Justin has $57.18 in his checking account. He deposits his paycheck of $256.79. He then buys $68.42 in groceries, $50.00 in gas, and 2 movies for $15.58 each. What is the new balance in Justin’s checking account?

Answer:

[tex]\mathrm{Domain\:of\:}\:\frac{x-1}{x+3}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<-3\quad \mathrm{or}\quad \:x>-3\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-3\right)\cup \left(-3,\:\infty \:\right)\end{bmatrix}[/tex]

Therefore, the 4th option i.e. (−∞, −3) (−3, ∞) is the correct answer.

Step-by-step explanation:

Given the expression

[tex]f\left(x\right)=\frac{x-1}{x+3}[/tex]

We know that the domain is the set of all the input or argument values for which is the function is real and defined.

From the given expression, we need to make sure the denominator of a rational function can be anything but 0, because 0 would make the function undefined.

Thus, we need to find undefined points such as:

x+3 = 0

x = -3

Therefore, the function domain must be:

x < -3 or x > -3

In other words,

[tex]\mathrm{Domain\:of\:}\:\frac{x-1}{x+3}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<-3\quad \mathrm{or}\quad \:x>-3\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-3\right)\cup \left(-3,\:\infty \:\right)\end{bmatrix}[/tex]

Therefore, the 4th option i.e. (−∞, −3) (−3, ∞) is the correct answer.

Answer:

The correct answer is,

Answer:

The value of x = 65.4°

Step-by-step explanation:

Given

hypotenuse = 12

To determine

The value of ∠x = ?

Using the trigonometric ratio

cos x = adjacent / hypotenuse

here:

substituting adjacent = 5, hypotenuse = 12 in the formula

cos x = adjacent / hypotenuse

cos x = 5 / 12

x = arccos (5/12)

x = 65.4°

Therefore, the value of x = 65.4°

Answer:

The answer is 65.3 to the nearest tenth

Step-by-step explanation:

You'll use the Pythagoras theorem to find the unknown side first

then you'll use the sin rule to solve for x

Answer:

36:18= 16:9

2 eggs for every guest

Answer:

[tex]k>-3[/tex]

Step-by-step explanation:

We have the equation:

[tex]-3x^2-6x+k=0[/tex]

Where a = -3, b = -6, and c = k.

And we want to determine values of k such that the equation will have real, unequal roots.

In order for a quadratic equation to have real, unequal roots, the discriminant must be a real number greater than 0. Therefore:

[tex]b^2-4ac>0[/tex]

Substitute:

[tex](-6)^2-4(-3)(k)>0[/tex]

Simplify:

[tex]36+12k>0[/tex]

Solve for k:

[tex]12k > -36[/tex]

[tex]k>-3[/tex]

So, for all k greater than -3, our quadratic equation will have two real, unequal roots.

Notes:

If k is equal to -3, then we have two equal roots.

And if k is less than -3, then we have two complex roots.

[tex]\huge\sf{Answer :- }[/tex]

Exterior angle of the polygon = ( 360/ n )°

where,

➙ ( 360/ 20 )°

➥ 18°

Answer:

answer of this qn will 360÷20= 18degree

Answer:

3. Adjacent and Supplementry

Answer:

x equals 3 so multiply 3x3 and it will give you 9 and add that to 6 and you get 15. x equals 3 for the one that equals 5.

Answer:

3x + 16 = 15

3x = 15-16

3x = -1

x = -1/3

Answer:

£4410

Step-by-step explanation:

Step one:

given data

Principal P= £4000

Rate= 5%= 0.05

time t= 2 years

Final amount A= ??

Required

The final amount

Step two:

The expression for the final amount of compound interest is

[tex]A= P(1+r)^t\\\\A=4000(1+0.05)^2\\\\A=4000(1.05)^2\\\\A=4000*1.1025[/tex]

A=£4410

Answer:

Step-by-step explanation:

Given: i. AB||DE

          ii. AC≅DC

Prove: ΔABC≅ΔDEC

From the two triangles, it can be observed that;

m<BAC≅m<EDC (alternate angles)

m<ABC≅m<DEC (alternate angles)

m<BCA≅m<ECD (vertically opposite angles)

m<BAC + m<ABC + m<BCA = m<EDC + m<DEC + m<ECD = [tex]180^{o}[/tex] (sum of angles in a triangle)

Since the three angles of the triangles are congruent respectively, then;

ΔABC≅ΔDEC (AAA congruence property)

Answer:

=106

Step-by-step explanation:

PMDAS

First thing you do is the parenthesis

6+4(5)^2

then the exponent

6+4(25)

then multiply

6+100

then add

106

Hope this helps (:

Answer:

150

Step-by-step explanation:

First do what is in the parenthesis:

(2+3)

(6)

Then exponents:

[tex](6)^{2}[/tex]

(36)

Then Multiplication:

4(36)

144

Then Add:

144+6

150

Answer:

240

Step-by-step explanation:

-8(10×-3)

(10×3)=30

30×-8=240

Answer: the last one

Step-by-step explanation:

um so the set begins with 40 and ends with 100 (look at that on the number line)

and so the median is essentially that middle line in the box, which is around 80

i assume yk how to calculate medians so I calculated the median of the first and the last answer

the first one was like 70, and the last one was like 78.9 which is close enough to 80

so i think its the last one

Answer:

It is answer number four.

Step-by-step explanation:

40 and 100 represent the outliers so both numbers must be included.

80 must also be included as it is the mean or average test grade.

Answer:

65 %

Step-by-step explanation:

13/20 = 65/100

Answer:

65%

Step-by-step explanation:

20/100 =1/5

5*13=65

Answer:

0+2+-4=-2

Step-by-step explanation:

Answer:

321%

Step-by-step explanation:

hope I helped Kkkkkkkk

Answer:

Step-by-step explanation:

3/5(-60)(-2/3)=24

choice C

Answer:

78

Step-by-step explanation:

Answer:

76

Step-by-step explanation:

To find the area you multiply both sides, the opposite of multiplication is division. Take 6992 and divide it by 92 to get the missing side of 76.

Answer:

Tomas has a 15% commission :)

Step-by-step explanation: Because 15% equals 15%

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete. However, a possible question is "calculate the depth of the lake after certain number of hours (say 2 hours)"

Given

[tex]Rate = \frac{1}{4}ft/hr[/tex]

[tex]Depth = 279ft[/tex]

First, we calculate the depth receded.

If the rate is 1/4ft per hour

Then

The Depth receded in 2 hours is:

[tex]Receded = \frac{1}{4} * 2[/tex]

[tex]Receded = \frac{2}{4}[/tex]

[tex]Receded = 0.5ft[/tex]

The new depth is then calculated as:

[tex]New\ Depth = 279ft - 0.5ft[/tex]

[tex]New\ Depth = 278.5ft[/tex]

Answer:

the first step in solving an equation with a variable on each sides is to get the variable on one side. This is done by reversing the addition or subtraction of one of the terms with the variable.

Step-by-step explanation:

Answer:

[tex]\mathrm{A.\:}x+2y=a[/tex]

Step-by-step explanation:

In standard form [tex]ax+by=c[/tex], any point the line passes through will make the inequality true. We can simply use any point given to find the equation of the line:

We can write the following system of equations from two points from the table:

[tex]\begin{cases}d\cdot3a+e\cdot(-a)=f\cdot a\\d\cdot5a+e\cdot(-2a)=f\cdot a\end{cases}[/tex]

Solving, we get:

For [tex]a \notin 0[/tex],

[tex]d=1,\\e=2,\\f=1[/tex]

Therefore, our equation is:

[tex]dx+ey=fa,\\1x+2y=1a,\\\fbox{$x+2y=a$}[/tex].

Answer:

y = 2x - 3.5

Step-by-step explanation:

2x² + 2y = 4x + 2x² - 7

2y = 4x + 2x² - 7 - 2x²

2y = 4x - 7

y = (4x - 7) / 2

y = 2x - 3.5

2x² + 2y = 4x + 2x² - 7

4x + 2y = 4x + 2x² - 7

4x + 2y = 4x + 4x - 7

4x+2y=8x-7

2y = 4x - 7

Answer:

dy/dx

= d/dx [2x² + 5x - 3]

= 4x + 5.

Hence at x = 1, dy/dx = 4(1) + 5 = 9.

The slope of the tangent is 9.

d/dx (3/x)

= d/dx (3x^-1)

= 3 * d/dx (x^-1)

= 3 * [-1 * x^(-2)]

= -3/x².

Answer:

Step-by-step explanation:

Median: First write in ascending order. If number of data's is odd, median is the middle data.

If number of data's is even, then median = average of n/2th and (n+2)/2th term.

1) 1 , 3 , 5 , 5 , 6

Median = 5

2) 3,4,10,2,1

Ascending order: 1,2,3,4,10

Median = 3

3) 4, 5,7,11

Median = (5+7)/2 = 12/2 = 6

4) 1,1,2,6

Median = (1+2)/2 = 3/2 = 1.5

5) 2,2,3,3,,5,7

Median = 3+3/2 = 6/2 = 3

6)1,2,4,6,7,7

Median = (4+6)/2 = 10/2 = 5

7) 2,2,3,6,7,8

Median = (3+6)/2 = 9/2 = 4.5

8)1,2,3,14,17,18

Median = (3+14)/2 = 17/2 = 8.5

Mean= Sum of all the items÷ number of items

1)Mean = (1+2+3+2)÷4 = 8÷2 = 4

2)Mean=(4+3+2+4+2)÷5 = 15÷5 = 3

3)Mean = (5+4+6+1)÷4 = 16÷4 = 4

4)Mean = (2+5+1+4+7+5)÷6 = 24÷6 = 4

5)Mean =(10+11+9+12+8)÷5=50÷5 = 10

6)Mean = (1 + 2 + (-2)+1+(-2) )÷5 = -2÷5 = -0.4

7)Mean = (4+(-2)+3+(-3)+3)÷5 = 5÷5 = 1

8)Mean = (4+5.5+3+5.5)÷4=18÷4 = 4.5

Answer:

Median

1) 5

2) 3

3) 5+7=12/2=6

4)1+2=3/2=1.5

5)3+3=6/2=3

6) 4+6=10/2=5

7) 3+7=10/2=5

8)14+3=17/2=8.5

Mean

1) 2

2) 3

3)4

4)4

5) 10

6) 0

7) 1

8) 4.5

Step-by-step explanation:

Median is the middle number, make sure the list of in order from smallest to highest.

2) 1, 2, 3, 4, 10

if you have two numbers in the middle add them together then divide by 2

4) 1, 1, 2,6

5)2, 2, 3, 3, 5, 7

6) 1, 2, 4, 6, 7, 7

7)2, 2, 3, 7, 6,8

8)1, 2, 3, 14, 17, 18

Mean is when you add all the numbers together and divide by how many there are.

1) 1+3+2+2=8/4=2