All categories

1 year ago

The graph shows the quadratic function f, and the table shows the quadratic function g.

1 answer:

6 0

Analyzing the quadratic functions, it is found that the correct option is D. The functions f and g have the same axis of symmetry, but the minimum value of f is less than the minimum value of g.

<h3>How to analyze the function?</h3>

Looking at the graph, Function f has a minimum value of 1 at x = -3. Hence, the axis of symmetry is x = -3.

Function g has a minimum value of 6 at x = -3. Hence, the axis of symmetry is also x = -3.

Therefore, the functions f and g have the same axis of symmetry, but the minimum value of f is less than the minimum value of g.

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For which system of equations is (5, 3) the solution? A. 3x – 2y = 9 3x + 2y = 14 B. x – y = –2 4x – 3y = 11 C. –2x – y = –13 x

Alla [95]

The correct answer is:

D) $\left \{ {{2x-y=7} \atop {2x+7y=31}} \right.$ .

Explanation:

We solve each system to find the correct answer.

For A:
$\left \{ {{3x-2y=9} \atop {3x+2y=14}} \right.$

Since we have the coefficients of both variables the same, we will use elimination to solve this.

Since the coefficients of y are -2 and 2, we can add the equations to solve, since -2+2=0 and cancels the y variable:
$\left \{ {{3x-2y=9} \atop {+(3x+2y=14)}} \right. 
\\
\\6x=23$

Next we divide both sides by 6:
6x/6 = 23/6
x = 23/6

This is not the x-coordinate of the answer we are looking for, so A is not correct.

For B:
$\left \{ {{x-y=-2} \atop {4x-3y=11}} \right.$

For this equation, it will be easier to isolate a variable and use substitution, since the coefficient of both x and y in the first equation is 1:
x-y=-2

Add y to both sides:
x-y+y=-2+y
x=-2+y

We now substitute this in place of x in the second equation:
4x-3y=11
4(-2+y)-3y=11

Using the distributive property, we have:
4(-2)+4(y)-3y=11
-8+4y-3y=11

Combining like terms, we have:
-8+y=11

Add 8 to each side:
-8+y+8=11+8
y=19

This is not the y-coordinate of the answer we're looking for, so B is not correct.

For C:
Since the coefficient of x in the second equation is 1, we will use substitution again.

x+2y=-11

To isolate x, subtract 2y from each side:
x+2y-2y=-11-2y
x=-11-2y

Now substitute this in place of x in the first equation:
-2x-y=-13
-2(-11-2y)-y=-13

Using the distributive property, we have:
-2(-11)-2(-2y)-y=-13
22+4y-y=-13

Combining like terms:
22+3y=-13

Subtract 22 from each side:
22+3y-22=-13-22
3y=-35

Divide both sides by 3:
3y/3 = -35/3
y = -35/3

This is not the y-coordinate of the answer we're looking for, so C is not correct.

For D:
Since the coefficients of x are the same in each equation, we will use elimination. We have 2x in each equation; to eliminate this, we will subtract, since 2x-2x=0:

$\left \{ {{2x-y=7} \atop {-(2x+7y=31)}} \right. 
\\
\\-8y=-24$

Divide both sides by -8:
-8y/-8 = -24/-8
y=3

The y-coordinate is correct; next we check the x-coordinate Substitute the value for y into the first equation:
2x-y=7
2x-3=7

Add 3 to each side:
2x-3+3=7+3
2x=10

Divide each side by 2:
2x/2=10/2
x=5

This gives us the x- and y-coordinate we need, so D is the correct answer.

7 0

3 years ago

Which function is increasing at the highest rate? A. B. A linear function on a coordinate plane passes through (minus 1, 3), and

xenn [34]

The highest rate on increasing is of 12x -6y = -24; Option B is the correct answer.

The options are given in the image attached with the answer

<h3>What is a Function ?</h3>

A function is a law that relates a dependent variable and an independent variable.

It is asked among the options given , which is increasing at the highest rate.

To increase at a rate , the value of the slope , m should be > 0

For the Option 1

for a straight line function , the slope is given by

m = ( y₂ -y₁)/(x₂-x₁)

m = ( -3 -3)/(2- (-1)) = -6 /3 = -2

Therefore the function is decreasing

For Option 2

12x - 6y = -24

-6y = -12x -24

y = 2x +4

m = 2 (increasing)

For option 3

m = (-4 + 5)/(2-1) = 1

For Option 4

(8,0) (0,-4)

m = (-4 -0) /(0-8) = 4/8 = 1/2

The highest rate on increasing is of 12x -6y = -24

Therefore Option B is the correct answer.

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6 0

2 years ago

I’m trying to get this math test done, can I please have some help?

Sati [7]

Answer: B

Step-by-step explanation:

If you use slope-intercept form, you can see that B uses the equation y = 5x - 4, and you can also see that it is linear since it is proportional. The only coordinate plane that has a nonlinear line is D.

5 0

2 years ago

A.) SSS B.) AAS C.) ASA D.) SAS

Vlada [557]

Side BC is congruent to side BC.

Using the congruent angles and the angle bisectors, you can get two angles congruent to two other angles, so you use ASA to prove the triangles congruent. Then you use CPCTC to prove the sides congruent.

Answer: C.) ASA

7 0

3 years ago

38. Evaluate f (3x +4y)dx + (2x --3y)dy where C, a circle of radius two with center at the origin of the xy

lina2011 [118]

It looks like the integral is

$\displaystyle \int_C (3x+4y)\,\mathrm dx + (2x-3y)\,\mathrm dy$

where C is the circle of radius 2 centered at the origin.

You can compute the line integral directly by parameterizing C. Let x = 2 cos(t ) and y = 2 sin(t ), with 0 ≤ t ≤ 2π. Then

$\displaystyle \int_C (3x+4y)\,\mathrm dx + (2x-3y)\,\mathrm dy = \int_0^{2\pi} \left((3x(t)+4y(t))\dfrac{\mathrm dx}{\mathrm dt} + (2x(t)-3y(t))\frac{\mathrm dy}{\mathrm dt}\right)\,\mathrm dt \\\\ = \int_0^{2\pi} \big((6\cos(t)+8\sin(t))(-2\sin(t)) + (4\cos(t)-6\sin(t))(2\cos(t))\big)\,\mathrm dt \\\\ = \int_0^{2\pi} (12\cos^2(t)-12\sin^2(t)-24\cos(t)\sin(t)-4)\,\mathrm dt \\\\ = 4 \int_0^{2\pi} (3\cos(2t)-3\sin(2t)-1)\,\mathrm dt = \boxed{-8\pi}$

Another way to do this is by applying Green's theorem. The integrand doesn't have any singularities on C nor in the region bounded by C, so

$\displaystyle \int_C (3x+4y)\,\mathrm dx + (2x-3y)\,\mathrm dy = \iint_D\frac{\partial(2x-3y)}{\partial x}-\frac{\partial(3x+4y)}{\partial y}\,\mathrm dx\,\mathrm dy = -2\iint_D\mathrm dx\,\mathrm dy$

where D is the interior of C, i.e. the disk with radius 2 centered at the origin. But this integral is simply -2 times the area of the disk, so we get the same result: $-2\times \pi\times2^2 = -8\pi$ .

3 0

2 years ago