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dsp73
3 years ago
10

Helaine graphed the equation 12x - 4y = 3. What was the slope of Helaine's line?

Mathematics
2 answers:
irina1246 [14]3 years ago
4 0

Answer:  The slope of the graph is 3.

Step-by-step explanation:

The equation of a line in slope intercept for is given by :-

y=mx+c, where m is the slope of the line.

The given equation of  the line graphed by Helaine = 12x - 4y = 3

Now, rewrite the above equation in slope-intercept form by adding 4y  and  subtracting 3 from both sides , we get

4y=12x-3

Divide 4 on both sides , we get

y=3x-\dfrac{3}{4} which is the slope-intercept form.

\Rightarrow\text{Slope}=3

Hence, the slope of Helaine's line =3

harkovskaia [24]3 years ago
3 0

Answer:

The slope of this line is 3.

Step-by-step explanation:

Solve 12x - 4y = 3 for y to obtain the equation in slope-intercept form:

Add 4y to both sides, obtaining 12x = 3 + 4y

Subtract 3 from both sides:  12x - 3 = 4y

Finally, divide all terms by 4:  y = 3x - 3/4

The slope of this line is 3.

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Plz help ill give you brainlist
anastassius [24]
Vertical angles are formed when two lines intersect, and two angles that are on opposite sides of both lines.

The angles on the west side and the east side form two vertically opposite angles (commonly called vertical angles, but much less descriptive).
It is because the west angle is to the left of both lines, and the east angle is to the right of both lines.

Vertically opposite angles (vertical angles) are congruent.  Therefore we can form the equation
110 = 5x
Divide both sides by 5 to get
110/5=22 = 5x/5 = x
or 
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6 0
2 years ago
1. Find the domain of the given function. (1 point)
Vika [28.1K]
1) Find the domain of the given function. f(x) = square root of quantity x plus three divided by quantity x plus eight times quantity x minus two.
 using a graphical tool    see the attachment  
the answer is C) x ≥ -3, x ≠ 2  
 2. Identify intervals on which the function is increasing, decreasing, or constant.
g(x) = 2 - (x - 7)2
 using a graphical tool     
see the attachment
 the answer is  C) Increasing: x < 7; decreasing: x > 7
3. Perform the requested operation or operations.
f(x) = 4x + 7, g(x) = 3x2
Find (f + g)(x).
 (f + g)(x) = f(x) + g(x) 
(f + g)(x) = 4x + 7 + 3x^2 
(f + g)(x) = 3x^2 + 4x + 7
 The answer is  C) 4x + 7 + 3x2
 4. Perform the requested operation or operations.
f(x) = x minus five divided by eight. ; g(x) = 8x + 5, find g(f(x)).
 f(x)=(x-5)/8    g(x)=8x+5
g(f(x))=8((x-5)/8)+5=x-5+5=x
the answer is  B) g(f(x)) = x   
5. Find f(x) and g(x) so that the function can be described as y = f(g(x)).y = nine divided by square root of quantity five x plus five. 
 y=f(g(x))=9/((5x+5) ^1/2)
let do
g(x)=5x+5...........so
f(x)= 9/( x^1/2)
the answer is  A) f(x) = nine divided by square root of x. , g(x) = 5x + 5

6. A satellite camera takes a rectangular-shaped picture. The smallest region that can be photographed is a 4-km by 4-km rectangle. As the camera zooms out, the length l and width w of the rectangle increase at a rate of 3 km/sec. How long does it take for the area A to be at least 4 times its original size?
Original size- >4km*4km=16 km2
4 times its original size---------------4*(16km2)-----64 Km2----------- > 8 km by 8 Km
Therefore
3km----------------------------- 1 sec
(8km-4km)---------------------x
X=4/3=1.33 sec
The answer is D) 1.33 sec

7. Find the inverse of the function.
f(x) = the cube root of quantity x divided by seven. - 9
to solve, replace f(x) with y , switch x and y, solve for y and replace y with f⁻¹(x)

f(x)=((x/7)-9) ^(1/3)
replace f(x) with y
y=((x/7)-9) ^(1/3)
switch x and y
x=((y/7)-9) ^(1/3)
solve for y
x^3=((y/7)-9)
x^3+9=y/7
y=7(x^3+9)
the answer is C) f-1(x) = 7(x3 + 9)  

8. Describe how the graph of y= x2 can be transformed to the graph of the given equation.y = (x - 14)2 – 9

using a graphical tool     see the attachment  the answer is C) Shift the graph of y = x2 right 14 units and then down 9 units  

9. Describe how to transform the graph of f into the graph of g. f(x) = alt='square root of quantity x minus nine.' and g(x) = alt='square root of quantity x plus five. '

f(x)=(x-9) ^1/2  g(x)=(x+5) ^1/2 
using a graphical tool     see the attachment

the answer is C) Shift the graph of f left 14 units

10. If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact.
f(x) = -16x5 - 7x4 – 6
The answer is B) Degree: 5; leading coefficient: -16

11. Write the quadratic function in vertex form.y = x2 + 4x + 7 

Complete the square on the right side of the equation
Use the form ax2+bx+cax2+bx+c, to find the values of a, b, and c.
a=1,b=4,c=7
Consider the vertex form of a parabola.
a(x+d)2+e
Find the value of dd using the formula d=b/2a
d=4/(2*1)=2
Find the value of e using the formula e=c−b2/4a
e=7−4=3
Substitute the values of a, d, and e into the vertex form a(x+d)2+e
(x+2)2+3
The answer is A) y = (x + 2)2+ 3

12. Find the zeros of the function.
f(x) = 3x3 - 12x2 - 15x
using a graphical tool   (see the attachment)x1=-1
x2=0
x3=5
The answer is C) 0, -1, and 5

13. Find a cubic function with the given zeros.7, -3, 2
X1=7
X2=-3
X3=2
f(x)=(x-7)(x+3)(x-2)=(x2-4x-21)(x-2)=x3-6x2-13x+42
the answer is C) f(x) = x3 - 6x2 - 13x + 42  

14. Find the remainder when f(x) is divided by (x - k).f(x) = 7x4 + 12x3 + 6x2 - 5x + 16; k = 3 
 f(x)=7(3)4+12(3)3+6(3)2-5(3)+16=946
  The answer is the B) 946

15.  Use the Rational Zeros Theorem to write a list of all potential rational zerosf(x) = x3 - 10x2 + 4x - 24

The constant term of () is -24

 The leading coefficient is 1.

We have to only consider the factors of the constant (leading coefficient = 1)

The factors are 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 12, -12, 24, -24

The answer is A) ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24

6 0
3 years ago
If y=3x 2 find the value of y when x=-3
Sholpan [36]
Y=3(-3) x 2
y= -9 x 2
y=-18
.............
3 0
3 years ago
WILL GIVE BRAINLIEST TO BEST RESPONSE!
Monica [59]

You are given the X value, replace x with 2 in the first equation to solve for y:

y=2x +3

y = 2(2) +3

y = 4+3

y = 7

Now replace y with 7 and x iwth 2 in the second equation and solve for k:

y = -x +k

7 = -2 +k

Add 2 to both sides:

9 = k

so k = 9

The point is given as k-2, which is 9-2 = 7, which is what y equals in the first equation.

K = 9

5 0
3 years ago
Brianna wants to buy a digital camera for a photography class. One store offers the camera for $53 down and a payment plan of $1
Basile [38]

Answer:

The second store is cheaper in 12 months.

Step-by-step explanation: do 53+19(12), which is 281 for store one at 12 months. Do 73+15(12), which is 253 at 12 months. If you compare it, the second store is cheaper

7 0
3 years ago
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