From the information in the graph, which team showed the least amount of improvement over last year?


A.
Jets


B.
Bears


C.
Colts


D.
Rangers

Answer:

[tex]x_{1} = -1 - \sqrt{\frac{2}{3}}  ; x_{2} = -1 +\sqrt{\frac{2}{3}}[/tex]

Step-by-step explanation:

-6x -1 + 5x² = 8x²     Move all terms to the right-hand side

0 = 8x² - 5x² + 6x +1     Combine like terms

3x² + 6x + 1 = 0

Apply the quadratic formula

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

a = 3; b = 6; y = 1

[tex]x = \frac{-6\pm\sqrt{6^2 - 4\times 3 \times1}}{2\times 3}[/tex]

[tex]x = \frac{-6\pm\sqrt{36-12}}{6}[/tex]

[tex]x = \frac{-6\pm\sqrt{24}}{6}[/tex]

[tex]x = \frac{-6\pm \sqrt{4\times6}}{6}[/tex]

[tex]x = \frac{-6\pm 2\sqrt{2}}{6}[/tex]

[tex]x = -1 \pm \sqrt{\frac{2}{3}}[/tex]

[tex]x_{1} = -1 +\sqrt{\frac{{2}}{3}}; x_{2} = 1 -\sqrt{\frac{{2}}{3}}[/tex]

The graph below shows the roots at x₁ =-1.816 and x₂ = -0.184.

To convert the slope-intercept form of a line, y = 6x - 4, to standard form, subtract 6x from both sides of the equation. The resulting standard form is -6x + y = -4.

You asked about writing the equation y = 6x - 4 in standard form. The standard form for the equation of a line in mathematics is usually given as Ax + By = C, where A, B, and C are constants, and A should ideally be a positive integer. To convert the given equation into standard form, we want to rearrange it so that both x and y are on the same side of the equation and the constant is on the other side.

Here are the steps to convert y = 6x - 4 to standard form:

Therefore, the standard form of the equation is -6x + y = -4.

Answer:

the segment that states the radius is AC.

Step-by-step explanation:

Final answer:

Mr. Jimerson will earn $27.60 per hour after receiving a 15% raise on his original $24 per hour salary, resulting in a $3.60 increase per hour.

Explanation:

Mr. Jimerson earns $24 per hour working and qualifies for a 15% raise in salary. To calculate his new hourly salary after the raise, first determine the amount of the raise by finding 15% of his current hourly wage. Since 15% can be written as 0.15, we multiply his current wage by 0.15 to find the raise amount.

0.15 × $24 = $3.60

Next, add this raise amount to his original hourly wage to find his new salary:

$24 + $3.60 = $27.60 per hour

Therefore, Mr. Jimerson's salary after the raise will be $27.60 per hour.

The calculation shows that 13 crates weigh 170 pounds less than 15 crates.

To find out how much less 13 crates of apples weigh than 15 crates of apples, we need to first determine the weight of the two different amounts of crates.

We know that one crate weighs 85 pounds.

So, for 15 crates, we multiply 15 by 85 to get the total weight:

= 15 crates x 85 pounds per crate = 1275 pounds

Next, we calculate the weight for 13 crates:

= 13 crates x 85 pounds per crate = 1105 pounds

Now, we subtract the weight of 13 crates from the weight of 15 crates:

= 1275 pounds - 1105 pounds = 170 pounds

Therefore, 13 crates of apples weigh 170 pounds less than 15 crates of apples.

Answer:

2550 m  

Step-by-step explanation:

Change in elevation = 400 – (-2150)

Change in elevation = 400 + 2150

Change in elevation = 2550 m

Answer:

x=9

Step-by-step explanation:

These two angles are equal because they are corresponding angles and the two lines are parallel.

13x-7 = 11x+11

Subtract 11x from each side

13x-11x -7 = 11x-11x+11

2x-7 = 11

Add 7 to each side

2x-7+7 = 11+7

2x = 18

Divide each side by 2

2x/2 = 18/2

x =9

Answer:

All the real numbers between [tex]\pm 90^\circ[/tex] including [tex]\pm 90^\circ[/tex].

Step-by-step explanation:

T(p) models the average yearly temperature based on degree latitude of the location.

Since the lines of latitude runs from East to West and extending from [tex]-90^\circ[/tex] to [tex]+90^\circ[/tex], they can be included in the domain.

Also, the degrees of latitude can be fractional units, positive units, or negative units. Therefore, the domain appropriate for this function is All the real numbers between [tex]\pm 90^\circ[/tex] including [tex]\pm 90^\circ[/tex].

Answer:

D = all real numbers between ± 90, inclusive

Step-by-step explanation:

Degrees of latitude can be fractional units, positive units, or negative units.

Answer:

3x = t and it costs 15 dollars in total with x = 5.

Step-by-step explanation:

The 3 represents her friends and x represents the cost of one ticket. The variable t represents the total cost or tickets. If x equals 5, then it would be 15 because of 3x.  

Hope it helps :)

Answer:$52.50

Step-by-step explanation:

Hi There!

--------------------------------------------

Remember to follow PEMDAS.

--------------------------------------------

Problem #1:

= (25 - 6.25) + (5 · 3)²

= (18.75) + (15)²

= 18.75 + 225

= 243.75

--------------------------------------------

Problem #2:

= (8 + 3)² + 10 · (-4)

= (11²) + 10 · (-4)

= 121 + 10 · (-4)

= 121 + (-40)

= 81

--------------------------------------------

Hope This Helps :)

Hello,

So Y variable is what you would start with.

20 <= he'll start off with for a

40 <= what he'll start off with for b

And X variables would be the # of hours you're working.

10 <= meaning every hour worked is worth 10 dollars

5 <= meaning every hour worked will be paid 5 dollars

So let's just say for option a he works two hours

(Option A)

10 (2) + 20

20 + 20

= 40

(Option B)

5 (2) + 40

10 + 40

50

As for your equations

Y = 10x + 40

Y= 5x + 40

Answer:

Converse of triangle proportionality theorem

Step-by-step explanation:

We are given that in a triangle ABC, D and E are some points in AB and AC respectively.

D and E divide AB and AC such that

AD/DB =AE/DC

To prove that DE is parallel to third side BC>

This can be proved using converse of triangle proportionality theorem

REcollect the triangle proportionality theorem that

If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion

So converse is is a line intersects the other sides make proportional intercepts then the line is parallel to the third side.

Answer:

The answer is Converse of the Pythagorean theorem

Step-by-step explanation:

Answer:

y = [tex]\frac{96}{5}[/tex]

Step-by-step explanation:

given that y and x are proportional then the equation relating them is

y = kx ← k is the constant of proportionality

to find k use the given condition y = 12 when x = 5

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{12}{5}[/tex]

y = [tex]\frac{12}{5}[/tex] x ← equation of proportionality

when x = 8, then

y = [tex]\frac{12}{5}[/tex] × 8 = [tex]\frac{96}{5}[/tex]

Since you already know that two of the sides equal 10.8 mi which concludes to an isosceles triangle you'll add them which comes to 21.6 and lastly you just subtract 31 from 21.6 which is 9.4

Answer:

(4,2)

Step-by-step explanation:

Answer:

she would have to pay 42 dollars for 14 rides

so $3 for each ride 3* 14 is 42 or just add 3, 14 times

Answer:

q1 = 3x^2 + 6x + 16

Step-by-step explanation:

2 || 3    0     4    -  32

           6    12       32

========================

     3    6    16         0

q(x) + r(x)/(x - 2)

r(x) = 0

q(x) = 3x^2 + 6x + 16

This does not factor down any further unless you have take complex number. The only real root isw

x = 2

Just in case you have done complex numbers

x2 = -1 + 2.0817i

x3 = -1 - 2.0817i

Answer:

Yes, x + 12

Step-by-step explanation:

Simplify the following:

3 x - 2 x + 12

Grouping like terms, 3 x - 2 x + 12 = (3 x - 2 x) + 12:

(3 x - 2 x) + 12

3 x - 2 x = x:

Answer: x + 12

Answer:

Yes, it is.

Step-by-step explanation:

3x + 12 - 2x =

Use the commutative property of addition to change the order of the addition.

= 12 + 3x - 2x

Use the distributive property of addition over multiplication in reverse (which is factoring).

= 12 + x(3 - 2)

Do the operation: 3 - 2 = 1

= 12 + x * 1

Simplify x * 1 to just x.

= 12 + x

Use the commutative property of addition.

= x + 12

There you have x + 12 from 3x + 12 - 2x by using properties and operations.

Answer:

f(2) = 0

Step-by-step explanation:

Evaluate the function at x = 2.

f(x) = -3x^2 + 6x

f(2) = -3(2^2) + 6 * 2

f(2) = -3(4) + 12

f(2) = 0

Answer:

2, 240

Step-by-step explanation:

In the table, the values should be

Year 1   725  

Year 2   579

Year 3   696

Since Year 4 sold 112% of the previous 3 years combined, we add 725+579+696=2000. We can find 112% by writing a proportion.

[tex]\frac{112}{100} =\frac{x}{2000}[/tex]

We solve through cross multiplication of numerator and denominator of the opposite fraction.

[tex]112(2000)=100(x)\\224000=100x\\2,240=x[/tex]

Answer:

A) -56

Step-by-step explanation:

B) First, you have to ignore the plus sign, and recognize that the second negative number means you are subtracting that number.

If this is correct, please like the comment so others can know, too!

Answer:

0 solutions

Step-by-step explanation:

same slope, different y intercepts so they never intersect

Answer:

As both slopes are equal, and the values of b are different it means that the two lines are parallel and the system of equations does not have any solution. (Please see the picture below)

Step-by-step explanation:

1. First write the system of equations:

[tex]y=6x+2[/tex]

[tex]3y-18x=12[/tex]

2. Solve y for the second equation:

[tex]3y-18x=12[/tex]

[tex]3y=18x+12[/tex]

[tex]y=\frac{18x+12}{3}[/tex]

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

3. Re write both equations in the form y=mx+b, where m is the slope and b is the value of y when x=0 :

[tex]y=6x+2[/tex]

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

As both slopes are equal, and the values of b are different it means that the two lines are parallel and the system of equations does not have any solution.

Answer:

x=2.49

Step-by-step explanation:

3(x−0.50)=5.97

Distribute the 3

3x - 3*.5 = 5.97

3x -1.5 = 5.97

Add 1.5 to each side

3x -1.5+1.5 = 5.97+1.5

3x = 7.47

Divide each side by 3

3x/3 = 7.47/3

x=2.49

Answer:

≈ $2.92 per visit

Step-by-step explanation:

10 times each month

so 12 months = 12 x 10 = 120

an annual fee of $350

$350 / 120 ≈ $2.92

Answer:

[tex]\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1[/tex]

Step-by-step explanation:

we are given

[tex]\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1[/tex]

we can simplify left side and make it equal to right side

we can use trig identity

[tex]sin(3a)=3sin(a)-4sin^3(a)[/tex]

[tex]cos(3a)=4cos^3(a)-3cos(a)[/tex]

now, we can plug values

[tex]\frac{(3sin(a)-4sin^3(a))-(4cos^3(a)-3cos(a))}{sin(a)+cos(a)} [/tex]

now, we can simplify

[tex]\frac{3sin(a)-4sin^3(a)-4cos^3(a)+3cos(a)}{sin(a)+cos(a)} [/tex]

[tex]\frac{3sin(a)+3cos(a)-4sin^3(a)-4cos^3(a)}{sin(a)+cos(a)} [/tex]

[tex]\frac{3(sin(a)+cos(a))-4(sin^3(a)+cos^3(a))}{sin(a)+cos(a)} [/tex]

now, we can factor it

[tex]\frac{3(sin(a)+cos(a))-4(sin(a)+cos(a))(sin^2(a)+cos^2(a)-sin(a)cos(a)}{sin(a)+cos(a)} [/tex]

[tex]\frac{(sin(a)+cos(a))[3-4(sin^2(a)+cos^2(a)-sin(a)cos(a)]}{sin(a)+cos(a)} [/tex]

we can use trig identity

[tex]sin^2(a)+cos^2(a)=1[/tex]

[tex]\frac{(sin(a)+cos(a))[3-4(1-sin(a)cos(a)]}{sin(a)+cos(a)} [/tex]

we can cancel terms

[tex]=3-4(1-sin(a)cos(a))[/tex]

now, we can simplify it further

[tex]=3-4+4sin(a)cos(a))[/tex]

[tex]=-1+4sin(a)cos(a))[/tex]

[tex]=4sin(a)cos(a)-1[/tex]

[tex]=2\times 2sin(a)cos(a)-1[/tex]

now, we can use trig identity

[tex]2sin(a)cos(a)=sin(2a)[/tex]

we can replace it

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

so,

[tex]\frac{sin(3a)-cos(3a)}{sin(a)+cos(a)} =2sin(2a)-1[/tex]

Answer:

To prove : sin(3a)-cos(3a)/sin(a)+cos(a) = 2sin(2a)-1                                      

Step-by-step explanation:

\frac{\sin3a-\cos3a}{\sin a+\cos a}=2\sin 2a-1\\\cos3a=4\cos^{3}a-3\cos a\\\sin 3a=3\sin a-4\sin ^{3}a\\substituting the value, we get\\L.H.S= \frac{3\sin a-4\sin ^{3}a-[4\cos ^{3}a-3\cos a]}{\sin a+\cos a}\\\frac{3(\sin a+\cos a)-4(\sin ^{3}a+4\cos ^{3}a)}{\sin a+\cos a}\\\frac{3(\sin a+\cos a)-4[(\cos a+\sin a)(\cos ^{2}a+\sin ^{2}a-\sin a\cos a)]}{\sin a+\cos a}\\\frac{3(\sin a+\cos a)-4[(\cos a+\sin a)(1-\sin a\cos a)]}{\sin a+\cos a}\\\frac{(\sin a+\cos a)[3-4(1-\sin a\cos a)]}{\sin a+\cos a}\\\frac{(\sin a+\cos a)[3-4+4\sin a\cos a]}{\sin a+\cos a}\\\frac{(\sin a+\cos a)(-1+4\sin a\cos a)}{\sin a+\cos a}\\-1+4\sin a\cos a\\-1+2\sin 2a\\2\sin 2a-1=R.H.S

Since, sin(2a)= 2sin(a)cos(a)

2sin(2a)= 4sin(a)cos(a)

Answer:

aproximatley 6 units

Step-by-step explanation: