Please help!! Katherine O'Donnell obtained a personal loan of $1,800 at 10% for 12 months. The monthly payment is $165.00.
What is the new principal after the first payment?

Answer:

x = 4 mm

y = 15 mm

Step-by-step explanation:

x = 12 mm / 3 = 4 mm

y = 3 × 5 mm = 15 mm

Answer: 1 1/2 cup of water

Step-by-step explanation: 3 3/4 - 2 1/4 = 1/2   |  3 - 2 = 1   |  3/4 - 1/4 = 2/4 = 1/2

Answer:

  (a)  ∠1 and ∠5

Step-by-step explanation:

Complementary angles are angles whose measures total 90°. The angles do not have to be adjacent.

__

In this geometry, we can see that angles 1 and 2 are complementary, as are angles 4 and 5, since their respective sums are right angles. Angles 2 and 5 are vertical angles, so have the same measure.

  ∠1 + ∠2 = 90° . . . . . . adjacent angles that total a right angle

  ∠1 +∠5 = 90° . . . . . substitute ∠5 for ∠2, since measures are equal

This means angles 1 and 5 are complementary.

If we start at zero and move a units to the right, and then move the same number of units to the left, we will be back at 0. We can also represent this symbolically. Since a and b are the same distance from zero but are on opposite sides of zero, we know that they are opposites, so b = -a

Answer:

If we start at zero and move a units to the right, and then move the same number of units to the left, we will be back at 0. We can also represent this symbolically. Since a and b are the same distance from zero but are on opposite sides of zero, we know that they are opposites, so b = -a.

Answer:

sqrt (120)

Step-by-step explanation:

Use pythag theorem

Leg1 ^2 + Leg2^2 = Hypot ^2

 13^2    + Leg2^2  =  17^2

    Leg2^2  =  17^2  -  13^2

    Leg2  =  sqrt (120)

Answer:

2 = 22

3 = 19

5 = 13

6 = 10

Step-by-step explanation:

To help with future questions, take whatever is for the x and plug it into the equation

Answer:

22,19,13,10

Step-by-step explanation:

First, Replace the x in the equation with parenthesis (), then inside of the () put the x value in the table so it would look like: y=28-3(2). Then solve by multiplying 2 by 3 so you have y=28-6. Then just subtract 6 from 28 to get 22. Rinse and repeat for the rest of the values. Your first value will be 22, second 19, third 13, and lastly 10. Hope this helps!

Answer:

68 is the perimeter.

Step-by-step explanation:

You can find the perimeter by adding up all of the sides. 13 + 11 + 3 + 7 = 34. To find the other sides of the shape you do 11 + 7 and 13 + 3. 11 + 7 = 18. 13 + 3 = 16. 18 + 16 = 34. 34 + 34 = 68.

Answer:

38.08 m²

Step-by-step explanation:

Given:

Formula:

[tex]\text{Area of trapezium} = \dfrac{\text{Sum of parallel sides}}{2} \times \text{Height}[/tex]

[tex]\implies \text{Area of trapezium} = \dfrac{\text{Sum of parallel sides}}{2} \times \text{Height} \\\\\\ \implies \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \dfrac{\text{10.8 + 2.8}}{2} \times 5.6[/tex]

[tex]\\\\\\\implies \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \dfrac{\text{13.6}}{2} \times 5.6 \\\\\\ \implies \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = {\text{13.6}} \times 2.8 \\\\\\ \implies \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \boxed{38.08 \ \text{m}^{2}}[/tex]

Answer:

a=84.25cm

Step-by-step explanation:

Answer:

An exponent is a number that is to a certain value, like 5^2.

The ^2 means multiply by itself by itself ONCE,

so it would be 5x5.

5^3 means multiply it by itself TWO TIMES,

and going on and on.

Let's say you have a test and the question it's asking is to simplify 5^4.

It's 5x5x5x5, multiplying it by itself FIVE TIMES.

Hope this helped!

Answer:

A. Volume

Step-by-step explanation:

Volume is how much space is in a substance so that means it is A

Answer:

Volume

Step-by-step explanation:

The amount of space that a substance or object occupies is called Volume.

Answer:

From what I can actually read:

Step-by-step explanation:

289 x 76= 21946

25 x 68= 1700

36 x 75= 2700

200 x 60= 12000

200 x 70= 14000

683 x 18= 12294

548 x 63= 34524

629 x 8= 5032

529 x 37= 19537

548 x 63= 34524

100 x 10= 1000

551 x 64= 35264

456 x 12= 5472

42 x 8= 336

68 x 14= 952

And it dosen't matter if you have a multi- numberd equation, because either way you can use a calculator to do the math. and a trick for multiplying by 10 or 100 or 1000: is lets say you have 5 x 1000, instead of doing any math just multiply 1 x 5= 5 then add 3 zero's because 1000 has 3 zeros. You can do this with any number like 10,100,1000,10000 ; you could go on forever.

Answer:

x = 24.0

Step-by-step explanation:

We will need to use one of the trigonometric ratios to find x.  

If we use 58 as the reference angle, we can use tan to find x, as [tex]tan=\frac{opposite}{adjacent}[/tex]

[tex]tan (58)=\frac{x}{15}\\ 15*tan(58)=x\\x=24.005\\x=24.0[/tex]

[tex]\sin \angle F~~= \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\~~~~~~~~~~~~=\dfrac{GE}{EF}\\\\~~~~~~~~~~~~=\dfrac 2 3\\\\\implies \angle F=\sin^{-1} \left(\dfrac 23} \right)=41.8^{\circ}\\\\\text{Hence the measure of angle F is}~ 41.8^{\circ}[/tex]

Answer: 48

Step-by-step explanation:

Answer:

same as other answer

Step-by-step explanation:

The dimension of the box is 50in by 10in by 15in

The volume of an object is the quantity of substance it contains.

The formula for calculating the volume of the box is expressed as:

V = lwh

where:

Given the following parameters

length = 5w
height = w + 5

Substiute

7500 = 5w(w)(w+5)
7500 = 5w²(w+5)
1500 = w³+5w²
w³+5w² - 1500 = 0

Factorize to determine the width

On factorizing, the width of the box is 10 inches

Recall that:

l = 5w
l = 5(10)

l = 50inches

Get the height

h = w + 5
h = 10 + 5
h = 15inches

Hence the dimension of the box is 50in by 10in by 15in

Learn more on volume of box here: https://brainly.com/question/14957364

Answer:

238

Step-by-step explanation:

Given equation:  [tex]a^2+1=6a[/tex]

Rearrange so that it is equal to zero:

[tex]\implies a^2-6a+1=0[/tex]

Quadratic formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0[/tex]

Using the quadratic formula to solve the given equation:

[tex]\implies a=\dfrac{-(-6) \pm \sqrt{(-6)^2-4(1)(1)} }{2(1)}[/tex]

[tex]\implies a=\dfrac{6 \pm \sqrt{32}}{2}[/tex]

[tex]\implies a=3 \pm 2\sqrt{2}[/tex]

[tex]\implies a^2=17 \pm 12\sqrt{2}[/tex]

Substituting this into [tex]7\left(a^2+\dfrac{1}{a^2}\right)[/tex]

[tex]\implies 7\left(17 \pm 12\sqrt{2}+\dfrac{1}{17 \pm 12\sqrt{2}}\right)[/tex]

For [tex]17+12\sqrt{2}[/tex]:

[tex]\implies 7\left(17+12\sqrt{2}+\dfrac{1}{17+12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{(17+12\sqrt{2})^2}{17+12\sqrt{2}}+\dfrac{1}{17+12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{(17+12\sqrt{2})^2+1}{17+12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{289+408\sqrt{2}+288+1}{17+12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{578+408\sqrt{2}}{17+12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{34(17+12\sqrt{2})}{17+12\sqrt{2}}\right)[/tex]

[tex]\implies 7(34)[/tex]

[tex]\implies 238[/tex]

For [tex]17-12\sqrt{2}[/tex]:

[tex]\implies 7\left(17-12\sqrt{2}+\dfrac{1}{17-12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{(17-12\sqrt{2})^2}{17-12\sqrt{2}}+\dfrac{1}{17-12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{(17-12\sqrt{2})^2+1}{17-12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{289-408\sqrt{2}+288+1}{17-12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{578-408\sqrt{2}}{17-12\sqrt{2}}\right)[/tex]

[tex]\implies 7\left(\dfrac{34(17-12\sqrt{2})}{17-12\sqrt{2}}\right)[/tex]

[tex]\implies 7(34)[/tex]

[tex]\implies 238[/tex]

Answer:

3-is 85

2- is 95

4-95

Step-by-step explanation:

for 1 is 85

85-180=95

If Boyce had started investing when he was 20 the amount he would have more than he does in his retirement savings would be b. $321,946.93.

First convert the interest to a monthly rate:

= 4% / 12 months

= 1 / 3 %

Period:

= (63 - 34) x 12 months a year

= 348 months

Amount saved:

= Amount x ( (1 + rate) ^ number of periods - 1) / rate

= 450 x ( (1 + 1/3%)³⁴⁸ - 1 ) / 1/3%

= $294,811.07

If he started saving at 20, the number of periods would be:

= (63 - 20) x 12

= 516 months

Amount saved:
= 450 x ( (1 + 1/3%)⁵¹⁶ - 1 ) / 1/3%

= $616,758

The difference is:

= 616,758 - 294,811.07

= $321,946.93

Find out more on future value savings at https://brainly.com/question/26662056.

Answer:

(x² + 14x)/(9x²)

Step-by-step explanation:

To do this calculation process:

The first term: 2x/x² = 2/x.

Then: (2/x) + (x - 4)/(9x).

We should common the denominator by multiplying the denominators of the two terms (9x)(x) = 9x² and dividing each denominator by the common denominator.

So, it will be equal:

[(2)(9x) + (x - 4)(x)]/9x² = (18x + x² - 4x)/9x² = (x² + 14 x)/9x².

Answer:

2010

Step-by-step explanation:

I do not think so

Answer:

$ 2 per 100g,

Step-by-step explanation:

100g = 1/6 of 600g so:

Cost per 100g = 12 * 1/6

= $ 2.

Answer:

$2

Step-by-step explanation:

12 divided by 6

Answer:

the answer is not you or anything is not

hi hope this is what you were looking for, hope this helps.

Answer:

a. 144m

b. After 2 secs

c. Ball hits the ground after 5 secs.

d. 128m

Step-by-step explanation:

A To find max height, find derivative of equation, let it equal zero, and sub in value into original equation: h(t) = -16t² + 64t + 80 h'(t)=-32t+64 -32t+64=0 32t=64 t=2 h(2) = -16(2²) + 64(2) + 80 h(2) = -64+128+80 = 144m B When h=144, t=2. Therefore, the ball reaches its max height after 2 secs. C When the ball hits the ground, h=0: -16t² + 64t + 80=0 t²-4t-5=0 (simplified) (t-5)(t+1)=0 t=5 and t=-1 Discount t=-1 (time cant be neg). Ball hits the ground after 5 secs. D Find h when t=1: h(t) = -16t² + 64t + 80 h(1) = -16(1²) + 64(1) + 80 h(1) = -16+64+80 h(1) = 128m.

Answer:

$180 + $72 = $252

Step-by-step explanation:

$180 * 40%

$180 * 0.40 = $72

$180 + $72 = $252

As no graph is shown some basic information of parabola can be helpful

And a coordinate is given check it whether it is equal to second part of options

We get

Last two are radar now

As a must be negative option D has such similarities.

Answer:

[tex]\sf y = -0.006x^2 + 0.35x + 6\quad and\quad y = 0.2x[/tex]

Step-by-step explanation:

As the archer shoots the arrow up, the trajectory of the arrow can be modeled as a parabola that opens downwards.  Therefore, this is a quadratic equation with a negative leading coefficient.

From inspection of the answer options, the path of the arrow is :

[tex]y=-0.006x^2+0.35x+6[/tex]

This means the options for the line equation are [tex]y=-x[/tex] and [tex]y=0.2x[/tex]

We are told that the point of intersection of the line and the parabola is at (46.5, 9.3).  As both the x-value and y-value are positive, the equation of the line must be [tex]y=0.2x[/tex]

To confirm, substitute [tex]x=46.5[/tex] into the equation:

[tex]\implies y=0.2(46.5)=9.3[/tex]

Answer:

7 inches

Step-by-step explanation:

The area of a parallelogram is Base x Height.

Area = 28 in^2 = (4 in)*(Height)

Height = 7 inches