Karen, Trey, and Dante have a total of 75 in their wallets. Karen has 5 more than Trey. Dante has 2 times what Karen has. How much do they have in their wallets?

[tex]\text{Given that,}\\\\f(x) = x^3+ax^2-7x+b \\\\\text{Since}~ (x+2)~ \text{and}~ (x-3)~ \text{are factors of f(x),}\\\\f(-2) = 0 ~ \text{and}~ f(3)=0\\\\\\ \text{Now,}\\\\f(-2)=0\\\\\ \implies (-2)^3+a(-2)^2-7(-2)+b =0\\\\\implies -8 +4a +14+b =0\\\\\implies 4a +b +6 =0~~~....(i)\\\\\\f(3) = 0\\\\\implies 3^3+a(3^2) -7(3) +b =0\\\\\implies 27 +9a -21 +b =0\\\\\implies 9a +b +6 =0~~....(ii)\\\\\\(ii)-(i):\\\\9a+b+6 - 4a-b - 6 = 0\\\\\implies 5a =0\\\\\implies a = 0\\[/tex]

[tex]\text{Substitute a=0 in equation (i):}\\\\4(0) +b +6 =0\\\\\implies b+6 =0\\\\\implies b =-6\\\\\text{Hence, a = 0 and}~ b =-6[/tex]

Answer:

14,001

Step-by-step explanation:

old machine: 1,100+.12x

new machine: 1,520+.09x

if you plug in 14,000 for x, you get

old machine: 2,780

new machine: 2,780

therefore, you need 1 over 14,000 for it to be worth it because

if you plug in 14,001 for x, you get

old machine: 2,780.12

new machine: 2,780.09

which makes the new machine $.03 cheaper at this point (and the more snaps attached, the more the new machine will be worth it)

hope this helps!

In attachment I have answered this problem.

The value of x {0 < x < (π/2)} satisfying (cos x / cosec x + 1) + (cos x / cosec x-1) = 2 ​is x = π/4.

Since cos x /(cosec x + 1) + cos x /(cosec x - 1) = 2 ​

Taking the L.C.M (cosecx + 1)(cosecx - 1), we have

[cosx(cosecx - 1) + cosx(cosecx + 1)]/(cosecx + 1)(cosecx - 1) = 2

[cosxcosecx - cosx + cosxcosecx + cosx]/(cosec²x - 1²) = 2

[cosx/sinx - cosx + cosx/sinx + cosx]/(cosec²x - 1²) = 2

[cotx - cosx + cotx + cosx]/(cosec²x - 1) = 2

collecting like terms, we have

[cotx + cotx + cosx - cosx ]/(cosec²x - 1) = 2

[2cotx + 0]/(cosec²x - 1) = 2

2cotx/(cosec²x - 1) = 2

cotx/(cosec²x - 1) = 1

Since cot²x + 1 = cosec²x ⇒ cot²x = cosec²x - 1

So, cotx/(cosec²x - 1) = 1

cotx/cot²x = 1

1/cotx = 1

tanx = 1

Taking inverse tan of both sides, we have

x = tan⁻¹(1)

x = 45°

x = 45 × π/180

x = π/4

So, the value of x {0 < x < (π/2)} satisfying (cos x / cosec x + 1) + (cos x / cosec x-1) = 2 ​is x = π/4.

Learn more about trigonometric equations here:

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Answer:

y > - x - 4

Step-by-step explanation:

1) Find the equation of the line

2) The equation of the line is y = - x - 4

3) Identify where the graph is shaded

4) It is shaded above and to the right of the line

5) This means that it is more positive/ greater than the unshaded areas

6) Switch the = sign to > to signify the inequality

7) All done!

Step-by-step explanation:

the delimiter line is going through the points (-4, 0) and (0, -4).

the line function

y = mx + b

m is the slope of the line, b is the y-intercept (the y value when x = 0).

the slope is the ratio of "y coordinate change / x coordinate change" when going from one point to another.

so, for the 2 found points :

x changes by +4 (from -4 to 0)

y changes by -4 (from 0 to -4).

the slope m is then

-4/+4 = -1

and the y-intercept is -4 (as explained).

so, the line is

y = -x - 4

and the graphic says that all values greater than our equal to the line values are valid, so

y >= -x - 4

Answer:

carbon take x(1)+4(-2)=0

x(1)-8=0

x(1)=8

x=8

Answer:

Try this on for size

Step-by-step explanation:

Based on the total of intervals vs the number of intervals Amy attended her CA percentage is 75%

The CA percentage measures the commitment of an employee to be logged in during the intervals that were assigned to him/her to work.

In this way, the CA percentage is equal to 100% if the employee worked as scheduled. Moreover, this percentage can be affected by factors such as:

In the case of Amy, there is a total of 12 intervals and it is known:

Based on this information, let's calculate her CA:

Learn more about percentage in: https://brainly.com/question/8011401

Answer:

$8x + $12y = $120

Step-by-step explanation:

x = amount of juice

y = amount of pizza

$120 = his total money

Answer:

[tex]\left \{ {{y=-2} \atop {x=3}} \right.[/tex]

Step-by-step explanation:

[tex]\left \{ {{-6x - y = -16} \atop {-6x - 5y = -8}} \right. <=> \left \{ {{4y= -8} \atop {-6x-5y =-8}} \right. <=> \left \{ {{y=-2} \atop {-6x-5y=-8}} \right. <=> \left \{ {{y=-2} \atop {-6x-5*(-2)=-8}} \right. <=> \left \{ {{y=-2} \atop {-6x=-18}} \right. <=> \left \{ {{y=-2} \atop {x=3}} \right.[/tex]

Answer:

y=7

Step-by-step explanation:

Answer:

Freezer B has 8 more cubic feet than Freezer A.

Step-by-step explanation:

Volume of Freezer A = 8 * 4 * 2 = 64 ft^3.

Volume of Freezer B = 6 * 4 * 3 = 72 ft^3.

72 - 64 = 8 ft^3.

Answer:

Freezer B has 8 more cubic feet than Freezer A.

Step-by-step explanation:

Answer:

ddd

Step-by-step explanation:

Answer:

y=1x-2

Step-by-step explanation:

Well this one is already given

When x=0, it's the y intercept

and it gives the slope, so we got it :D

Answer:

y=x-2

Step-by-step explanation:

y-y1=m(x-x1)

y-(-2)=1(x-0)

y+2=1(x)

y+2=x

y=x-2

Answer: 34/100

Step-by-step explanation:

it is 34% out of 100, so it is 34/100. Reduced is 17/50

Answer:

Step-by-step explanation:

=> x + 3x + 3y + 3z = 21

=> 4x + 3y + 3z = 21

=> 4x + 3y + 3z - 3y = 21 - 3y

=> 4x + 3z = 21 - 3y

=> 4x + 3z - 3z = 21 - 3y - 3z

=> 4x = 21 - 3y - 3z

[tex] = > \frac{4x}{4} = \frac{21 - 3y - 3z}{4} [/tex]

[tex] = > x = \frac{21 - 3y - 3z}{4} (ans)[/tex]

Given :

To Find :

Solution :

[tex]\qquad { \dashrightarrow \: { \sf{x + 3x + 3y + 3z = 21}}}[/tex]

Adding the like terms :

[tex]\qquad { \dashrightarrow \: { \sf{4x + 3y + 3z = 21}}}[/tex]

Transposing 3y to the other side which then becomes negative :

[tex]\qquad { \dashrightarrow \: { \sf{4x + 3z = 21 - 3y}}}[/tex]

Now, Transposing 3z to the other side which then becomes negative :

[tex]\qquad { \dashrightarrow \: { \sf{4x = 21 - 3y - 3z}}}[/tex]

Dividing both sides by 4 :

[tex]\qquad { \dashrightarrow \: { \sf{ \dfrac{4x}{4} = \dfrac{21 - 3y - 3z}{4} }}}[/tex]

[tex]\qquad { \dashrightarrow \: { \sf{{x} = \dfrac{21 - 3y - 3z}{4} }}}[/tex]

Therefore, the value of x = 21 – 3y – 3z/4

Answer:

WT = 63

Step-by-step explanation:

Given Δ SDE is similar to Δ SWT then the ratio of corresponding sides are in proportion, that is

[tex]\frac{WT}{DE}[/tex] = [tex]\frac{ST}{SE}[/tex] , substitute values

[tex]\frac{5x+3}{56}[/tex] = [tex]\frac{4x-3}{40}[/tex] ( cross- multiply )

56(4x - 3) = 40(5x + 3) ← distribute parenthesis on both sides

224x - 168 = 200x + 120 ( subtract 200x from both sides )

24x - 168 = 120 ( add 168 to both sides )

24x = 288 ( divide both sides by 24 )

x = 12

Then

WT = 5x + 3 = 5(12) + 3 = 60 + 3 = 63

Answer:y=12 x=00

Step-by-step explanation:

you can not

The required equation that represents the graph is y = x + 30

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

The standard linear equation is given as y = mx + b

Where,

m is the slope

b is the y-intercept

Using the coordinates (20, 50) and (40, 70)

Get the slope of the line:

m = 70-50/40-20

m = 20/20

m = 1

Since the line cuts the y-axis at y = 30, hence the y-intercept is 30.

Therefore, the Required equation that Shows the graph is y = x + 30

Learn more about linear equations here:

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#SPJ2

Answer:

elga is 32 and alvin is 49

Answer:

it is A bacause the fractions for that one are correct

Step-by-step explanation:

Answer:

C 43

Step-by-step explanation:

happy holidays

Answer:

Since the two triangles are similar, the two medians AC and FH are in proportion. The proportionality rate is [tex]k=\frac{48}8=6[/tex]. That is the same ratio of the sides., so AD is k times the corresponding side FG, or [tex]\overline {AD} = k\overline{FG} = 6\times 9 = 63[/tex]

Answer: It is D

Step-by-step explanation:

[tex]\\\\\\x^2 -8x +16 = 0\\\\\implies x^2 - 2(4) + 4^2 =0\\\\\implies (x-4)^2 =0\\\\\implies x -4 =0\\\\\implies x =4\\\\\text{This equation has only one solution.}[/tex]

Answer: ooo ok i got it. it is nice

Answer:

Step-by-step explanation:

Parallel lines have identical slopes

y = 3x + b

add in the desired point

10 = 3(2) + b

b = 4

B.  y = 3x + 4

Answer:

1) -3/4

2) (6, 0), (0, -4)

3) connect (0,-2) and (8,0) together

Step-by-step explanation:

1) (-2) - (-5) / (-1) - 3 = -3/4

2) x = 0 -3y=12 y = -4, y= 0 2x =  12 x = 6, x intercept = (6, 0) y intercept = (0, -4)

3) x - 4y = 8 this could be written as y = x/4 - 2 and y intercept is (0, -2) and x intercept is (8, 0) so connect these points together and make a line

#1

#2

Inetercept form x/a+y/b=1

x inetercept at 6 and y intercect at -4

#3

Graph attached

[tex]\dfrac{\sqrt[3]{343}}{\sqrt[3]{-343}}=\dfrac{\sqrt[3]{343}}{-\sqrt[3]{343}}=-1[/tex]

Answer:

Look at images below ^^

Step-by-step explanation:

I'm not sure if they are correct, since I'm not there yet. But I hope it's correct.

Answer:

Area = 4x^2 + 12x + 9

Perimeter = 8x + 12

Step-by-step explanation: