Y=4x-9 complete the missing value in the solution to the equation

Bruce overdrew his checking account by $19, for which his bank charged him a $35 overdraft fee. If he deposits $60, what will hi

eimsori [14]

He overdrew his account by $19, so he is at $-19. His bank charges $35 fee. -19 - 35 = -54. He deposits $60, so 60 + (-54) = 6. He has $6 as his ending balance.

3 0

3 years ago

Read 2 more answers

What complex number is represented by the polar coordinates (4, -pi/4)

nexus9112 [7]

Answer:

$\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}$

Step-by-step explanation:

A complex number is defined as z = a + bi. Since the complex number also represents right triangle whenever forms a vector at (a,b). Hence, a = rcosθ and b = rsinθ where r is radius (sometimes is written as <em>|z|).</em>

Substitute a = rcosθ and b = rsinθ in which the equation be z = rcosθ + irsinθ.

Factor r-term and we finally have z = r(cosθ + isinθ). How fortunately, the polar coordinate is defined as (r, θ) coordinate and therefore we can say that r = 4 and θ = -π/4. Substitute the values in the equation.

$\displaystyle \large{z=4[\cos (-\frac{\pi}{4}) + i\sin (-\frac{\pi}{4})]}$

Evaluate the values. Keep in mind that both cos(-π/4) is cos(-45°) which is √2/2 and sin(-π/4) is sin(-45°) which is -√2/2 as accorded to unit circle.

$\displaystyle \large{z=4\left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2}}{2}i \right)}\\\\\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}$

Hence, the complex number that has polar coordinate of (4,-45°) is $\displaystyle \large{z=2\sqrt{2} -2 \sqrt{2}i}$

3 0

1 year ago

Jose estimates that if he leaves his car parked outside his office all day on a weekday, the chance that he will get a parking t

Elan Coil [88]

Answer:

Therefore, the probability is P=0.74.

Step-by-step explanation:

We know that Jose estimates that if he leaves his car parked outside his office all day on a weekday, the chance that he will get a parking ticket is 26%.

Therefore the probability that he will get a parking ticket is P1=0.26.

We calculate the probability that he will not get a parking ticket.

We get:

P=1-P1

P=1-0.26

P=0.74

Therefore, the probability is P=0.74.

8 0

3 years ago

1) a + b + a +b=

mestny [16]

Answer:

3728827272-28277372

c

293728272

e

38838373828737

l

83826382

o

82372882

a

283638272

d

726372826

v

282882

e

2928292282828

r

282828272727272772

t

727263826282728

y

3 0

2 years ago

1-69.

timofeeve [1]

The question above was not written properly

Complete Question

Lacey and Haley are rewriting expressions in an equivalent, simpler form.

a. Haley simplified x³⋅ x² and got

x⁵

Lacey simplified x³ + x² and got the same result! However, their teacher told them that only one simplification is correct. Who simplified correctly and how do you know?

b. Haley simplifies 3⁵⋅ 4⁵ and gets the result 12^10, but Lacey is not sure.

Is Haley correct? Be sure to justify your answer.

Answer:

a) Haley is correct, Lacey simplified wrongly.

b) Haley is incorrect

Step-by-step explanation:

a. Haley simplified x³⋅ x² and got

x⁵

Lacey simplified x³ + x² and got the same result! However, their teacher told them that only one simplification is correct. Who simplified correctly and how do you know?

For Question a, when it comes to simplifying algebraic expression that has to do with powers, there are certain rules that should be followed.

For example

x^a × x^b = x^(a + b)

For Haley, she simplified x³⋅ x² and got

x⁵

She is correct because this follows the product rule of powers or exponents above

= x³⋅ x² = x³+² = x⁵

For Lacey she is wrong because:

x³ + x² ≠ x⁵

x³ + x² when simplified as quadratic equation = x²(x + 1)

b. Haley simplifies 3⁵⋅ 4⁵ and gets the result 12^10, but Lacey is not sure.

Is Haley correct? Be sure to justify your answer.

For question b, when we have two distinct or different numbers with the same power(exponents) the rule states that:

x^a × y^a = (x × y)^a = (xy)^a

Haley is simplified wrongly. She did not apply the rule above

Haley simplified 3⁵⋅ 4⁵ = (3 × 4) ⁵+⁵

= 12^10, this is wrong.

The correct answer according to the rule =

3⁵⋅ 4⁵ = (3 × 4) ⁵ = 12⁵

Therefore,

3⁵⋅ 4⁵ ≠ 12^10

3⁵⋅ 4⁵ = 12⁵

Haley is wrong.

3 0

3 years ago