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2 years ago

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Complementary angles sum up to equal 90 degrees. Find the measure of each angle in the figure below. Note that since the angles

make up a right angle, they are complementary to each other.

1 answer:

Scorpion4ik [409]2 years ago

4 0

Are you sure you wouldn't add it together?

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On any given day, Juan will break even if he earns as much money as he spends. On day 5, he records the expression 16 + (–16). D

viktelen [127]

Yes

I’m assuming 16 is the amount he earned and (-16) is the amount he spent

16 + (-16) = 16-16 = 0

Juan spent the same amount of money as he earned that day and broke even

5 0

2 years ago

Read 2 more answers

Craig has $1850 dollars in a bank account that he uses to make automatic payments of $400.73 on his car loan. If Craig stops mak

Ivenika [448]

Given:

Amount in the bank account = $1850

Monthly payment of can loan = $400.73

To find:

When would automatic payments make the value of the account zero?

Solution:

Craig stops making deposits to that account. So, amount $1850 in the bank account is used to make monthly payment of can loan.

On dividing the amount by monthly payment, we get

$\dfrac{1850}{400.73}=4.61657$

It means, the amount is sufficient for 4 payment but for the 5th payment the amount is not sufficient.

Therefore, the 5th automatic payments make the value of the account zero.

6 0

2 years ago

Which of the following are terms in the sum of the given polynomials? 3x2,-2x2y, 2xy2, 4y2, xy2, -y2,2x2y

vampirchik [111]

Create the sum of the given polynomial terms.
f(x,y) = 3x² - 2x²y + 2xy² + 4y² + xy² - y² + 2x²y
= 3x² + 3xy² + 3y²

Test the given terms to see if they belong in f(x,y).
3: NO
3x²: YES
3y²: YES
3xy²: YES
4x²: NO

Answer:
The terms in the sum of the given polynomials are 3x², 3y², and 3xy².

6 0

2 years ago

In equilateral ∆ABC with side a, the perpendicular to side AB at point B intersects extension of median AM in point P. What is t

Sergeeva-Olga [200]

Answer:

Perimeter = (2 + √3)·a

Step-by-step explanation:

Given: ΔABC is equilateral and AB = a

The diagram is given below :

AM is a median , PB ⊥ AB , PM = b

Now, by using properties of equilateral triangle, median is perpendicular bisector and each angle is of 60°.

We get, ∠AMB = 90°. So, by linear pair ∠AMB + ∠PMB = 180° ⇒ ∠PMB = 90°. Also, ∠ABC = 60° and ∠ABP = 90° (given) So, ∠PBM = 30°

Since, AM is perpendicular bisector of BC. So,

$MB = \frac{a}{2}$

Now in ΔAMB , By using Pythagoras theorem

$AB^{2}=AM^{2}+MB^{2}\\AM^{2}=AB^{2}-MB^{2}\\AM^{2}=a^{2}-(\frac{a}{2})^{2}\\AM=\frac{\sqrt{3}\cdot a}{2}$

Now, in ΔBMP :

$sin\thinspace 30^{o}=\frac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\sin\thinspace 30^{o}=\frac{\text{MB}}{\text{PB}}\\\\PB=\frac{\text{MB}}{\text{sin 30}}\\\\PB=\frac{\frac{a}{2}}{\frac{1}{2}}\implies PB = a\\\\tan\thinspace 30^{o}=\frac{\text{Perpendicular}}{\text{Base}}\\\\tan\thinspace 30^{o}=\frac{\text{MB}}{\text{PM}}\\\\PM=\frac{\text{MB}}{\text{tan 30}}\\\\PM=\frac{\frac{a}{2}}{\frac{1}{\sqrt3}}\implies PM=b= \frac{\sqrt{3}\cdot a}{2}$

Perimeter of ABM = AB + PB + PM + AM

$\text{Perimeter = }a+a+b+ \frac{\sqrt{3}\cdot a}{2}\\\\=2\cdot a + \frac{\sqrt{3}\cdot a}{2} +\frac{\sqrt{3}\cdot a}{2}\\\\=2\cdot a +\sqrt{3}\cdot a\\\\=(2+\sqrt3})\cdot a$

Hence, Perimeter of ΔABP = (2 + √3)·a units

3 0

2 years ago

Greg has $2,571.68 in his bank account and makes automatic monthly rental payments of $321.46 for a car loan. If he stops making

Anestetic [448]

Answer:

8 months

Step-by-step explanation:

Given that:

Amount of money present in the bank account = $2,571.68

Automatic monthly rental payments for car loan = $321.46

Any deposits in the bank account are stopped.

To find:

The number of months taken so that the automatic payments make the value of the account as zero?

Solution:

Let the number of months taken to make the value of the account zero = $m$ months

To find the value of $m$ , we need to divide the total amount initially present in bank account with the monthly rental payment amount.

Therefore, the equation to find the value of $m$ , can be written as:

$m = \dfrac{2571.68}{321.46}$

On solving the above equation, we get the value as following:

$\bold{m=8}$ months

5 0

2 years ago