Gus has a checking account balance of $75. His bank will fund the a debit card purchase that creates a negative balance up to a limit of $200, but charges a $35 fee per transaction for any purchase made in overdraft. Gus made a purchase of $100 yesterday, and another purchase of $27 today. He used a debit card for each purchase. Then, he deposited a check for $25. What is Gus' current account balance?

Answer:

7

Step-by-step explanation:

10-3=7

Using translation concepts, it is found that the correct statement is given by:

B) Translation creates an image congruent to the given image.

D) Translation creates an image similar to the given image.

A translation is represented by a change in the image position, keeping the angles and the length's of the sides.

The translated image is congruent and similar to the original image, hence options B and D are correct.

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Answer:

D) Translation creates an image similar to the given image.

Step-by-step explanation:

Answer:

[tex]y=\dfrac{1}{2}x+\dfrac{5}{2}[/tex].

Step-by-step explanation:

If a line passing through two points, then the equation of line is

[tex](y-y_1)=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

It is given that the passing through (1,3) and (-9,-2).  So, equation of line in point slope form is

[tex]\Rightarrow (y-3)=\dfrac{-2-3}{-9-1}(x-1)[/tex]

[tex]\Rightarrow (y-3)=\dfrac{1}{2}(x-1)[/tex]

Slope intercept form of a line is

[tex]y=mx+b[/tex]

where, m is slope and b is y-intercept.

Now,

[tex](y-3)=\dfrac{1}{2}(x-1)[/tex]

[tex]\Rightarrow (y-3)=\dfrac{1}{2}(x}-\dfrac{1}{2}(1)[/tex]

[tex]\Rightarrow y=\dfrac{1}{2}(x}-\dfrac{1}{2}+3[/tex]

[tex]\Rightarrow y=\dfrac{1}{2}x+\dfrac{5}{2}[/tex]

Therefore, the required equation is [tex]y=\dfrac{1}{2}x+\dfrac{5}{2}[/tex].

Answer:

The Answer is C

Step-by-step explanation:

i think This is correct

Answer:

work is shown and pictured

Answer:

(4x + 5)(4x + 5)

Step-by-step explanation:

Took test.

Want a more in-depth explanation? Try visiting the Math Nation site.

Answer:

15:2; there are 2 counselors to every 15 campers

Step-by-step explanation:

Answer = 42.8

Step-by-step explanation:

All right triangles have one right (90-degree) angle, and the hypotenuse is the side that is opposite or the right angle, or the longest side of the right triangle.[1] The hypotenuse is the longest side of the triangle, and it’s also very easy to find using a couple of different methods. This article will teach you how to find the length of the hypotenuse using the Pythagorean theorem when you know the length of the other two sides of the triangle. It will then teach you to recognize the hypotenuse of some special right triangles that often appear on tests. It will finally teach you to find the length of the hypotenuse using the Law of Sines when you only know the length of one side and the measure of one additional angle

The right answer is -2.

please see the attached picture for full solution..

Hope this helps..

Good luck on your assignment

Answer: The social structure of the workplace changed as a result of the Industrial Revolution as well, because laws were passed that allow people to receive days off from work, capped hours and reasonable condition

Step-by-step explanation:

Answer:

92

Step-by-step explanation:

If the ratio of adults to kids is

2:23

it will also be equal as

8:92

Multiplying each half times 4!

Answer:

109.2

Step-by-step explanation:

If the number being divided does not end in 5 or 0, it being divided by 5 will not be equal. Therefor it might be better to try and use a calculator if you can't do it in your head.

Explanation:

First lets do the long division method. First we need to fit 5 into 5. That would be 1. So we write a 1 above the 546. Then we need to fit 5 into 4. Well it doesn't fit so we write a zero move another number. How many 5s fit into 46 well that would be 9. All we have left is a remainder of 1 which cannot fit into 5 and there are no more numbers

Answer:

If you want a decimal that would be 109.2 or 109 1/5

Answer:

cancel out as much of the equation as possible by doing inverse operations so add the 7 to both sides

x2 + 2x = 7

Divide by 2

x2 = 3.5

divide by 2 again

x = 1.75

now change x with 1.75 to check

1.75 x 2 = 3.5

3.5 + 3.5 - 7 = 0 so 1.75 is correct

Hope this helps

Step-by-step explanation:

Answer: a

Step-by-step explanation:

Answer:

121

Step-by-step explanation:

The exterior angle  measurement is equal to the sum of the opposite interior angles

34+ 87 = z

121 = z

[tex]answer \\ = 44 \ \frac{7}{8} \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]

2x +3y=3

7x-3y=24

solve the above equations

2x+3y=3

+7x-3y=24

9x=27

x=27/9

x=3

substitute the value of x in 2x+3y=3

2(3)+3y=3

6+3y=3

3y=3-6

3y=-3

y=-3/3

y=-1

so the solution is

{x=3,y=-1}

Answer:

C : (3, -1)

Step-by-step explanation:

Answer:

Step-by-step explanation:

surface area=4×5+2×1/2×3×4+5×5+3×6

=20+12+25+18

=75

Answer:

Step-by-step explanation:

[tex]\sqrt{-2}=\sqrt{2}i\\\\\sqrt{-18}=\sqrt{2*3*3}i=3\sqrt{2}i\\\\\sqrt{-2}+\sqrt{-18}= \sqrt{2}i+3\sqrt{2}i\\ =(1+3)\sqrt{2}i\\\\=4\sqrt{2}i[/tex]

Answer:

[tex] \boxed{Fencing \: need \: to \: buy \: for \: the \: entire \: perimeter = \frac{40}{3} \: yards} [/tex]

Step-by-step explanation:

Length of rectangular garden (l) = 16 feet

Width of rectangular garden (w) = 4 feet

[tex] 3 \: feet = 1 \: yard \\ \\ 1 \: feet = \frac{1}{3} \: yard [/tex]

[tex] \\ = > Perimeter \: of \: rectangular \: garden = 2(l + w) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2(16 + 4) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times 20 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 40 \: feets \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =40 \times \frac{1}{3} \: yards \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{40}{3} \: yards[/tex]

Answer:

x = 8

Step-by-step explanation:

Add [tex]\frac{1}{3}x[/tex] to both sides.

x + 1 = 9

Subtract one on both sides.

x = 8

Answer:

x = 8

Step-by-step explanation:

2/3x + 1 = -1/3x + 9

x + 1 = 9

x = 8

Answer:

144 degrees.

Step-by-step explanation:

Draw yourself a diagram with 2 horizontal lines and a transversal cutting across it.

After labeling, you will see that angle 4 is the same as angle 1. You can also see that angle 1 and 2 add up to 180, as they are sitting on a straight line.

First, before we get to the angle of 4, we have to find the value of x:

1) angle 1 + angle 2 = 180

3x + 12x = 180

2) solve the above equation for x

15x = 180

3) divide both sides by 15 for x

x= 12 degrees

We know that angle 4 is the same as angle 2, which is 12x degrees.

So, now that we know what x is, 12 x 12 degrees =  144 degrees.

Hope this helped : )

The measure of angle ∠4 is 144°

Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.

Corresponding angles

When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position

Alternate Interior Angles

Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.

Alternate Exterior Angles

The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.

Consecutive Interior Angles

When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.

Given data ,

The measure of angle 1 = ( 3x )°

The measure of angle 2 = ( 12x )°

Angle 1 and Angle 2 are on the straight lines

So , the sum of the measures of angles = 180°

On simplifying the equation , we get

3x + 12x = 180

15x = 180

Divide by 15 on both sides of the equation , we get

x = 12

Substituting the value of x in the equation , we get

The measure of angle 2 = measure of angle 4 ( corresponding angles )

So , the measure of angle 4 = ( 12x )°

And , the measure of angle ∠4 = 144°

Hence , the angle ∠4 = 144°

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Answer:

The ? is 4x * (-2x) = -8x².

Answer:

-8x^2

Step-by-step explanation:

-2x*4x=-8x^2

that's pretty much all the work here, I don't know what else to add in the explanation except for that this is a grid that is supposed to help you learn quadratic factoring

hope this is the right answer

Answer:

see explanation

Step-by-step explanation:

15

The x- coordinate of E is the same as the vertex F

The y- coordinate of E is the same as the vertex G

E = (b, c )

The x- coordinate of D is the same as vertex G

The y- coordinate of D is the same as vertex F

D = (a, 0 )

16

The x - axis is an axis of symmetry in the rhombus , thus

D is a reflection of B so D = (0, b )

The y- axis is an axis of symmetry in the rhombus, thus

E is a reflection of C so E = (a, 0 )

Answer:

a1 = 0.5; common ratio = 5

Step-by-step explanation:

Let the common ratio = r

a2 = 2.5

a3 = 2.5r

a4 = 2.5r * r = 2.5r^2

We are told a4 = 62.5, so

2.5r^2 = 62.5

Divide both sides by 2.5

r^2 = 25

r = 5

a2 = a1 * r

a1 = a2/r = 2.5/5 = 0.5

Answer: a1 = 0.5; common ratio = 5

Answer:

First, solve for the volume of the tray by the equation V = L x W x H. Convert first all the dimensions to inches. The operation gives an answer of volume equal to 236.22 in³. Converting the amount of paint available to in³. This gives an answer of 231 in³. Hence, the answer is letter B. 

Step-by-step explanation:

Answer:

The correct option is (B)

(B) x-y = 6 , 3x+4y = 4

Step-by-step explanation:

As we can see in the graph given below, both lines intersect at (4, -2), which should be the solution of given equations:

Find the values of x and y for (B);

x - y = 6 ⇒ (i)

3x + 4y = 4 ⇒ (ii)

Lets consider equation (i)

x - y = 6

x = 6 + y

Substitute in equation (ii)

3(6+y) + 4y = 4

18 + 3y + 4y = 4

7y = -14

y = -2

Substitute in equation (i)

x - (-2) = 6

x + 2 = 6

x = 6 - 2

x = 4

As solution of part C is also (4, -2), it represents the graph

You can also find the (x, y) for other options the similar way, which will show you they don't have the same value

Answer:

its  B

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given sin α = –4∕5 and sin β = 1∕2

To get α from sin α = –4∕5,

α = arcsin(-4/5)

α = arcsin (-0.8)

α = -53.13°

If angle α is in quadrant III, then α = 180+53.13 = 233.13° (sin is negative in the 3rd quadrant)

Similarly for sin β = 1∕2

β = arcsin(1/2)

β = arcsin(0.5)

β = 30°

Since  β is in quadrant II,  β = 180-30 = 150°

To find  cos (α + β). where α = 233.13° and  β = 30°

cos (α + β)= cos (233.13 + 150)

= cos 383.13°

cos (α + β) = 0.9196

Answer:

20x^2 +19x - 60

Step-by-step explanation:

3x( 4x+5) -4 (-x-3) (2x -5)

Distribute

12x^2 +15x - 4 (-x-3) (2x -5)

FOIL

12x^2 +15x - 4( -2x^2 -6x +5x +15)

12x^2 +15x - 4( -2x^2 -x +15)

Distribute

12x^2 +15x +8x^2 +4x -60

Combine like terms

20x^2 +19x - 60

Answer:

20x ^2 + 19x -60

Step-by-step explanation:

12345678910121314151617181920

Answer: I think is c

Step-by-step explanation:

Answer:

They got the same answer

Step-by-step explanation:

A slope is completely linear, and the rate of change is constant, so no matter what points are chosen, the rate of change will be the same.

Answer:

5

Step-by-step explanation:

the median means the number in the middle so the number in the middle would be 5