Qadir has $400.56 in his Friendly Debit card checking account. He uses the card to pay $450.50 to fix his furnace. Four days later, he deposits $150.00 into his checking account. How much money will Qadir have left in his account when the money is taken out to pay for the repair?

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Explanation:

Let's go through each of the answer choices to see which are true and which are false.

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Choice A

The general slope intercept form is y = mx+b

m = slope and b = y intercept.

For y = 3x+1, the boundary line of the first inequality, the slope is 3.

For y = -x+2, the slope is -1.

None of the slopes are 2.

Choice A is false.

We'll use the concept of slope again in choice E.

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Choice B

The "or equal to" part of the inequality sign is what directly determines the boundary line being solid. This is because we include points on the boundary.

Choice B is true.

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Choice C

Plug x = 1 and y = 3 into the first inequality

[tex]y \le 3x+1\\\\3 \le 3(1)+1\\\\3 \le 3+1\\\\3 \le 4\\\\[/tex]

The last inequality is true, so the first inequality is true when (x,y) = (1,3). This makes (1,3) a solution to [tex]y \le 3x+1\\\\[/tex]

Repeat those steps for the other inequality given to us

[tex]y \ge -x+2\\\\3 \ge -1+2\\\\3 \ge 1\\\\[/tex]

which is also true, so that makes (1,3) also a solution to [tex]y \ge -x+2\\\\[/tex]

The point (1,3) is a solution to both inequalities at the same time, making it a solution to the system overall.

Choice C is true

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Choice D

When y is fully isolated, the "less than" inequality indicates the shading is below the boundary. This is due to us considering points of y coordinates smaller than the boundary line. So we'll shade below the boundary for [tex]y \le 3x+1\\\\[/tex]

We don't do the same for [tex]y \ge -x+2\\\\[/tex]. Instead, we'll shade above the solid boundary line.

Choice D is false.

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Choice E

If two lines have equal slopes, but different y intercepts, then we have parallel lines. Parallel lines never intersect.

If on the other hand, the slopes are different values, then the two lines will intersect somewhere on the xy grid. There will only be exactly one point of intersection.

The given system has boundary lines of slopes 3 and -1, for the first and second inequality respectively. Refer back to choice A.  These differing slopes tell us that the boundary lines intersect somewhere.

Choice E is true

Let's go through all the options one at a time and look for the correct ones

Option 1: The slope of one boundary line is 2

We have 2 equations of lines, where the coefficients of are 3 and -1 respectively

because the coefficient of x denotes the slope of a line, we know that the lines have the slope 3 and -1, not 2

Hence, this option is Incorrect

Option 2: Both boundary lines are solid

In order for the boundary lines to be solid, the inequality must have an 'equal to', like ≤ (less than or equal to) or ≥ (greater than or equal to)

we can see that that's the case in our case and hence, this option is Correct

Option 3: A solution to the system is (1, 3)

To confirm this, we'll plug these coordinates into the given inequalities and see if it stands correct

y ≤ 3x + 1

3 ≤ 3(1) + 1

3 ≤ 4 which is correct because 3 is less than 4

Second equation:

y ≥ 2 - x

3 ≥ 2 - 1

3 ≥ 1

Which is also true because 3 is greater than 1

Now, we can say that (1 , 3) is a solution to the system because it satisfies both the equations and is Correct

Option 4: Both inequalities are shaded below the boundary lines

For an inequality to be shaded below the boundary line, it must have the ≤ inequality (in case of solid line) and < inequality (in case of dotted line)

because the second inequality listed includes the ≥ inequality, which was not mentioned above, it won't be shaded below

another way to think about it is that any 'greater than' inequality will shade everything above the line and the 'lesser than' inequality will shade below the line

which means that this option is Incorrect

Option 5: The boundary lines intersect

In order for the boundary lines to intersect, they must have have different slopes.

as we mentioned in the explanation of the first option, that the slopes of the lines is 3 and -1, which are different slopes

Therefore, this option is Correct

Answer:

90

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

i hope this helped :]

Answer:

87

Step-by-step explanation:

87 x 11= 946

946-88-79-83=696

696/8 = 87

Answer:

500

Step-by-step explanation:

(11-3)^3-2x6

first evaluate 11-3-->8

then cube it-->8^3=512

then multiply 2x6-->12

then subtract the two-->512-12=500

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\huge\textsf{Just do PEMDAS}[/tex]

[tex]\huge\textsf{Parentheses}[/tex]

[tex]\huge\textsf{Exponents}[/tex]

[tex]\huge\textsf{Multiplication}[/tex]

[tex]\huge\textsf{Division}[/tex]

[tex]\huge\textsf{Addition}[/tex]

[tex]\huge\textsf{Subtraction}[/tex]

[tex]\mathsf{(11 - 8)^3 - 2\times 6}[/tex]

[tex]\mathsf{11 - 8 = \boxed{\bf 3}}[/tex]

[tex]\mathsf{3^3 - 2 \times 6}[/tex]

[tex]\mathsf{3^3 = 3\times 3\times 3 = 9\times 3 = \boxed{\bf 27}}[/tex]

[tex]\mathsf{27 - 2 \times6 }[/tex]

[tex]\mathsf{2\times 6 = \boxed{\bf 12}}[/tex]

[tex]\mathsf{27 - 12}[/tex]

[tex]\boxed{\mathsf{\bf= 15}}[/tex]

[tex]\boxed{\boxed{\huge\textsf{Answer: \bf 15}}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

D y=0.5cos(2(x-pi))-2

Step-by-step explanation:

The Equation of the function is y=0.5 cos (4(x+π/2))-2

The correct option is B.

As, y=a cos (b(x+c))+d

Here, y max=-1.5 and y min=-2.5

So, d=(max + min)/2

d=(-1.5+(-2.5))/2

d=(-1.5-2.5)/2

d=(-4.0)/2

d=-2.0

and, the horizontal axis is

y=-2

Then, y= a cos(b(x+c))+(-2)

y=a cos (b(x+c))-2

The amplitude (a) is

a = max-d = d- min

a=-1.5-(-2)=-2-(-2.5)

a=-1.5+2=-2+2.5

a=0.5.

We have the period is π/2

P=2π/b

π/2=2π/b

πb=4π

b=4

Now, y=0.5 cos (4(x+c))-2

Thus, the required function is y=0.5 cos (4(x+π/2))-2.

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Answer:

82

Step-by-step explanation:

180 - 98=82

The sum of two angels is 180

Answer:

1/16 or 0.0625

Step-by-step explanation:

There are two numbers on the chart that are divisible by 3.

So the odds of spinning and getting one of those on the first try would be 2/8 or 1/4.

The odds are then multiplied by the chance of spinning it again on the second try, which would still be 1/4.

To get: 1/16

Answer:

$12487.86

Step-by-step explanation:

Given data

Cost of car=  $22,730

Rate of decrease= 9.5%

Time= 6 years

We can predict the value by using the exponential decay function'

A= P(1-r)^t

substitute

A= 22730(1-0.095)^6

A= 22730(0.905)^6

A= 22730*0.5494

A=$12487.86

Hence the value will be $12487.86

Answer:naneeeeee

Step-by-step explanation:

Answer:

7k+7

41

Step-by-step explanation:

Distribute the 7 -

7(k+1)

7 * k = 7k

7*1 = 7

so 7k + 1

Insert 3 instead of x, so it reads -

[tex]5[/tex][tex](3)^{2}[/tex] - 4

[tex]3^{2} = 9[/tex]

9 * 5 = 45

45 - 4 = 41

Answer:

  2i[tex]\sqrt{7}[/tex],-2i[tex]\sqrt{7}[/tex]

Answer:

x = 64

Step-by-step explanation:

Remark

The markings on the triangle tell us that the sides are equal. There is no marking on the third side, so it is not equal to the other two. The important fact is the angles opposite equal sides are also equal. That means that the angle on the lower right is equal to x.

Equation

So you have two angles = to x.

x + x + 52 = 180                     All triangles have interior angles of 180

2x + 52 = 180                         Combine the like terms on the left.

     - 52     -52                        Subtract 52 from both sides

2x =          128                        Divide by 2

2x/2 =      128/2

x = 64

9514 1404 393

Answer:

  D  (53π)/180

Step-by-step explanation:

There are π/180 radians in 1 degree, so in 53°, there are ...

  53(π/180) radians = (53π)/180 radians

Answer:

Pyramid Surface Area = .5 * Perim of Base * Slant Height

Slant Height^2 = 144^2 + 140^2

Slant Height^2 = 20,736 + 19,600

Slant Height^2 = 40,336

Slant Height = 200.8382433701

Surface Area = .5 * perim of base * slant height

Surface Area = .5 * 1,200 * 200.8382433701

Surface Area = 120,503 square meters

Source = www.1728.org/volpyrmd.com

Step-by-step explanation:

Answer:

Step-by-step explanation:

x = 6 + y

6 + y + y = 8

y = 1

x - 1 =6

x = 7

zx + zy = z(x + y) = 20

z = 2.5

Answer:

X = 7

Y = 1

Z = 2/5

Step-by-step explanation:

7-1 = 6

7+1 = 8

2/5 × 7 + 2/5 = 20

Answer:

B=(-3, -5)

Step-by-step explanation:

14 is the asnwer because sqaure root of 200 is 14.14213562 and if you round that it is 14

Answer:

V = r(40 - 3πr²)/2

Step-by-step explanation:

We know the area of a cylinder, A = 2πr² + 2πrh where r = radius and h = height.

Now, 2πr² = area of top and bottom and 2πrh = curved surface area

Since the cost of material for the top and bottom is 3 cents per square inch, the total cost of the materials for top and bottom = cost of material × area = 3 × 2πr² = 6πr²

Also, the cost of material for the curved is 2 cents per square inch, the total cost of the materials for the curved side = cost of material × area = 2 × 2πrh = 4πrh

The total cost of material = 6πr² + 4πrh

Since the total cost of material = 80 cents,

6πr² + 4πrh = 80

3πr² + 2πrh = 40  (1)

Now, the volume of a cylinder, V = πr²h

From (1), making h subject of the formula, we have

3πr² + 2πrh = 40  

2πrh = 40 - 3πr²  

h = (40 - 3πr²)/2πr

Substituting h into V, we have

V = πr²h

V = πr² (40 - 3πr²)/2πr

V = r(40 - 3πr²)/2

Answer:

Step-by-step explanation:

X is also 67°  Like the interior angle

Answer:

4

Step-by-step explanation:

2 out of 5 play so if there is 10 students 10*2/5 = 4 students

Answer:

4 students would play soccer

Step-by-step explanation:

To make the total students 10 instead of 5 we multiply the information by 2. 2/5 times 2 equals 4/10. So 4 out of 10 studento play soccer

Answer:

$3+x is less than or equal to $15

Step-by-step explanation:

I can't write the sign but it's < with a line under it

Step-by-step explanation:

y≥15-3

I am not sure

The finance charge payed by Jamal is $28.43.

A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

For the given situation,

Amount borrowed by Jamal for nine months = $316

His monthly payment = $38.27

Total amount payed by Jamal for nine months = [tex]9(38.27)[/tex]

⇒ [tex]\$344.43[/tex]

Thus his finance charge = [tex]344.43-316[/tex]

⇒ [tex]\$28.43[/tex]

Hence we can conclude that the finance charge payed by Jamal is $28.43.

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