Angles 1 and 2 are supplementary



Angle 1 = 30°

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It will take 308 months for Diego to pay the complete loan.

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,

SI = P×T×R

where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.

The interest that will be charged on the principal amount is,

SI = $159,000×30×0.0505 = 240,885

Now, the total amount that Diego needs to pay is the sum of interest and principal, therefore,

Total amount = $159,000 + $240,885 = $399,885

Further, since each month Diego is paying $1300, therefore, the number of months it will take to pay the complete loan is,

Number of months = $399,885/$1300 = 307.6 ≈ 308

Hence, it will take 308 months for Diego to pay the complete loan.

Learn more about Simple Interest:

https://brainly.com/question/2793278

#SPJ1

Answer:

[tex]\displaystyle z=\frac{5}{2}\biggr(\cos\frac{11\pi}{6}+i\sin\frac{11\pi}{6}\biggr)[/tex]

Step-by-step explanation:

A complex number in polar form is [tex]z=r(\cos\theta+i\sin\theta)[/tex] where [tex]r=\sqrt{x^2+y^2}[/tex] and [tex]\displaystyle \theta=\tan^{-1}\biggr(\frac{y}{x}\biggr)[/tex], thus:

[tex]r=\sqrt{x^2+y^2}=\sqrt{(\frac{5\sqrt{3}}{4})^2+(-\frac{5}{4})^2}=\sqrt{\frac{75}{16}+\frac{25}{16}}=\sqrt{\frac{100}{16}}=\frac{10}{4}=\frac{5}{2}[/tex]

[tex]\displaystyle \theta=\tan^{-1}\biggr(\frac{y}{x}\biggr)=\tan^{-1}\biggr(\frac{-\frac{5}{4}}{\frac{5\sqrt{3}}{4}}\biggr)=\tan^{-1}\biggr(-\frac{\sqrt{3}}{3}\biggr)=\frac{11\pi}{6}[/tex]

Thus, the complex number in polar form is [tex]\displaystyle z=\frac{5}{2}\biggr(\cos\frac{11\pi}{6}+i\sin\frac{11\pi}{6}\biggr)[/tex]

Quarts they pick altogether 173/24 quarts.

A unit of volume or capacity in the US Customary System, used in liquid measure, equal to 2 pints or 32 ounces (0.946 liter).

Jennifer picked= 1 5/6= 11/6 quarts

Lila picked= 7/4 quarts

Elliott picked =3/2 quarts

Wendie picked= 17/8 quarts

Total quarts they picked together is= 11/6+7/4+3/2+17/8

                                                           = 44+42+36+51/24

                                                           = 173/24 quarts

Hence, they picked 173/24 quarts together.

Learn more about quarts here:

https://brainly.com/question/13798723

#SPJ1

6 full teams will be made.

If you take 62 and divide it by 9, you'll get a value of 6.88... or it can also be notated as 6 remainder 8. You will be able to make 6 full teams but your last team will only have 8 members, which does not have the full 9 members.

Answer:

Step-by-step explanation:

Emma has £37 in her bank account she starts putting £7 into her account each week write and solve an equation to find how many weeks it will take for emma to have £100 in her bank account r

(100 - 37) : 7 =

63 : 7 = 9

check

37 + 9 * 7 = 100

the answer is good

Answer:

Step-by-step explanation:

Answer: x = 0, x = -3, x = 2

Step-by-step explanation:

f(x) = x^3 + x^2 - 6x

f(x) = 0

x^3 + x^2 - 6x = 0

x(x^2 + x - 6) = 0

x = 0 or

x^2 + x - 6 = 0

D = b^2 - 4ac = 1 - 4*(-6) = 25

x = (-b - sqrt(D))/(2a) = (-1 - 5)/2 = -3 or

x = (-b + sqrt(D))/(2a) = (-1 + 5)/2 = 2

Answer:

hope this will help you ( ◜‿◝ )♡

Step-by-step explanation:

[tex]volume = \frac{4}{3} \times \pi {r}^{3} \\ = \frac{4}{3} \times 3.14 \times ( {10}^{3} ) \\ = 4186.666mm {}^{3} [/tex]

[tex]\large\boxed{\bold{Formula:V= \frac{4}{3}\pi{r}^{3}}}[/tex]

[tex]\large\boxed{\bold{\red\pi\red=\red3\red.\red1\red4}}[/tex]

In this question the radius is given so we'll simply have to substitute and solve.

Let's solve!

Instead of π we are asked to use 3.14

Substitute the values according to the formula.

[tex]V= \frac{4}{3}\times 3.14 \times {10}^{3}[/tex]

Calculator value:

[tex]\bold{V= 4186.666667 \: {mm}^{3}}[/tex]

Now, we have to round off to the nearest hundredth.

The value in the thousandths place is greater than 5 so we'll have to round up by adding 1 to the hundredths place.

Final answer:

[tex]\large\boxed{\bold{V= 4186.67 \: {mm}^{3}}}[/tex]

Hence, the volume of the given sphere is 4186.67 cubic millimeters.

Answer:

circle

Definition: A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle.

Answer:

x=-10

Step-by-step explanation:

2(x+3)=x-4

2x+6=x-4

-2x   -2x

6=-x-4

+4    +4

10=-x

-1    -1

-10=x

[tex] \Large{\boxed{\sf x = 10}} [/tex]

[tex] \\ [/tex]

Given equation:

[tex] \sf 2(x + 3) = x - 4 [/tex]

[tex] \\ [/tex]

Expand the left side using the following distributive property:

A(B + C) = AB + AC

[tex] \\ [/tex]

Here, A = 2, B = x, and C = 3.

We get:

[tex] \sf 2(x) + 2(3) = x - 4 \\ \\ \sf 2x + 6 = x - 4 [/tex]

[tex] \\ [/tex]

Now, subtract 6 from both sides:

[tex] \sf 2x + 6 - 6 = x - 4 - 6 \\ \\ \sf 2x = x - 10 [/tex]

[tex] \\ [/tex]

Subtract x from both sides :

[tex] \sf 2x - x = x - 10 - x \\ \\ \\ \boxed{\boxed{\sf x = -10}} [/tex]

[tex] \\ \\ [/tex]

▪️Learn more about first-degree equations here:

↣https://brainly.com/question/19225782

The velocity of a particle when it moves on a straight line along the x-axis will be V= 42 m/s

Velocity is defined as the ratio of the distance moved by the object in a particular time. The velocity is a vector quantity so it needs both the magnitude and the direction.  

Here we have a displacement function:-

F(t)=3t⁴-5t³+6t-7

So to find out the velocity we will differentiate the above equation with respect to t.

d(F(t)/dt=12t³-15t²+6

V=12t³-15t²+6

Put the value of t=2 seconds

V=12x(2x2x2)-15x(2x2)+6

V=42 meters per second

Hence the velocity of a particle when it moves on a straight line along the x-axis will be V= 42 m/s

To know more about Velocity follow

https://brainly.com/question/25749514

#SPJ1

Answer:

x = 9

y = 116

Step-by-step explanation:

116 and y are vertically opposite angles.

Vertically opposite angles are equal.

So,

y = 116

116 and ( 13x - 53 ) are linear pair angles.

Sum of linear pair angles is 180,

13x - 53 + 116 = 180

13x + 63 = 180

Subtract 63 on both sides,

13x = 180 - 63

13x = 117

Divide 13 on both the sides,

x = 117 / 13

x = 9

Answer:

1.5 Oz because it's just a random guess hopefully I'm right

I think

Answer:

[tex]x=3[/tex]

Step-by-step explanation:

Use the Intersecting Chords Theorem to solve for x:

[tex]\overline{\rm TP}\cdot\overline{\rm PR}=\overline{\rm QP}\cdot\overline{\rm PS}\\\\(x+3)(x)=(6-x)(2x)\\\\x^2+3x=12x-2x^2\\\\3x^2+3x=12x\\\\3x^2-9x=0\\\\3x(x-3)=0\\\\x=0,\: x=3[/tex]

The solution [tex]x=0[/tex] however, does not make sense because the chords have lengths, so [tex]x=3[/tex] is the only sensible answer.

Intersecting Chords Theorem States:

As Length cannot be zero or negative here. x = 3

Answer:

[tex]y = \frac{x - 3}{2}[/tex]

Step-by-step explanation:

To find the inverse of a function, simply 'switch' the x and y's and solve for y. [tex]y = 2x + 3[/tex] becomes [tex]x = 2y + 3[/tex]. Now, solving for y, we get [tex]y = \frac{x - 3}{2}[/tex].

hope this helped! :)

Answer:

4(3)(-2) = -24

Answer:

C) -24

Step-by-step explanation:

Given the expression: 4xy

Substitute the values above for the variables and multiply:

4(3)(-2)

12(-2)

-24

Final answer: -24

Hope this helps!

Answer:

3x + 12

Step-by-step explanation:

This is an 'expression'  ...there is no 'answer'  but it can be re-arranged

3(x+4) =   3 * x  +  3 * 4 =   3x + 12

Hey there!

3(x + 4)

= 3(1x + 4)

DISTRIBUTE 3 WITHIN the PARENTHESES

= 3(1x) + 3(4)

= 3(x) + 3(4)

= 3x + 12

Therefore, the answer should be:

3x + 12

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

Step-by-step explanation:

Here's the table!

1 Kilobyte = 1,024 Bytes

1 Megabyte = 1,024 Kilobytes

1 Gigabyte = 1,024 Megabytes

1 Terabyte = 1,024 Gigabytes

From this we can see that there are

Answer:

See the attached graph

Step-by-step explanation:

The solution is the labelled point of intersection in the graph

Answer:

there is the answer to your question

Answer: 31.0

Step-by-step explanation:

Answer:

Below.

Step-by-step explanation:

(a). The x estimations of the turning points are -1.8 and 1.1, according to the graph.

(b). Where the graph crosses the x axis are the solutions. x = -3, 0, and 2 are the values.

Answer:

38cm

Step-by-step explanation:

set 3x-5 and 19-x equal to eachother, since, given as its an isoscles triangle, they should be equal. After you work out the equation, you're left with x=6. So now you plug that it.

3(6)-5=13

19-(6)=13

2(6)=12

Now you add them all together, so the perimeter is 38 cm.

Answer:

Then numbers 7 , 8 , 14 , -6 , 10 are output values of the function

Because matrix A has 3 rows, and matrix B has 2 columns, matrix C will be a 3x2 matrix. 3 rows, 2 columns.

Answer:

it is c I hope this helps you.

If Rudy successfully adds $50,000 to the value of his house, his new annual homeowner's insurance premium be c. $1,291.30.

The annual homeowner's insurance premium is the insurance charge that the homeowner pays as an insurance premium annually.

The insurance premium is calculated using some set formulas determined by these factors:

Insurance premium rate = $0.37 per $100

Current insurance premium = $1,106.30

Added value to the house = $50,000

Added premium = $185 ($50,000 x $0.37/$100)

New insurance premium = $1,291.30 ($1,106.30 + $185)

Thus, if Rudy successfully adds $50,000 to the value of his house, his new annual homeowner's insurance premium be c. $1,291.30.

Learn more about the annual homeowner's insurance premium at https://brainly.com/question/26133348

#SPJ4

Answer:

it's C......................

Step-by-step explanation:

i got 100% on egde

Step-by-step explanation:

Rearrange the equations to solve.

cos(-3 • pi) = -1

cos((-3pi) / 4 radians) = -0.707

cos(5 • pi) = -1

cos((5pi) / 4 radians) = -0.707

They are the same because when multiplied, they are the same value, and always will be that way. They also have the same identity if you simplify and compare the results of that equation.

The value of cos (-3π/4) and the value of cos (5π/4) are same.

Trigonometric ratios are the ratios which is described for two sides of a right angled triangle.

The main three trigonometric ratios are sine, cosine and tangent functions.

We know that,

cos (-3π/4) = cos (3π/4)

Now,

cos (3π/4) = cos (π + π/4)

And,

cos (5π/4) = cos (π - π/4)

Now, we know that,

cos (π + x) = -cos (x) and cos (π - x) = -cos (x)

So the value of cos (π + π/4) = -cos( π/4) and cos (π - π/4) = -cos( π/4)

Hence cos (3π/4) = cos (5π/4) = -cos( π/4)

Hence both the values are same.

Learn more about Cosine Functions here :

https://brainly.com/question/17954123

#SPJ2