32 -  32*(1/4)

V = 24 m/s

g*t  =  24 * sen 50⁰

t =  24* 0,7660/ 9,8  

t =  1,8759

2*t  = 2*1,8759

t₂  = 3,7518 seg

x₂  =  Vox * t₂

x₂  =  24* 0,6428*3,7518

x₂  =  57,88 m

Y para el tercer bote Vo =  24 - 24(1/4)        Vo = 18 m/s     α = 40⁰

t = 18 *0,6428/9,8

t  = 1,18

2t  = t₃  = 2*1,18

t₃ = 2,36 seg

x₃  = Vox * 2,36                Vox = Vo*cos 40      Vox = 18*0,7660  

Vox = 13,79

x₃  = 13,79*2,36

x₃  = 32,54 m

La distancia total será

d = x₁  + x₂ + x₃

d  =  90,49  + 57,88 + 32,54

d = 180,91 m

y el tiempo total será la suma de los tiempos

t =  t₁  +  t₂  +  t₃

t  = 5,65 + 3,75 + 2,36

t = 11,76 seg

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: 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

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:  800 feet²

Step-by-step explanation:

Lets remove the brackets from the function's expression

A(x) = -2x²+80x

So we got the quadratic function and we have to find the x that corresponds to function's maximum. Let it be X max

As we know Xmax= (X1+X2)/2 , where X1 and X2 are the roots of the function A(x)

Lets find X1 and X2

x(80-2x)=0

x1=0   80-2*X2=0

x2=40

So Xmax= (0+40)/2=20

So Amax= A(20)= 20*(80-2*20)=20*40=800 feet²

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:

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:

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:

43\ 12 , 35/ 6

Step-by-step explanation:

43\ 12 , 35/ 6

Answer:  B: (3, -7)

Step-by-step explanation:

4x + 4y = -9

         y = 2x - 13

Use Substitution:

4x + 4(2x - 13) = -9

4x + 8x - 52 = -9

       12x - 52 = -9

               12x = 43

                   [tex]x=\dfrac{43}{12}[/tex]

None of the options provided are valid so either there is a typo on your worksheet or you typed in one of the equations wrong.

Plan B: Input the choices into the equation to see which one makes a true statement.

               4x + 4y = -9

A) (x, y) = (-3, -7)

               4(-3) + 4(-7) = -9

                -12   +   -28 = -9

                             -40 ≠ -9

B) (x, y) = (3, -7)

               4(3) + 4(-7) = -9

                12   +   -28 = -9

                             -16 ≠ -9

C) (x, y) = (3, 7)

               4(3) + 4(7) = -9

                12   +   28 = -9

                            40 ≠ -9

D) (x, y) = (-3, 7)

               4(-3) + 4(7) = -9

                -12   +   28 = -9

                              16 ≠ -9

Obviously there is something wrong with the first equation because none of the options provide a true statement.

               y = 2x - 13

A) (x, y) = (-3, -7)

               -7 = 2(-3) - 13

               -7  = -6    -13

                -7 ≠ -19

B) (x, y) = (3, -7)

               -7 = 2(3) - 13

               -7  = 6    -13

                -7 = -7                   this works!!!

C) (x, y) = (3, 7)

               7 = 2(3) - 13

               7  = 6    -13

                7 ≠ -7

D) (x, y) = (-3, 7)

               7 = 2(-3) - 13

               7  = -6    -13

                7 ≠ -19

Option B is the only one that provides a true statement so this must be the answer.

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: [tex](f \circ g) (10)= -18\ .[/tex]

Step-by-step explanation:

Given: [tex]f (x) = -9x - 9[/tex] and [tex]g (x) = \sqrt{x - 9}[/tex]

To find : (f o g) (10)

For this we first find (f o g) (x)= [tex]f(g(x))[/tex]

[tex]=f(\sqrt{x-9})\\\\=-9(\sqrt{x-9})-9[/tex]

Now,

[tex](f \circ g) (10)=-9(\sqrt{10-9})-9\\\\=-9\sqrt{1}-9\\\\=-9-9=-18[/tex]

Hence, the value of [tex](f \circ g) (10)= -18\ .[/tex]

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:

700

Step-by-step explanation:

500+10*20=700

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

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:

d)

Step-by-step explanation:

the general form is ax + by = c

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)