. Alex received a statement from his bank that listed his checking account total balance as -$42.50. What does this number mean?

The bank owes Alex $42.50.

O Alex wrote checks for $42.50 more than the amount he had in his checking account.

O Alex is still able to write checks up to a total of $42.50.

O The bank deleted $42.50 from Alex's checking account​

Answer:

Step-by-step explanation:

You want the values of three expenditures, given three relations between them.

(The first thing to realize is that the question isn't about averages at all. It is about values that are described as averages.)

Let f, j, c represent the (average) amounts spent on flowers, jewelry, and gift certificates, respectively. The three given relations are ...

  f + j + c = 53.42

  j = 4.40 + c

  f + c = 15.58 + j

Using the second equation to substitute for j in the third, we have ...

  f +c = 15.58 +(4.40 +c)

  f = 19.98 . . . . . . . . . . . . . . simplify

Using this and the second equation to substitute into the first, we have ...

  19.98 +(4.40 +c) +c = 53.42

  24.38 +2c = 53.42

  2c = 29.04

  c = 14.52

Then ...

  j = 4.40 +c = 4.40 +14.52 = 18.92

The average expenditures are ...

__

Additional comment

This solution is one of many ad hoc methods that could be used. There are also graphing and matrix methods available for solving a set of equations like this. The attachment shows a calculator matrix solution.

The simplified form of the function f(x) = (x² - 4x + 4) / (x² - 4) will be f(x) = (x - 2) / (x + 2).

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The function is given below.

f(x) = (x² - 4x + 4) / (x² - 4)

Simplify the equation, then we have

f(x) = (x² - 4x + 4) / (x² - 4)

f(x) = (x - 2)² / [(x - 2)(x + 2)]

f(x) = (x - 2) / (x + 2)

The simplified form of the function f(x) = (x² - 4x + 4) / (x² - 4) will be f(x) = (x - 2) / (x + 2).

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Answer: 4/9

Step-by-step explanation:

[tex]\displaystyle\\(\frac{27}{8} )^{-\frac{2}{3}} =\\\\(\frac{3*3*3}{2*2*2})^{-\frac{2}{3}}=\\\\ (\frac{3^3}{2^3} )^{-\frac{2}{3}} =\\\\((\frac{3}{2})^3)^{-\frac{2}{3} } =\\\\(\frac{3}{2})^{-\frac{3*2}{3}} =\\\\(\frac{3}{2})^{-2}=\\\\(\frac{2}{3})^2 \\\\\frac{2^2}{3^2} =\\\\\frac{4}{9}[/tex]

Answer:

(4,-4)

is the way from AtoB

Answer:11/15

Step-by-step explanation:

you have to change them to common denominators.

i chose 15.

to make the denominator for 1/3 into 15 you have to multiply it by 5 which means you have to multiply the numerator (1) by the same thing which gives you 5/15

to make the denominator for 2/5 into 15 you have to multiply the denominator by 3 so you have to multiply the numerator (2) by the same thing which gives you 6/15

you now have the equation 5/15 + 6/15

to add them together you leave the bottom numbers the same and add the top ones which gives you 11/15

Answer:

0.7333333333333333 = 11/15

Step-by-step explanation:

1/3 = 5/15

2/5 = 6/15


add them, and now you get

(5+6)/15 = 11/15

Answer:

120

Step-by-step explanation:

call the number x,

then x+1090-450

so x+640=760

x=760-640

x=120

hope this works :)

Answer:

120 is the number u thought of first

Step-by-step explanation:

1090-450=640

if we add 120 into 1090

then it will be 1210

so 1210-450=760

The two values that serves as the root of the equation are  -1-√7 and  -1+√7

Given the quadratic equation below;

X² + 2X (-6) = 0

x^2 + 2x - 6 = 0

Using the general formula

x = -2±√2²-4(1)(-6)/2(1)

x = -2±√4+24/2

x = -2±√28/2

x =  -2±2√7/2

x = -1±√7

Hence the two values that serves as the root of the equation are  -1-√7 and  -1+√7

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1. Yes, the equation represent the proportionality relationship.

2. Yes, the unit rate of changes of y with respect to x is [tex]\frac{2}{3}[/tex].

3.Yes, The slope of the line is [tex]\frac{2}{3}[/tex]

Given a picture in that we can see a graph and 3 option.

We have to check weather that 3 option satisfy the equation and what are they.

Given equation [tex]y=\frac{2}{3}x[/tex]

1st option: Is the equation represent the proportionality relationship.

Yes, the equation represent the proportionality relationship.

If we see the proportionality rule that is

The equation y = kx represents a proportionate relationship between two quantities y and x that have the same proportionality constant, k.

A proportionate relationship exists if an equation in a different form can be rewritten as shown above.

Here, the equation is in the form of y=kx.

Therefore, Yes, the equation represent the proportionality relationship.

2nd option: the unit rate of changes of y with respect to x is [tex]\frac{2}{3}[/tex].

Yes, the unit rate of changes of y with respect to x is [tex]\frac{2}{3}[/tex].

The amount of change in y for a change of one unit in x is the unit rate of change of y with respect to x.

The slope is [tex]\frac{2}{3}[/tex].

Therefore, Yes, the unit rate of changes of y with respect to x is [tex]\frac{2}{3}[/tex].

3rd option: The slope of the line is [tex]\frac{2}{3}[/tex]

Yes, The slope of the line is [tex]\frac{2}{3}[/tex]

It is possible to simplify the equation of the slope to the form

y=mx+b, where m is the slope of the line and b is constant.

y is the dependent variable and x is the independent variable.

By the equation [tex]y=\frac{2}{3}x[/tex]

Therefore, Yes, The slope of the line is [tex]\frac{2}{3}[/tex]

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The value of the given statement rounding to the nearest thousandth = 0.714.

Dependent occurrences are ones that are dependent on previous events. The outcomes of prior events have an impact on these occurrences. Dependent events are two or more occurrences that are dependent on one another. If one event is altered by chance, another is most likely to differ.

The independent and dependent factors are the two most crucial variables in a research experiment. The experimental has authority over the independent variable. The variable that varies in reaction toward the independent variable is known as the dependent variable.

P(A) = 0.74

P(B) = 0.85

P(A|B) = 0.84

Using  dependent events formula:

P(A∩B) = P(A/B) × P(B)

            = 0.84 X 0.85

            = 0.714

The value of the given statement rounding to the nearest thousandth = 0.714.

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Answer:

x = 21°

Step-by-step explanation:

180 - 159 = 21

Alternate angles (see image below) are equal, so x = 21

Using corresponding angles and adjacent angles concept, the value of x from the given parallel lines is 21°.

Given that, straight line m parallel to straight line n and t is the transversal.

The corresponding angles definition tells us that when two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other.

Here, y°=159°

Now, y°+x°=180° (Adjacent angles on straight line)

159°+x°=180°

x°=21°

Therefore, the value of x from the given parallel lines is 21°.

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Answer: 106

Step-by-step explanation:

because there is 106 headphones 106 people can get and there is 16 blankets 156 people can get so 106 people can get headphones and blankets  

Answer: I could be wrong but I'm pretty sure it's 12^9 but again I could be wrong

Step-by-step explanation:

Answer:

the other 20%

Step-by-step explanation:

calculate 20% of 65498

Answer:

13,099.6 square miles

Step-by-step explanation:

80%*65,498=

80/100 * 65,498=

4/5 * 65,498=52,398.4 square miles of land area

65,498-52,398.4=       ==> subtract the total area of Wisconsin by the total land area to get the total area that isn't land.

65,498.0-52,398.4=13,099.6 square miles of area that isn't land

Answer:

x = 4.8

Step-by-step explanation:

since the quadrilaterals are similar then the ratios of corresponding sides are in proportion , that is

[tex]\frac{MJ}{DA}[/tex] = [tex]\frac{LM}{CD}[/tex] ( substitute values )

[tex]\frac{x}{6}[/tex] = [tex]\frac{2.4}{3}[/tex] ( cross- multiply )

3x = 6 × 2.4 = 14.4 ( divide both sides by 3 )

x = 4.8

Answer:

a-b+8=42
a-b=42-8
a-b=36
espero t sirva

Answer:

b=34

Step-by-step explanation:

Answer:

k= -3

Step-by-step explanation:

Since we know the line will go through the point (2,-2), we can plug these values into our x,y variables to solve for k. Our 2 is the x-value and our -2 is the y-value.

y = kx+4

-2 = k(2)+4

To get k by itself, we first have to subtract the 4 from both sides.

-2-4 = k(2)+4-4

-6 = k(2)

Then, we can divide each side by the 2 to get our answer.

-6/2 = k(2)/2

k = -3

Answer:

k=-3

Step-by-step explanation:

Answer: (sidenote, I'm sorry if I answered incorrectly ;-;)

C: 4/5 or D 5/4

Step-by-step explanation:

if you solve the numbers inside the radical symbol you'll get 16807. it's hard for it to be separated into 4 groups since it can only be separated in 5, that being 7*7*7*7*7.

so, by process of elimination i suggest you answer either c or d

Answer:57.7

Step-by-step explanation:

Answer is x > -5

fid comon demoninator

Answer: x>−5

Step-by-step explanation:

[tex]6(\frac{x}{2} +4) > 9[/tex]

Divide both sides by 6. Since 6 is positive, the inequality direction remains the same.

[tex]\frac{x}{2} +4 > \frac{9}{6}[/tex]

Reduce the fraction    

[tex]\frac{9}{6}[/tex]

 to lowest terms by extracting and canceling out 3.

[tex]\frac{x}{2} +4 > \frac{3}{2}[/tex]

Multiply both sides of the equation by 2. Since 2 is positive, the inequality direction remains the same.

x+8>3

Subtract 8 from both sides.

x>3−8

Subtract 8 from 3 to get −5.

x>−5

Answer:

[tex]\overline{BC} \cong \overline{EF}[/tex]

Step-by-step explanation:

Corresponding parts of congruent triangles are congruent.

The 107th derivative of f(x) =cos(x) is sin(x).

The derivative of y = f(x) function is the rate of change of  y  with respect to the independent variable x.

Derivative is represented by [tex]\frac{d}{dx}[/tex] and

First derivative to y is given by  [tex]\frac{d}{dx}f(x) = \lim_{h\to \00} \frac{f(x+h)-f(x)}{h}[/tex]

Second derivative [tex]\frac{d^{2}y }{dx^{2} } = \frac{d}{dx} (\frac{dy}{dx} )[/tex] and so on higher derivatives can be defined.

[tex]\frac{d(sinx)}{dx} = cosx\\\frac{d(cosx)}{dx} = -sinx[/tex]

Given f(x) = cos(x)

Then the first derivative of cos(x) is [tex]\frac{d(cosx)}{dx} = -sinx[/tex]

The second derivative of cos(x) is [tex]\frac{d^{2}(cosx) }{dx^{2} } = \frac{d}{dx} (\frac{dcosx}{dx} ) = \frac{d(-sinx)}{dx} =-cosx[/tex]

Third derivative [tex]\frac{d^{3}(cosx) }{dx^{3} } = \frac{d }{dx } (\frac{d^{2} cosx}{dx^{2} } ) = \frac{d(-cosx }{dx } = sinx[/tex]

[tex]\frac{d^{4}(cosx) }{dx^{4} } = \frac{d(sinx) }{dx } = cosx\\\frac{d^{5}(cosx) }{dx^{5} } = \frac{d(cosx) }{dx } = -sinx\\\\\frac{d^{6}(cosx) }{dx^{6} } = \frac{d(-sinx) }{dx } = -cosx\\\\\frac{d^{7}(cosx) }{dx^{7} } = \frac{d(-cosx) }{dx } = sinx\\[/tex]

Eighth derivative if cos(x) is  cos(x)

and so on

Therefore , the first , fifth , ninth ,... derivative of f(x) =cos(x)  is -sin(x)

The second, sixth, tenth.... derivative of f(x) =cos(x)  is -cos(x)

The fourth , eighth , 12th,... derivative of f(x) =cos(x)  is cos(x)

We can say that very multiple of fourth derivative of f(x) =cos(x)  is cos(x)

We can write 107 as 104 + 3

As 104 is multiple of 4 therefore 104th derivative of cos(x) is cos(x)

[tex]\frac{d^{107}(cosx) }{dx^{107} } = \frac{d^{3} }{dx^{3} } (\frac{d^{104} cosx}{dx^{104} } ) \\\frac{d^{107}(cosx) }{dx^{107} } = \frac{d^{3}(cosx) }{dx^{3} } = sinx[/tex]

Therefore, the 107th derivative of f(x) =cos(x) is sin(x).

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The total price of the pick up truck is $27,241.

What is mathematic expression?

A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Base price = $22,225.

Additional options pricing,

6-speed transmission =  $2,908

cruise control = $240

trailer towing package = $230

power windows =  $738

destination charge = $900

All the other charges will be added to the base price if a person chooses all the options available, therefore,

= 22,225 + 2,908 + 240 + 230 + 738 + 900

= $27241

Therefore, The total price of the pick up truck is $27,241.

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FALSE because they are two different ratios

Answer:

{2401, {-2401

Step-by-step explanation:

Sorry couldnt type the root symbol on my ipad.

Answer:

x= 5/12,y=− 5/4

​

Step-by-step explanation:

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

6x−12y=24,4x+2y=8

Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.

6x−12y=24

Add 12y to both sides of the equation.

6x=12y+24

Divide both sides by 6.

x= 6/1 (12y+24)

Multiply  6

1 times 24+12y.

x=2y+4

Substitute 4+2y for x in the other equation, 4x+2y=8.

4(2y+4)+2y=8

Multiply 4 times 4+2y.

8y+16+2y=8

Add 8y to 2y.

10y+16=8

Subtract 16 from both sides of the equation.

10y=−8

Divide both sides by 10.

y=− 5/4

​Substitute − 5/4  for y in x=2y+4. Because the resulting equation contains only one variable, you can solve for x directly.

x=2(− 5/4 )+4

Multiply 2 times − 5/4 .

x=− 5/8 +4

Add 4 to − 5/8 .

x= 5/12