On Saturday, Darnel earned $65 raking his neighbor's leaves and cleaning her garage. On Sunday, he earned $25 helping another neighbor rake leaves. He deposited his earnings in his bank account on Monday. What was the total change in Darnel's bank account relative to where it started?

Answer:

(a) When a = 4 and b = -5,  a² + b² - a·b = 61

(b) When a = 4 and b = -5,  a³·b + a·b² = -220

(c)  [tex]When \ a = 4 \ and \ b = -5, \ \dfrac{a - b}{a + b} + a -b = 0[/tex]

(d) When a = 4 and b = -5, (a + b)² - (a - b)² = 82

Step-by-step explanation:

The question relates to evaluation of expressions, given the values of the variables, "a" and "b"

Where;

a = 4 and b = -5

(a) For a² + b² - a·b, we have;

a² + b² - a·b = 4² + (-5)² - 4 × (-5) = 16 + 25 + 20 = 41 + 20 = 61

(b) For a³·b + a·b² we have;

a³·b + a·b² = 4³·(-5) + 4·(-5)² = 64 × (-5) + 4 × 25 = -320 + 100 = -220

(c) For [tex]\dfrac{a - b}{a + b} + a -b[/tex], we have;

[tex]\dfrac{a - b}{a + b} + a -b = \dfrac{4 - (-5)}{4 + (-5)} + 4 - (-5) = \dfrac{4 + 5}{4 -5} + 4 + 5= \dfrac{9}{-1} + 4 + 5 = -9 + 4 + 5 = 0[/tex]

[tex]\therefore when \ a = 4 \ and \ b = -5, \ \dfrac{a - b}{a + b} + a -b = 0[/tex]

(d) For (a + b)² - (a - b)² we have;

(a + b)² - (a - b)² = (4 + (-5))² - (4 - (-5))² = (4 - 5)² - (4 + 5)² = (-1)² - 9² = 1 + 81 = 82

When a = 4 and b = -5, (a + b)² - (a - b)² = 82

Answer:

-8x+2

Step-by-step explanation:

i got a 100 on this test

Answer:

no.2 no.5

Step-by-step explanation:

i don't know how to explain

have a good rest of your day

Answer:

question (1) c^2=a^2+b^2

Step-by-step explanation:

pythagoras theorem

Answer:

The traveller's speed is 5ft/s and the walkway speed is 3ft/s

Step-by-step explanation:

Given

Represent the traveller's speed with T and the walkway's speed with W.

When the traveller walk against the walkway, we have:

[tex]T - W = 2[/tex] ---- i.e. 2ft/s against the walkway

When the traveller walk with the walkway, we have:

[tex]T + W = 8[/tex] ---- i.e. 8ft/s with the walkway

Required

Solve for W and T

[tex]T - W = 2[/tex] --- (i)

[tex]T + W = 8[/tex] --- (ii)

Add (i) and (ii)

[tex]T + T - W + W = 2 + 8[/tex]

[tex]T + T = 2 + 8[/tex]

[tex]2T = 10[/tex]

Divide both sides by 2

[tex]\frac{2T}{2} = \frac{10}{2}[/tex]

[tex]T = \frac{10}{2}[/tex]

[tex]T = 5[/tex]

Substitute 5 for T in (ii)

[tex]T + W = 8[/tex]

[tex]5 + W = 8[/tex]

Make W the subject

[tex]W = 8 - 5[/tex]

[tex]W = 3[/tex]

Hence, the traveller's speed is 5ft/s and the walkway speed is 3ft/s

Answer:

c

Step-by-step explanation:

i took the quiz

Answer:

The answer is C) 15

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

:)

Answer:

8

Step-by-step explanation:

I believe one of the rules of angles states that angle (4x-6) = angle (7x-30).

so 4x-6 = 7x-30

moving like terms together,

7x-4x = -6 + 30

3x = 24

x = 24/3

x = 8

Answer:

The equation in slope-intercept form perpendicular to the given equation [tex]y = -3x + 4[/tex] through the given point (6,-2) is [tex]\mathbf{y=\frac{1}{3}x}[/tex]

Step-by-step explanation:

We need to write an equation in slope-intercept form perpendicular to the given equation through the given point

y = -3x + 4

(6,-2)

The general equation in slope intercept form is: [tex]y=mx+b[/tex] where m is slope and b is y-intercept.

We need to find slope and y-intercept.

Finding slope:

The given line is perpendicular to required line, so there slopes are opposite

The slope of given line [tex]y = -3x + 4[/tex] is m = -3, (By comparing it with general equation y=mx+b, we get m = -3)

The slope of required line is: [tex]m = \frac{1}{3}[/tex]

Finding y-intercept:

y-intercept can be found by using slope [tex]m = \frac{1}{3}[/tex] and the point(6,-2)

[tex]y=mx+b\\-2=\frac{1}{3}(-6)+b\\-2=-2+b\\b=-2+2\\b=0[/tex]

So, we get y-intercept b =0

Equation of required line:

So, the equation of required line having slope [tex]m = \frac{1}{3}[/tex] and y-intercept b =0 is:

[tex]y=mx+b\\y=\frac{1}{3}x+0\\y=\frac{1}{3}x[/tex]

So, the equation in slope-intercept form perpendicular to the given equation [tex]y = -3x + 4[/tex] through the given point (6,-2) is [tex]\mathbf{y=\frac{1}{3}x}[/tex]

Answer:

4x-3 or A

Step-by-step explanation: because there are 4 x's and 3 "-" which makes it 4x-3

Answer:

Hi, this is a strange problem but I believe the answer is A) 4x-3.

Step-by-step explanation:

I think the X symbols represent "X"es and the dashes represent single negative digits. I may be wrong, but I think this is what your teacher is most likely looking for. Good luck! :)

Answer:

-4/3 hrs

Step-by-step explanation:

trust me I just got it right ;)

The hour change rate is [tex]-\frac{4}{3}[/tex]

'A scatter plot uses dots to represent values for two different numeric variables.'

According to the given problem,

Since the data shows mostly a linear trend, we can draw a line to estimate the rate of change.

The line approximately goes through (0,23) and (12,7).

Using the slope formula,

m = [tex]\frac{y_{2}- y_{1} }{x_{2}-x_{1} }[/tex]

Substituting the respective values,

m = [tex]\frac{7-23}{12-0}[/tex]

m = [tex]-\frac{4}{3}[/tex]

Hence, we can conclude that each additional hour spent on video games is associated with approximately a [tex]-\frac{4}{3}[/tex] hour change in time spent on homework on average.

Learn more about Scatter Plots here:

https://brainly.com/question/25280625

#SPJ2

SHDHSB SSHD EUDXD EJDJXJEX SJDJWIDIJDWN SSHWIJJSJ

Step-by-step explanation:

XJDUXIDB DUDUU

Answer:

44

Step-by-step explanation:

Number who use balls only = 7 / 20

Number who use rings only = 3/7

Fraction who use both :

1 - (7/20 + 3/7)

1 - 0.7785714

= 0.2214285

If number of jugglers is less than 200

Number of jugglers who use both :

0.2214285 * 200

= 44.285714

Number of jugglers who use both should be about 44

Answer: c

Step-by-step explanation:

Answer:

1/8

Step-by-step explanation:

Answer:

x=23

Step-by-step explanation:

You simplify both sides of the equation, then isolate the variable.

Answer:

x=23

Step-by-step explanation:

Answer:

(for your second question) 23.69

Step-by-step explanation:

Answer:

28cm

Step-by-step explanation:

7x4

or

7+7+7+7

Answer:

pythagorean theorem is a^2+B^2=c^2

plug in (3)^2+(4)^2=(5)^2

9+16=25

Answer:

4:7  7 being to total number of marbles (part to whole ratio)

There are 16 blue marbles were in the bag before I added more.

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.

Given that;

The ratio of blue marbles to yellow marbles is 4 : 3.

And,  If I add 5 blue marbles and remove 3 yellow marbles, the ratio will be 7:3.

Now,

Since, The ratio of blue marbles to yellow marbles is 4 : 3.

Hence, Number of blue marbles = 4x

Number of yellow marbles = 3x

And, If I add 5 blue marbles and remove 3 yellow marbles, the ratio will be 7:3.

Then, We can formulate;

⇒ 4x + 5 / 3x - 3 = 7x / 3x

⇒ (4x + 5) / (3x - 3) = 7 / 3

⇒ 3 (4x + 5) = 7 (3x - 3)

⇒ 12x + 15 = 21x - 21

⇒ 15 + 21 = 21x - 12x

⇒ 36 = 9x

⇒ x = 4

Thus, The number of blue marbles = 4x

                                                      = 4 × 4

                                                      = 16

Learn more about the ratio visit:

https://brainly.com/question/169670

#SPJ2

Answer:

Y = 40

X = 101

W = 20

Step-by-step explanation:

All of the triangles Angles should equal 180!

Answer:

20%

Step-by-step explanation:

Answer: 6

Step-by-step explanation:

Answer:

The description of the rotation is 180 degrees clockwise or counterclockwise rotation

Step-by-step explanation:

Here, we want to get the kind of rotation that maps the triangle into its new coordinates

we have this as;

(x,y) to (-x, -y)

that will be ;

a 180 degrees rotation or counter clockwise rotation

180 rotation so A

Step-by-step explanation:

Answer:

6; 8; 10

Step-by-step explanation:

First side: x

Second side: x+2

Third side: x+4

x + x + 2 + x + 4 = 24

3x + 6 = 24

3x = 18

x=6

First side: 6

Second side: 8

Third side: 10

Answer:

The ratio is 20:30, or 2:3 in simplest form

Plzzzzz give me Brainliest!  

Answer:

2/5 or 40%

Step-by-step explanation:

20 out of fifty is hard so make it 40 out of 100 and it's easy 40%

Answer:

R(t) = 10 + 0.50t

Step-by-step explanation:

Answer: C

Step-by-step explanation: I know I'm late by about 2 weeks but your answer is C.

Answer:

Tax amount = $15.00 x 0.06 =0.9

Total amount of the basketball = $15.00 x 1.06 = $15.90

Answer:

Tax amount = $15.00 x 0.06 =0.9Total amount of the basketball = $15.00 x 1.06 = $15.90

Step-by-step explanation:

Answer:

Michelle < Staci < Kelly < Kyle

Kyle is the greatest distance from work, while Michelle is the closest to work.

Step-by-Step Explanation:

1 kilometer = 0.62137119 mile(s)

4.5 miles = 0.62137119 × 4.5 = 2.79617036 kilometers

4,200 meters = 4.2 kilometers

670,000 centimeters = 6.7 kilometers

So,

Michelle = 2.8 kilometers (rounded up)

Kelly = 5.6 kilometers

Staci = 4.2 kilometers

Kyle = 6.7 kilometers

So,

Michelle < Staci < Kelly < Kyle

Kyle is the greatest distance from work, while Michelle is the closest to work.

Hope this helps! ^^