A debt of $9000 is to be amortized with 4 equal semiannual payments. If the interest rate is 7%, compounded semiannually, what is the size of each payment?

Answer:

f(d)=0.1d^2+d+2

Step-by-step explanation:

t(d)=−0.2d2+4d+12

a(d)=−0.3d2+3d+10

how many more teenagers than adults attend the festival on any day?

==>

f(d) = t(d) - a(d)

=0.1d^2+d+2

Answer:  -2

This is because (-2)^5 = -32. Applying the fifth root to both sides lets us say [tex]-2 = \sqrt[5]{-32}[/tex]

There are four other roots but they are complex. Effectively, we are solving the equation [tex]x^5 + 32 = 0[/tex]

Answer:

The only true statement is:

"The system of linear equations 8x - 3y = 10 and 16x - 6y = 22 has no solution."

Step-by-step explanation:

First, some definitions.

A system of linear equations has infinite solutions if both equations define the same line, has no solutions if we have two parallel lines, has one solution in all the other cases.

Where two lines are parallel if we can write them as:

a*x + b*y = c

a*x + b*y = d

where c and d are different numbers.

Now we can analyze the given statements:

a)

6x - 5y = 8

12x - 10y = 16

has no solution?

If we divide both sides of the second equation by 2, we get:

(12x - 10y)/2 = 16/2

6x - 5y = 8

We get the first equation, then both equations define the same line, thus the system has infinite solutions, then the statement is false.

b)

7x + 2y = 6

14x + 4y = 16

has infinite solutions?

Let's divide the second equation by 2, then we get:

(14x + 4y)/2 = 16/2

7x + 2y = 8

If we rewrite our system of equations, we get:

7x + 2y = 6

7x + 2y = 8

These are parallel lines, thus, this system has no solutions.

So the statement is false.

c)

8x - 3y = 10

16x - 6y = 22

has no solution?

Again, let's divide the second equation by 2 to get:

(16x - 6y)/2 = 22/2

8x - 3y = 11

If we rewrite our system:

8x - 3y = 10

8x - 3y = 11

These are parallel lines, thus the system has no solutions, so this statement is correct.

d)

9x + 6y = 14

18x + 12y = 26

Has infinite solutions?

Dividing the second equation by 2 we get:

(18x + 12y)/2 = 26/2

9x + 6y = 13

So the equations are different (are parallel lines again) so this system has not infinite solutions.

Then the statement is false.

Answer:

The answer to your question is the third choice.

Step-by-step explanation:

a)          6x - 5y = 8

          12x - 10y = 16

We observe that these lines are the same so they have infinite solutions.

b)

           7x + 2y = 6

          14x + 4y = 16

These lines are parallel because they have the same slope, so they do not cross, there is no solution.

c)

            8x - 3y = 10

           16x - 6y = 22

These lines are parallel because they have the same slope, so they do not cross, there is no solution.

d)

           9x + 6y = 14

          18x + 12y = 26

These lines are parallel because they have the same slope, so they do not cross, they do not have an infinite number of solutions.

Answer:

First find the SA of the triangular figure

4 x 3 = 12 cm^2 (the triangles on the sides)

2 x 3 = 6 cm^2 (the back square)

2 x 5 = 10 cm^2 (the slanted square)

*I'm not sure if this question includes the bottom of the triangle but here it is anyways

4 x 2 = 8 cm^2

Including the bottom the SA of the triangular figure is:

12 + 6 + 10 + 8 = 36 cm^2

Find the SA of the rectangular shape

4 x 2 = 8 cm^2 (the bottom square)

2 x 6 = 12 x 2 = 24 cm^2 (the sides)

4 x 6 = 24 x 2 = 48 cm^2 (the front and back)

Add them up

8 + 24 + 48 = 80 cm^2

If you wanted to find the SA of the whole figure it would be:

12 + 6 + 10 + 8 + 24 + 48 = 108 cm^2

Hope this helps!

Answer:

A. 1/2 cups

Step-by-step explanation:

13/15 is close to 1

1/5 is a small amount

9/20 is just over 1/2

5/11 is just under 1/2

7/15 is just under 1/2

Estimate: 1 + 1/2 + 1/2 + 1/2 + a little = 2 1/2

He needs 3 cups, so he needs another 1/2 cup.

Answer: A. 1/2 cups

Answer:

it a 1/2

Step-by-step explanation:

Answer:

11 is the answer.....

Step-by-step explanation:

6x-15+39+90 = 180

C = 25 deg

a ≈ 10.72 ft

b ≈ 11.83 ft

Answer:

C = 25

a = 10.72

b = 11.83

Step-by-step explanation:

C:

Solve; 180 - (90 + 65)

a:

Tan(65) = a/5

Tan(65) * 5 = a

10.72 = a

b:

Cos(65) = 5/b

Cos(65) * b = 5

b = 5 / Cos(65)

b = 11.83

Hope this helps!

Answer:

LA = 2πrh

Step-by-step explanation:

The lateral surface area is the area of all the sides of a 3-dimensional object excluding its base and top.

The lateral area of a cylinder is the area of its surfaces excluding the area of its base and top

LA = 2πrh

The slope formula is the changes of two y-values over/to the changes of two x-values.

[tex] \large \boxed{m = \frac{y_2 - y_1}{x_2 - x_1} }[/tex]

Substitute two given points in the formula to find the slope. The m-term represents the slope from y = mx+b.

[tex]\large{m = \frac{10 - ( - 8)}{2 - 10} } \\ \large{m = \frac{10 + 8}{ - 8} } \\ \large{ m = \frac{18} { - 8} \longrightarrow \frac{9}{ - 4} } \\ \large \boxed{m = - \frac{9}{4} }[/tex]

Answer

Hope this helps and let me know if you have any doubts!

Answer:

m=-9/4

Step-by-step explanation:

Hi there!

The formula for the slope (m) calculated from two points is given as (y2-y1)/(x2-x1), where (x1,y1) and (x2,y2) are points

we are given the two points (2,10) and (10,-8)

to avoid any confusion, let's label the values of the points

x1=2

y1=10

x2=10

y2=-8

now substitute into the formula:

m=(-8-10)/(10-2)

subtract

m=(-18)/(8)

simplify (reduce to lowest terms)

m=-9/4

Hope this helps!

Answer:

22°

63°

m<H=22°

m<G=63°

Problem 1

--------------------------

Work Shown:

For any triangle, the three angles always add to 180

For any isosceles triangle, the base angles are congruent. The base angles are opposite the congruent sides. We see that angle O = angle H.

O+H+T = 180

H+H+T = 180

2H+T = 180

2H+22 = 180

2H = 180 - 22

2H = 158

H = 158/2

H = 79

=======================================================

Problem 2

--------------------------

Work Shown:

We'll use the same ideas as problem 1.

In this case, angle O = angle D = 63 since they are the base angles opposite the congruent sides.

D+G+O = 180

63+G+63 = 180

G+126 = 180

G = 180-126

G = 54

Answer:

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.

Answer:

Step-by-step explanation:

Given that:

[tex]y^2 (y^2-4) = x^2(x^2 -5)[/tex]

at point (0, -2)

[tex]\implies y^4 -4y^2 = x^4 -5x^2[/tex]

Taking the differential from the equation above with respect to x;

[tex]4y^3 \dfrac{dy}{dx}-8y \dfrac{dy}{dx}= 4x^3 -10x[/tex]

Collect like terms

[tex](4y^3 -8y)\dfrac{dy}{dx}= 4x^3 -10x[/tex]

[tex]\dfrac{dy}{dx}= \dfrac{4x^3 -10x}{4y^3-8y}[/tex]

Hence, the slope of the tangent line m can be said to be:

[tex]\dfrac{dy}{dx}= \dfrac{4x^3 -10x}{4y^3-8y}[/tex]

At point (0,-2)

[tex]\dfrac{dy}{dx}= \dfrac{4(0)^3 -10(0)}{4(-2)^3-8-(2)}[/tex]

[tex]\dfrac{dy}{dx}= \dfrac{0 -0}{4(-8)+16}[/tex]

[tex]\dfrac{dy}{dx}= 0[/tex]

m = 0

So, we now have the equation of the tangent line with slope m = 0 moving through the point (x, y) = (0, -2) to be:

(y - y₁ = m(x - x₁))

y + 2 = 0(x - 0)

y + 2 = 0

y = -2

Answer:

87

Step-by-step explanation:

Answer:

24 + y = 41

y = 17

Step-by-step explanation:

24 + y = 41

y + 24 = 41

y + 24 - 24 = 41 - 24

y = 17

Answer:

In 25 years I will have $ 27,137.65. Therefore, I will earn $17,137.65 interest.

Step-by-step explanation:

Given that I deposit $ 10,000 in an account earning 4% interest compounded monthly, to determine how much will you have in the account in 25 years and how much interest will I earn, the following calculation must be performed:

10,000 x (1 + 0.04 / 12) ^ 25x12 = X

10,000 x (1 + 0.00333) ^ 300 = X

10,000 x 2.7137 = X

27,137.65 = X

Therefore, in 25 years I will have $ 27,137.65. Therefore, I will earn $17,137.65 interest.

Answer:

Hi, there the answer is

These are the equations with exactly one solution

-5x + 12 = –12x – 12

-5x + 12 = 5x + 12

-5x + 12 = 5x – 5

Hope This Helps :)

Step-by-step explanation:

First degree equations

A first degree equation has the form

ax + b = 0

There are some special cases where the equation can have one, infinitely many or no solution

If , the equation has exactly one solution

If a=0 and b=0 the equation has infinitely many solutions, because it doesn't matter the value of x, it will always be true that 0=0

If a=0 and  the equation has no solution, because it will be equivalent to b=0 and we are saying it's not true. No matter what x is, it's a false statement.

We have been given some equations, we only need to put them in standard form

-5x + 12 = –12x – 12

Rearranging

7x + 24 = 0

It has exactly one solution because a is not zero

.......................

-5x + 12 = 5x + 12

Rearranging

-10x + 0 = 0

It has exactly one solution because a is not zero

.......................

-5x + 12 = 5x – 5

Rearranging

-10x + 17 = 0

It has exactly one solution because a is not zero

.......................

-5x + 12 = -5x – 12

Rearranging

0x + 24 = 0

It has no solution, no matter what the value of x is, it's impossible that 24=0

Answer: These are the equations with exactly one solution

-5x + 12 = –12x – 12

-5x + 12 = 5x + 12

-5x + 12 = 5x – 5

Answer:

[tex]14 + x \leqslant 26 \\ x \leqslant 26 - 14 \\ { \tt{x \leqslant 12}}[/tex]

Answer:

how old are you gghhjjzetstu9u

Answer:

4 ft

Step-by-step explanation:

let's find radius first

radius=diameter/2

=6/2

=3 ft

radii=3 ft

Now by using pythagoras theorem

a^2 + b^2 = c^2

3^2 + 3^2 =AB^2

9+9=AB^2

18=AB^2

[tex]\sqrt{18}[/tex] AB

4.24 =AB

4 ft =AB (after converting to nearest foot)

Answer:

Profit % on skates = 8.7 %

Step-by-step explanation:

Step 1 : Find cost price of skates

Cost price of helmet = £45

Let cost price of skate be = x

Selling price = £224

Cost price = (x + 45)

Total profit % = 40%

[tex]Profit \% = \frac{Selling \ price - cost \ price }{Cost \ price} \times 100[/tex]

[tex]\frac{40}{100} = \frac{224 - (x + 45)}{(x + 45)}\\\\40(x+ 45) = 100(224 - (x +45))\\\\40(x + 45) = 22400 - 100(x + 45)\\\\40(x +45) + 100(x+ 45) = 22400\\\\140(x + 25) = 22400\\\\x + 45 = \frac{22400}{140}\\\\x = 160 - 45 = \£ \ 115[/tex]

Total cost price = 45 + 115 = £160

Step 2 : Selling price of Helmet

Cost price of Helmet = £45

Let selling price of helmet be = y

Profit % of helmet = 120 %

[tex]Profit \% = \frac{selling \ price - cost \ price}{cost \ price}[/tex]

[tex]\frac{120}{100} = \frac{y -45}{45}\\\\\frac{120 \times 45}{100} = y -45\\\\54 = y - 45\\\\99 = y[/tex]

Step 3 : Selling price of skates

Total selling = selling price of helmet + selling price of skates

224 = 99 + selling price of skates

224 - 99 = selling price of skates

125 = selling price of skates

Step 4 : Profit percentage on skates

Cost price of skate = £ 115

Selling price of skate = £ 125

[tex]Profit \% \ on \ skates = \frac{selling\ price- cost \ price }{cost \ price} \times 100[/tex]

                           [tex]= \frac{125-115}{115} \times 100\\\\=\frac{10}{115} \times 100\\\\= 8.7 \%[/tex]

Answer:

The probability is [tex]\frac{24}{70}[/tex].

Step-by-step explanation:

topping options available: four vegetables, two meats, and two cheeses

Number of topping on one pizza = 4

Getting two vegetables = (4 C 2)

Getting one meat = (2 C 1)

Getting one cheese = (2 C 1)

Choosing 4 toppings out of 8 = (8 C 4)

probability that the pizza is ordered with exactly two vegetables, one meat, and one cheese

[tex]\frac{(4C2)\times (2C1)\times (2C1)}{(8C4)}\\\\\frac{6\times 2\times 2}{70}\\\\\frac{24}{70}[/tex]

Answer:

The coordinates of point E are (7,8).

Step-by-step explanation:

Point E:

Is given by (x,y).

DE: EF = 2:3.

This means that, for both coordinates x and y:

[tex]E - D = \frac{2}{2+3}(F-D)[/tex]

[tex]E - D = \frac{2}{5}(F-D)[/tex]

x-coordinate:

x-coordinate of D: 1

x-coordinate of F: 16

[tex]E - D = \frac{2}{5}(F-D)[/tex]

[tex]x - 1 = \frac{2}{5}(16-1)[/tex]

[tex]x - 1 = 2*3[/tex]

[tex]x = 7[/tex]

y-coordiante:

y-coordinate of D: 4

y-coordinate of F: 14

[tex]E - D = \frac{2}{5}(F-D)[/tex]

[tex]y - 4 = \frac{2}{5}(14-4)[/tex]

[tex]y - 4 = 2*2[/tex]

[tex]x = 8[/tex]

The coordinates of point E are (7,8).

Answer:

P = $98.77

Step-by-step explanation:

FV = p (1+i)^n -1

            i

pv = 700,000

i = .075/12 = .00625

n = (66 - 15)* 12 = 612

700,000 = P (( 1 + .00625)^ 612 -1 /.00625

4375 = P (1.00625)^612 -1)

P = $98.77

Answer:

page 1:

51 years

$98.78

639546.64 (i think)

Page 2:

213 months

17.8 years

321 months

26.8 years

1128.9 months

88.8 years

I would probably choose the second plan because it's rather unlikely that i live past 90

Step-by-step explanation:

page 1

Let's assume the payments are at the end of the month

66-15= 51 years

effective rate: .075/12=.00625

[tex]700000=x\frac{(1+.00625)^{51*12}-1}{.00625}\\x=98.77973387[/tex]

which i guess we can round to 98.78

700000-98.78*(51*12)= 639546.64

This number is really really high and so maybe you want to double check it

page 2

effective rate: .051/12=.00425

[tex]700000=5000\frac{1-(1+.00425)^{-n}}{.00425}\\.405=(1+.00425)^{-n}\\log_{1.00425}.405=-n\\n=213[/tex]

213 months

213/12= 17.8 years

[tex]700000=4000\frac{1-(1+.00425)^{-n}}{.00425}\\.25625=(1.00425)^{-n}\\log_{1.00425}.25625\\n=321[/tex]

321 months

321/12=26.8 years

[tex]700000=3000\frac{1-(1+.00425)^{-n}}{.00425}\\.008333333=(1.0045)^{-n}\\log_{1.0045}.00833333=-n\\n=1128.9[/tex]

1128.9 months

1128.9/12= 94.1 years

1066 months

1066/12= 88.8 years

Answer:

The golf ball was in the air for 4 seconds.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]

[tex]\Delta = b^{2} - 4ac[/tex]

In this question:

We have to find the amount of time it takes for the ball to hit the ground. We have that:

[tex]d(t) = -2t^2 + 7t + 4[/tex]

Which is a quadratic equation with [tex]a = -2, b = 7, c = 4[/tex].

How long is the golf ball in the air?

We have to find t for which [tex]d(t) = 0[/tex]

So

[tex]-2t^2 + 7t + 4 = 0[/tex]

[tex]\Delta = b^{2} - 4ac = (7)^2 - 4(-2)(4) = 81[/tex]

[tex]t_{1} = \frac{-7 + \sqrt{81}}{2*(-2)} = -0.5[/tex]

[tex]t_{2} = \frac{-7 - \sqrt{81}}{2*(-2)} = 4[/tex]

Time is a positive measure, so t = 4.

The golf ball was in the air for 4 seconds.

9514 1404 393

Answer:

  x = 8/7

Step-by-step explanation:

The only real zero of this linear function is the value of x that makes y=0:

  0 = -7x +8

  7x = 8 . . . . . . add 7x

  x = 8/7 . . . . . .divide by 7

Answer:

maybe if u translate it in English

Step-by-step explanation:

it wouldv been helpful if u mind?

Hope this help!!!

Have a nice day!!!

Answer:

what is the question?

Step-by-step explanation:

answer the question

Answer:

y - 10 = -1/2(x + 4)

General Formulas and Concepts:

Algebra I

Coordinates (x, y)

Point-Slope Form: y - y₁ = m(x - x₁)

Step-by-step explanation:

Step 1: Define

Identify variables

m = -1/2

Point (-4, 10) → x₁ = -4, y₁ = 10

Step 2: Find

Answer: [tex]y=-\frac{1}{2} x+8[/tex]

Step-by-step explanation:

An equation of a line can be in slope intercept form which is y=mx+b

m is the slope, b is the y intercept, x it the x coordinate, and y is the y coordinate. Since we know the slope is -1/2 and we know a x coordinate is -4 and a y coordinate is 10 we can sub them in and solve for the value of b.

[tex]y=mx+b\\10=(-\frac{1}{2})(-4)+b\\10=2+b\\10-2=2+b-2\\8=b[/tex]

The value of b is 8. We can now sub it in for our equation of the line. This time with x and y as variables.

y=-1/2x+8

Answer:

101 =x

Step-by-step explanation:

The measure of the exterior angle is equal to the sum of the opposite interior angles

143 = 42+x

Subtract 42 from each side

143-42 = 42+x-42

101 =x

Answer:

x = 101 degrees

Step-by-step explanation:

The sum of the external angle and its adjacent is 180 degrees

143 + y = 180

y = 37 degrees

The sum of the inner angles of a triangle is 180 degrees

37 + 42 + x = 180

79 + x = 180

x = 101 degrees