(06.03)
How can one half x − 5 = one third x + 6 be set up as a system of equations? (6 points)

Answer:

y=2x-10

Step-by-step explanation:

First step: Let's compute the slope. You can directly use the formula for slope given two points here but I just like to like them up and subtract vertically. Make sure you put 2nd difference on top of 1st difference (yes, like a fraction).

(7  ,  4)

-(4 ,  -2)

=======

3       6

So the slope is 6/3 =2.

So we know our line is in the form y=2x+b.

We have to find the y-intercept now.  To find b we will use a point that we know is on the line (you know two-just choose one of them) .  I will plug in (4,-2) giving me this equation -2=2(4)+b

       Solving:                              -2=8+b

                                      So            b=-10

The answer is y=2x-10

Answer:

20 mg / hour

Step-by-step explanation:

The first step is to find the mg/mL of dopamine.

If there are 52 mg / 26 mL, then there are 2 mg / 1 mL (just reduce the fraction).

If we are losing 10 mL / 1 hour, and there are 2 mg / mL, then the flow rate of dopamine mg / hour is 20.

You can also do this using dimensional analysis.

[tex]\frac{52 mg}{26 mL} (\frac{10 mL}{1 hour})[/tex]

Just cross out the units that cancel in the numerator and denominator (mL in this case), and you're left with mg / hour. Then multiply the numerators and divide by the denominators. You get the same answer.

The first step is to find the mg/mL of dopamine.

If there are 52 mg / 26 mL, then there are 2 mg / 1 mL (just reduce the fraction).

If we are losing 10 mL / 1 hour, and there are 2 mg / mL, then the flow rate of dopamine mg / hour is 20.

You can also do this using dimensional analysis.

[tex]\frac{52 mg}{26 mL} (\frac{10 mL}{1 hour})[/tex]

Just cross out the units that cancel in the numerator and denominator (mL in this case), and you're left with mg / hour. Then multiply the numerators and divide by the denominators. You get the same answer.

Answer: c

Step-by-step explanation:

Step-by-step explanation:

10.44 is correct as we have to add both dis and divide by both hrs

In this case, Taylor's average rate is 10 miles per hour.

To calculate Taylor's average rate during her trip, we can use the formula for average speed:

Calculate the total distance traveled: 62 miles - 32 miles = 30 miles.

Calculate the total time taken: 6 hours - 3 hours = 3 hours.

Divide the total distance by the total time to find the average speed: 30 miles / 3 hours = 10 miles per hour.

Answer:

The answer in the procedure

Step-by-step explanation:

we have

[tex]\frac{1}{3}x^{2} +2[/tex]

This is a vertical parabola open upward with the the vertex at (0,2)

The vertex is a minimum

The y-intercept is the point (0,2) (value of y when the value of x is equal to zero)

The graph does not have x-intercepts, therefore the solutions of the quadratic equation are complex number

using a graphing tool

see the attached figure

Answer:

Perimeter of the square  = 8x - 4 in

Step-by-step explanation:

Perimeter of the square = 4 * side

                                        = 4 * (2x - 1)

                                        = 8x - 4 in

Answer:

20 rad/sec

Step-by-step explanation:

The formula we are going to use is  [tex]v=\omega r[/tex]

Where

v is the linear velocity (here given 60 ft/s)

[tex]\omega[/tex]  is the angular velocity (what we sought to find)

r is the radius (which is half of diameter, hence, 6/3 = 3 ft)

Plugging these numbers in, we find the angular velocity as:

[tex]v=\omega r\\60=\omega*(3)\\\omega=\frac{60}{3}=20[/tex]

Note: the units is radians per second (rad/s)

Correct answer 20 rad/sec

Answer:

[tex]20 \frac{rad }{sec}[/tex]

Step-by-step explanation:

Hello.

let's see this way.

if you know the distance(a circumference 2πr) and the speed(60 ftps) you are able to find the time it takes a whole spin( a circle)

Step 1

find the distance and time

Let

[tex]V=60 \frac{feet}{sec} \\distance= circumference= 2*\pi *r\\diameter=6 feet\\radius=\frac{Diameter}{2}\ so,r=\frac{6}{2} =3 feet\\Hence\\\\distance= circumference= 2*\pi *3\\\\distance=18.84\\\\time=\frac{distance}{velocity}\\ put\ the\ values\\time=\frac{18.84 feet}{60 \frac{feet}{sec} } \\\\time=0.314\ sec[/tex]

now, for obtain the  angular velocity , divide  the circumference (use radians  2π radians=360 degrees )by the time it takes to complete a lap

[tex]\alpha =\frac{(2 \pi rad)}{time\ per\ lap}\\\\ \alpha =\frac{(2\pi rad)}{0.314 sec}\\ \alpha =20 \frac{rad}{sec}[/tex]

Have a great day

Answer:

x=1, y=-5

Step-by-step explanation:

Given equations are:

[tex]3x+10y=-47\ Eqn\ 1\\and\\5x-7y=40\ Eqn\ 2[/tex]

In order to solve the equation

Multiplying Eqn 1 by 5 and eqn 2 by 3 and subtracting them

So,

Eqn 1 becomes

15x+50y=-235

Eqn 2 becomes

15x-21y=120

Subtracting 2 from a

15x+50y - (15x-21y) = -235-120

15x+50y-15x + 21y = -355

71y = -355

y = -355/71

y =-5

Putting y= -5 in eqn 1

3x+10(-5) = -47

3x -50 = -47

3x = -47+50

3x = 3

x = 3/3

x = 1

Hence the solution is:

x=1, y=-5

Answer: x=1; y=-5

Step-by-step explanation: To solve this system we can use differente methods, in this case we are going to use substitution:

first equation: 3x+10y=-47

second equation: 5x-7y=40

we are going to isolate x from the first equation:

3x=-47-10y

[tex]x=\frac{-47-10y}{3}[/tex]

now we replace it in the second equation:

[tex]5*\frac{-47-10y}{3}-7y=40[/tex]

and now we solve for y:

[tex]\frac{-235-50y}{3} -7y=40[/tex]

[tex]\frac{-235-50y-21y}{3}=40[/tex]

[tex]-235-71y=40*3[/tex]

[tex]-235-71y=120[/tex]

[tex]-71y=120+235[/tex]

[tex]y=-355/71[/tex]

y=-5

now we replace the value of y in the first equation and solve for x:

[tex]x=\frac{-47-10y}{3}[/tex]

[tex]x=\frac{-47-10(-5)}{3}[/tex]

[tex]x=\frac{-47+50}{3}[/tex]

[tex]x=\frac{3}{3}[/tex]

x=1

Answer:

Option A - Permutation; number of ways = 210

Step-by-step explanation:

Given : At a competition with 7 runners, medals are awarded for first, second, and  third places. Each of the 3 medals is different.

To find : How many ways are there to  award the medals?        

Solution :

There are 7 runners but medals are three.

The first runner up got first medal as one is locked.

The second runner up got second medal as second is locked.

The third runner up got the third medal.

So, There is a permutation.

Number of ways to award the medals is [tex]^7P_3[/tex]

We know, [tex]^nP_r=\frac{n!}{(n-r)!}[/tex]

Substitute the values,

[tex]^7P_3=\frac{7!}{(7-3)!}[/tex]

[tex]^7P_3=\frac{7\times 6\times 5\times 4!}{4!}[/tex]

[tex]^7P_3=210[/tex]

Therefore, Option A is correct.

Permutation; number of ways = 210

Equations are used to represent the relationships between variables. In [tex]y=x^2 -1[/tex], the variables are x & y and the following observations are true for the given equation:

Given that:

[tex]y=x^2 -1[/tex]

[tex]x^2 \to[/tex] the square of x

So, means that: the y is 1 less than the square of x

From the attached table, we have:

[tex]x = -2; y = a[/tex]

This means that:

[tex]a = (-2)^2 - 1[/tex]

[tex]a = 4 - 1[/tex]

[tex]a =3[/tex]

Also, we have:

[tex]x = b; y = -1[/tex]

This means that:

[tex]-1 = b^2 - 1[/tex]

Collect like terms

[tex]b^2 =1-1[/tex]

[tex]b^2 =0[/tex]

Take square roots

[tex]b = 0[/tex]

Hence, the values of a and b are 3 and 0, respectively.

The graph options are not made available. So, I will plot the graph of [tex]y=x^2 -1[/tex].

See attachment for graph of [tex]y=x^2 -1[/tex]

Read more about graphs and equations at:

https://brainly.com/question/1971145

Answer: In short for ed2020 :

1. 3rd answer

Graph: A

Table: A=3 B=0

Answer:

One of the numbers is 5

The other number is 17

Step-by-step explanation:

You could do this just by guessing numbers. But I think you are intended to do it with algebra.

x + y = 22

y = 2*x + 7          Substitute the y value in this equation into the first equation

x + 2x + 7 = 22   Combine the xs on the left.

3x + 7 = 22          Subtract 7 from both sides.

3x+7-7=22- 7       Combine

3x = 15                 Divide by 3

3x/3 = 15/3           Combine

x = 5

x + y = 22             Substitute 5 for x

5 + y = 22            Subtract 5 from both sides.

5-5+y = 22-5

y = 17

Answer:

17 or 5

Step-by-step explanation:

I took the test

Answer:

Yes, the right angle is angle B

Step-by-step explanation:

we have

[tex]A(-2, 3), B(-3,-6),C(2,-1)[/tex]

Plot the vertices

see the attached figure

we know that

If triangle ABC is a right triangle

then

Applying the Pythagoras Theorem

[tex]AB^{2} =AC^{2}+BC^{2}[/tex]

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Find the distance AB

[tex]A(-2, 3), B(-3,-6)[/tex]

substitute in the formula

[tex]d=\sqrt{(-6-3)^{2}+(-3+2)^{2}}[/tex]

[tex]d=\sqrt{(-9)^{2}+(-1)^{2}}[/tex]

[tex]AB=\sqrt{82}\ units[/tex]

Find the distance BC

[tex]B(-3,-6),C(2,-1)[/tex]

substitute in the formula

[tex]d=\sqrt{(-1+6)^{2}+(2+3)^{2}}[/tex]

[tex]d=\sqrt{(5)^{2}+(5)^{2}}[/tex]

[tex]BC=\sqrt{50}\ units[/tex]

Find the distance AC

[tex]A(-2, 3),C(2,-1)[/tex]

substitute in the formula

[tex]d=\sqrt{(-1-3)^{2}+(2+2)^{2}}[/tex]

[tex]d=\sqrt{(-4)^{2}+(4)^{2}}[/tex]

[tex]AC=\sqrt{32}\ units[/tex]

Verify the Pythagoras theorem

[tex](\sqrt{82})^{2} =(\sqrt{32})^{2}+(\sqrt{50})^{2}[/tex]

[tex]82=82[/tex] ---> is true

therefore

Is a right triangle and the right angle is B

f(x) and y are two different ways of denoting the same thing. Thus...

f(x) = 9x - 8 is the same as y = 9x - 8

Inverse: the inverse of a function is the resulting equation when x and y switch places and the equation is solved for x

Switch the places of x and y in the given equation:

y = 9x - 8 ---> x = 9y - 8

Solve the new equation for y (isolate y on the left side of the equation)

x = 9y - 8

x + 8 = 9y - 8 + 8

x + 8 = 9y

(x + 8) / 9 = 9y / 9

(x + 8)/9 = y

y = (x + 8) / 9

y = [tex]\frac{x+8}{9}[/tex]

Now you have the inverse of f(x) = 9x - 8:

A) [tex]f^{-1}[/tex] =[tex]\frac{x + 8}{9}[/tex]

inverse

Answer:

A. [tex]f^{-1}(x)=\frac{x+8}{9}[/tex]

Step-by-step explanation:

We have been given a function [tex]f(x)=9x-8[/tex]. We are asked to find the inverse function for our given function.

First of all, we will rewrite [tex]f(x)[/tex] as [tex]y[/tex] as:

[tex]y=9x-8[/tex]

To find the inverse function, we will interchange x and y variables and then solve for y.

[tex]x=9y-8[/tex]

Now, we will add 8 on both sides of our given equation.

[tex]x+8=9y-8+8[/tex]

[tex]x+8=9y[/tex]

Switch sides:

[tex]9y=x+8[/tex]

Now, we will divide both sides of our equation by 9.

[tex]\frac{9y}{9}=\frac{x+8}{9}[/tex]

[tex]y=\frac{x+8}{9}[/tex]

Now, we will replace [tex]y[/tex] with [tex]f^{-1}(x)[/tex] as:

[tex]f^{-1}(x)=\frac{x+8}{9}[/tex]

Therefore, the inverse function for our given function would be [tex]f^{-1}(x)=\frac{x+8}{9}[/tex] and option A is the correct choice.

The perimeter is 11 inches.

One side is 2 inches shorter, so two sides would be 4 inches shorter total.

Subtract 4 from 11 to get 7 inches.

Divide 7 by 4 ( the number of sides):

7 / 4 = 1.75

The shorter side is 1.75 inches.

Now add 2 inches to that for the longer side:

1.75 + 2 = 3.75 inches.

Check: 3.75 + 3.75 + 1.75 + 1.75 = 11

The longer side is 3.75 inches.

Answer:

1,3,5,15

Step-by-step explanation:

these are the factors of 15

Answer:

Step-by-step explanation:

I must assume that you meant, "the sum of which four numbers equals 15?"

15 = 6 + 9

    = 3 + 3 + 9

    =  3 + 3 + 3 + 6

All of these sets (on the right side) add up to 15.  There are four numbers in the last set.

Answer:

5 + 2m = 23

Step-by-step explanation:

This equation can be solved as follows:

5 + 2m = 23

2m = 23 - 5

m = 18/2

m = 9 months

Linear functions are "graphs with straight lines." The formula to solving a linear function is [tex]y=f(x)=a+bx[/tex] Linear functions also have one independent variable and one dependent variable.

Hope this helps.

Answer:

0.

Step-by-step explanation:

If log(a) x = b

Then by the definition of a logarithm x = a^b.

So let log(4) 1 = y

then 1 = 4^y

but 4^0 = 1

so y = log(4) 1 = 0.

ANSWER

Prime

EXPLANATION

The given quadratic expression is

[tex] {2t}^{2} - 19 - 6t[/tex]

We rewrite in standard form to obtain

[tex]{2t}^{2} - 6t - 19[/tex]

Comparing to the standard quadratic function in t,

[tex]a {t}^{2} + bt + c[/tex]

We have

[tex]a = 2[/tex]

[tex]b = - 6[/tex]

[tex]c = - 19[/tex]

We find that the product

[tex]ac = 2 \times - 19 = - 38[/tex]

There are no two factors of -38 that sums up to -6.

This means that, the given polynomial does not have rational factors.

Therefore the polynomial is prime.

Answer: 95°

Step-by-step explanation: We are given information for Angles 1 and 4, which happen to be vertical angles, meaning they are congruent. Because of this, we can say 3x+10=4x-15, therefore x=25. Angles 1,2,3 and 4 must add up to 360°, and since we know angles 1 and 4 are 85° (3*25 + 10 = 85), we can find angles 2 and 3. 360° - 85° - 85° = Angle 2 + Angle 3. Angle 2 + Angle 3 = 190, and because Angles 2 and 3 are vertical angles and therefore congruent, we can divide 190 by 2 and get that Angles 2 and 3 equal 95°. Because lines b and c are parallel, any corresponding angles created by a transversal are congruent. This basically means Angles 3 and 7 must be congruent, therefore Angle 7 = 95°

Congruent - same meaning as equal

Vertical Angles - each of the pairs of opposite angles made by two intersecting lines.

Answer:    Im pretty sure it is D

Step-by-step explanation:  I don't really know how to explain it.

I hope it helps tho ;)

Tell me if im wrong.

Answer:  The correct option is

(D) rotation of 270 degrees counterclockwise and shifting 3 units up.

Step-by-step explanation:  We are given to select the correct transformations that were applied to triangle ABC to obtain triangle A'B'C'.

From the graph, we note that

the co-ordinates of the vertices of triangle ABC are A(3, 4). B(5, 6) and C(8, 1).

And, the co-ordinates of the vertices of triangle A'B'C' are A'(4, 0), B'(6, -2) and C'(1, -5).

We see that

if a point (x, y) is rotated 270 degrees counterclockwise and then shifted 3 units up, then its co-ordinates becomes

(x, y)   ⇒   (y, -x+3).

With this transformation rule,

A(3, 4)  ⇒  (4, -3+3) = (4, 0),

B(5, 6)  ⇒  (6, -5+3) = (6, -2)

and

C(8, 1)  ⇒  (1, -8+3) = (1, -5).

Since the resulting co-ordinates are the vertices of triangle A'B'C', so the required transformations rare

rotation of 270 degrees counterclockwise and shifting 3 units up.

Option (D) is CORRECT.

Answer:

N/A

Step-by-step explanation:

Which area of shaded segment?

Answer:

Area Of Shaded Segment =

In Pictures

Answer:

9/32

Step-by-step explanation:

BC = black circle

BS = black square

WC = white circle

WS = white square

Given:

(WC + WS) / (BC + BS) = 5 / 11

WC / WS = 3 / 7

BC / BS = 3 / 8

Find: (BC + WC) / (BC + BS + WC + WS)

Solve for WC and BC in the last two equations, then substitute into the first:

WC = 3/7 WS

BC = 3/8 BS

WC + WS = 5/11 (BC + BS)

3/7 WS + WS = 5/11 (3/8 BS + BS)

10/7 WS = 5/8 BS

WS = 7/16 BS

Therefore:

WC = 3/7 WS

WC = 3/16 BS

Substitute:

(BC + WC) / (BC + BS + WC + WS)

(3/8 BS + 3/16 BS) / (3/8 BS + BS + 3/16 BS + 7/16 BS)

(9/16 BS) / (2 BS)

9/32

Answer:

Option D. 3.73​

Step-by-step explanation:

we know that

[tex]tan(x+y)=\frac{tan(x)+tan(y)}{1-tan(x)tan(y)}[/tex]

and

[tex]sin^{2}(\alpha)+cos^{2}(\alpha)=1[/tex]

step 1

Find cos(X)

we have

[tex]sin(x)=\frac{1}{2}[/tex]

we know that

[tex]sin^{2}(x)+cos^{2}(x)=1[/tex]

substitute

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

[tex]cos^{2}(x)=1-\frac{1}{4}[/tex]

[tex]cos^{2}(x)=\frac{3}{4}[/tex]

[tex]cos(x)=\frac{\sqrt{3}}{2}[/tex]

step 2

Find tan(x)

[tex]tan(x)=sin(x)/cos(x)[/tex]

substitute

[tex]tan(x)=1/\sqrt{3}[/tex]

step 3

Find sin(y)

we have

[tex]cos(y)=\frac{\sqrt{2}}{2}[/tex]

we know that

[tex]sin^{2}(y)+cos^{2}(y)=1[/tex]

substitute

[tex]sin^{2}(y)+(\frac{\sqrt{2}}{2})^{2}=1[/tex]

[tex]sin^{2}(y)=1-\frac{2}{4}[/tex]

[tex]sin^{2}(y)=\frac{2}{4}[/tex]

[tex]sin(y)=\frac{\sqrt{2}}{2}[/tex]

step 4

Find tan(y)

[tex]tan(y)=sin(y)/cos(y)[/tex]

substitute

[tex]tan(y)=1[/tex]

step 5      

Find tan(x+y)

[tex]tan(x+y)=\frac{tan(x)+tan(y)}{1-tan(x)tan(y)}[/tex]

substitute

[tex]tan(x+y)=[1/\sqrt{3}+1}]/[{1-1/\sqrt{3}}]=3.73[/tex]

Answer:

D. 3.73

Step-by-step explanation:

Answer:

y = -4x - 6

Step-by-step explanation:

The equation of a line in point-slope form.

[tex] y - y_1 = m(x - x_1) [/tex]

is the equation of the line containing point (x1, y1) and having slope, m.

The given point of the perpendicular bisector is (-1, -2), so in this case, x1 = -1, and y1 = -2.

We need the slope of the perpendicular bisector. First we find the slope of the segment. We start at point (-5, -3). We go up 1 unit and 4 units to the right, and we are at another point on the segment. Since slope = rise/run, the slope of the segment is 1/4. The slopes of perpendicular lines are negative reciprocals, so the slope of the perpendicular bisector is the negative reciprocal of 1/4, so for the perpendicular bisector, m = -4.

Now we use the equation above and our values.

[tex] y - y_1 = m(x - x_1) [/tex]

[tex] y - (-2) = -4(x - (-1)) [/tex]

[tex] y + 2 = -4(x + 1) [/tex]

[tex] y + 2 = -4x - 4 [/tex]

[tex] y = -4x - 6 [/tex]

Answer:

Step-by-step explanation:

y = -4x - 6

Answer:

7y

Step-by-step explanation:

By cross multiplication

[tex] \frac{x}{7} = \frac{y}{5} \\ 5x = 7y[/tex]

Answer:

[tex]5x=7y[/tex]

Step-by-step explanation:

We have the following relationship

[tex]\frac{x}{7}=\frac{y}{5}[/tex]

Based on the relationship between the variables X and Y that we know, we must find out what the expression "5x" is in terms of the variable y.

Then we solve the equation for x

[tex]x=\frac{7y}{5}[/tex]

Now multiply by 5 both sides of equality

[tex]5x=\frac{5*7y}{5}[/tex]

[tex]5x=7y[/tex]

Finally we have that 5x equals 7y

Answer:

{-2,-1,0}

Step-by-step explanation:

The domain of a function is defined as the set of x values for which the function is real and defined. The x values represent independent or predictor variable.

The domain of the function is thus;

{-2,-1,0}

These are basically the x values of the function

Answer: Answer is below

Step-by-step explanation: The answer is that the opposite of a cosine is called a hypotenuse. The ratio of the triangle is called a tangent.

I hope this info helps! :V

Answer:

2

Step-by-step explanation:

The reason 2 is the Greatest Common Factor of 6 and 8 is because 2 is the only number (other than 1) that you can divide evenly by both numbers  without making a fraction. 6/2= 3 and 8/2= 4.

Answer:

Step-by-step explanation:

In general, factor the numbers given into their primes.

6: 2*3

8: 2 * 2 * 2

Take the most you can from the two numbers primes. In this case it is 2.

A slightly more interesting problem is the GCF of 12 and 18

12: 2 * 2 * 3

18: 2 * 3 * 3

Here the two numbers that are common to both factored numbers is 2 and 3

GCF = 2*3

GCF = 6

Answer:

y=6

Step-by-step explanation:

y = -x+7

We have the point (1,y)

That means x=1 and we want to find y

Let x=1

y = -1+7

y = 6

The point is (1,6)  where x=1 and y =6