What is the measure of angle GFH?

Choose the correct equation type for each system.

Lunna [17]

Answer:

Inconsistent= 1, & 3

Equivalent= 2&6

Consistent= 4&5

Step-by-step explanation:

Equivalent means both sides of the equation has similar results

Consistent means the equation has an order pair of x, y that make it true

Inconsistent means impossible to solve using a set of values for the variable

1. y=3x-2

3x-y=4----------------make y subject of equation as 3x-4=y

Equate the two equation

y=3x-2

y=3x-4

3x-2=3x-4---------------collect like terms

3x-3x=-4+2

0=-2---------------inconsistent

2. 1/2 y=-x+5------------multiply by 2 both sides to have y=-2x+10

2y=-4x+2

we have

y=-2x+10----------------------use y in this equation in the second equation

2y=-4x+20

2(-2x+10)=-4x+20

-4x+20=-4x+20----------------Equivalent

3. y=-x+4----------------use this in the second equation as

x=-y-6

x= - (-x+4)-6

x= x-4-6

x=x-10--------------collect like terms

x-x= -10

0= -10--------------inconsistent

4. y=4x+2

y=6x-10-----------equate the two

4x+2=6x-10----------collect like terms

4x-6x=-10-2

-2x=-12

x=6---------------------use to find y

y=4(6)+2=24+2=26

(x,y)=(6,26)---------consistent

5. y=2x+1

y=-2x+3

Equate the two equation

2x+1=-2x+3-------------collect like terms

2x+2x=3-1

4x=2

x=1/2----------use to find y

y=2 *1/2 +1 =1+1=2

(x,y) = (1/2, 2)---------------consistent

6. -2x +5y=0

y=2/5x-------------------use this in the first equation

-2x + 5(2/5 x)=0

-2x+2x =0

0=0-----------------------Equivalent

5 0

3 years ago

Dr. Hoover, a pediatrician, has 3 annual checkups and 2 sick visits scheduled next Tuesday,

Jet001 [13]

Dr. Hoover allot his time on Tuesday for an annual checkup is 147 minutes and for a sick visit is 42 minutes (Total 189 minutes)

On Wednesday appointment, he allot his time for an annual checkup is 147 minutes and for a sick visit is 21 minutes (Total 168 minutes)

solution

Let us assume, minutes for annual checkup denoted as x and

minutes for sick visit denoted as y

The equation of Tuesday visit is $3x + 2y = 189 minutes ------ 1$

The equation of Wednesday visit is $3x + 1y = 168 minutes ------ 2$

by changing the signs of the equation 2 and subtract it from the equation 1 we will get 1y = 21 minutes

to substitute y =1 in the equation 2 we get

$3x + 2(21) = 189$

$3x + 42 = 189$

$3x = 189 - 42$

$3x = 147$

$x = 147 ÷ 3 = 49 minutes$

then now we have substitute both x = 49 and y= 21 in equation ----- 2

we will prove that $3x + 2y = 189 = 3 (49) + 2(21) = 189$ $147+ 42 = 189 minutes$

so the Tuesday appointment , the time allotted for an annual checkup is 147 minutes and for a sick visit is 42 minutes (Total 189 minutes)

On Wednesday appointment, the time allotted for an annual checkup is 147 minutes and for a sick visit is 21 minutes (Total 168 minutes)

6 0

3 years ago

What is 7.42 as a fraction in simplest form?

inn [45]

7.42 as a fraction is 7420/1000. Now you need to simplify it. The easiest way to do this is to continuously divide the top and bottom by 2 as long as it is even. At this point it should be small enough to figure out the other factors, and finish simplifying it. This only simplifies to 371/50. While 371 is divisible by 7 and 53, 50 is not divisible by either of them, so the final solution is 371/30

Therefore 371/50 is 7.42 as a fraction.

8 0

3 years ago

Read 2 more answers

13. Write an equation for the given function given the amplitude, period, phase shift, and vertical shift.

aev [14]

Answer:

$y=4sin(\frac{\pi}{2} x+\pi)-2$

Step-by-step explanation:

The equation of a periodic function is in the form:

y = Asin(Bx + C) + D

Where A = amplitude, B = 2π / period, D = vertical shift, phase shift = -C / B.

Given that:

amplitude: 4, period 4 phase shift = vertical shift = -2

Hence:

A = amplitude = 4, B = 2π / period = 2π / 4 = π / 2, D = vertical shift = -2.

Phase shift = -C / B

C = -phase shift * B = - * -2 * π / 2 = π.

Therefore substituting gives:

$y=4sin(\frac{\pi}{2} x+\pi)-2$

8 0

3 years ago

How would I solve for the parabolic equation with these two given points. Please answer ASAP!!

monitta

So

y=ax^2+bx+c
(x,y)
sub the points and solve

(4.28,6.48)
6.48=a(4.28)^2+b(4.28)+c

(12.61,15.04)
15.04=a(12.61)^2+b(12.61)+c
well, for 3 variables, we need equations and therefor 3 points

maybe we are supposed to assume it starts at (0,0)
so then
0=a(0)^2+b(0)+c
0=c
so then
6.48=a(4.28)^2+b(4.28)
15.04=a(12.61)^2+b(12.61)

solve for a by subsitution
first equation, minut a(4.28)^2 from both sides
6.48-a(4.28)^2=b(4.28)
divide both sides by 4.28
(6.48/4.28)-4.28a=b
sub that for b in other equation

15.04=a(12.61)^2+b(12.61)
15.04=a(12.61)^2+((6.48/4.28)-4.28a)(12.61)
expand
15.04 =a(12.61)^2+(81.7128/4.28)-53.9708a
minus (81.7128/4.28) both sides
15.04-(81.7128/4.28)=a(12.61)^2-53.9708a
15.04-(81.7128/4.28)=a((12.61)^2-53.9708)
(15.04-(81.7128/4.28))/(((12.61)^2-53.9708))=a
that's the exact value of a
to find b, subsitute to get
(6.48/4.28)-4.28((15.04-(81.7128/4.28))/(((12.61)^2-53.9708)))=b

if we aprox
a≈-0.038573167896199
b≈1.6791118501845
so then the equation is
y=-0.038573167896199x²+1.6791118501845x

7 0

3 years ago