Complete the table below by finding the unknown principal P, rater, time t, and interest /.

Principal P

(a)

480,000

250,000

980,000

Rate r

6%

(b)

5.5%

0.8%

Time t

10

15

(c)

3.5

Interest /

9,000

180,000

68,750

(d)

12

[tex]z = 29°[/tex]

Step-by-step explanation:

According to the triangle angle sum theorem, the sum of the interior angles of a triangle is 180°. So for [tex]\triangle{ABD},[/tex] the sum of its interior angles is

[tex]43 + 59 + x = 180[/tex]

[tex]\Rightarrow x = 78°[/tex]

But [tex]\angle{x}[/tex] is supplementary with [tex]\angle{y}[/tex] so that

[tex]x + y = 180 \Rightarrow y = 180 - 78 = 102°[/tex]

Now that we know the value of y, we apply the triangle angle sum theorem to [tex]\triangle{BDC}[/tex] and we get

[tex]49 + y + z = 180 \Rightarrow 49 + 102 + z = 180[/tex]

Solving for z, we finally get

[tex]z = 29°[/tex]

9514 1404 393

Answer:

  7.  $10,459.28

  8.  $30,060.93

Step-by-step explanation:

Your table 12-2 will tell you the present-value multiplier of the annual payment for a 10-year annuity due will be ...

  7%: 7.515232

  11%: 6.537048

__

7. The 11% table value will be used with a payment of $1600 to find the present value:

  6.537048 × $1600 = $10,459.28 . . . present value of the annuity due

__

8. The 7% table value will be used with a payment of $4000 to find the present value:

  7.515232 × $4000 = $30,060.93 . . . present value of the annuity due

Answer:

4/3

Step-by-step explanation:

Answer:

These figures are not the same because the Slope of DE is not the same as the slope of JK.

Step-by-step explanation:

Slope of DE = -2/1

Slope of JK = -1

If they were similar, the slope would be the same, but the size would not.

-Chetan K

Answer: 12 feet up

Step-by-step explanation:

This problem models a right triangle, in which the ladder is the hypotenuse and the distance away from the wall is one of the legs.  Thus, you may use the Pythagorean Theorem (a^2 + b^2 = c^2)

[tex]a^2+b^2=c^2\\5^2+b^2=13^2\\25+b^2=169\\b^2=144\\b=12[/tex]

N.B. There are some very useful sets of numbers that can help you with this unit.

They are called Pythagorean triplets, and they are the sets of whole numbers that make right triangles.  The important ones are 3, 4, 5, and 5, 12, 13 (And their multiples, like 6, 8, 10(3,4,5 *2))

Hope it helps :) and let me know if you want me to elaborate further.

Answer:

32 bracelets

Step-by-step explanation:

First multiply each bracelet by 4 to get the correct amount:

3x4=12

4x5=20

Then, add the two.

12+20=32

Answer:

Step-by-step explanation:

Three-fourths of the difference of a number and 7 is negative fifteen:

Answer:

P = 12 + 5x

Step-by-step explanation:

P = a + b + c

P = 7 + (x + 4) + (4x + 1)

  = 7 + x + 4 + 4x + 1

  = 12 + 5x

Answer: A

Step-by-step explanation:

By replacing in the given equation:

y=-3x-7

y=-3(-2)-7

y=6-7

y=-1

But for choices B, C and D the given x values don't fit with the images.

Answer:

f(4) = 1.4

Step-by-step explanation:

f(x) = (3x/2) - (14/3)

We are given that x = 4

f(4) = (3(4)/2) - (14/3)

f(4) = (12/2) - (14/3)

f(4) = 6 - (14/3)

14/3 as a decimal is 4.6

f(4) = 6 - 4.6

f(4) = 1.4 (approximately)

x=4,5,6

x=4

[tex]\\ \sf\longmapsto y=3(4)+10[/tex]

[tex]\\ \sf\longmapsto y=12+10=22[/tex]

x=5

[tex]\\ \sf\longmapsto y=3(5)+10=15+10=25[/tex]

x=6

[tex]\\ \sf\longmapsto y=3(6)+10=18+10=28[/tex]

Step-by-step explanation:

y = 3x + 10

Soo :

y = 3(4) + 10 = 12 + 10 = 22

y = 3(5) + 10 = 15 + 10 = 25

y = 3(6) + 10 = 18 + 10 = 28

the first one is (B) i think

the second one is (B)

the third one is (B)

the fourth one is (A)

the fifth one is (A)

Step-by-step explanation:

This is an isosceles triangle because in an isosceles triangle angles opposite to each of the equal sides must also be equal. Since the diagram shows 2 equal angles we can say its isosceles.

So 3(x+2) = 24

8= x+2

x = 6

Answer:

x = 6

Step-by-step explanation:

The triangle given is an isosceles triangle.

Which means, the two sides and the two angles will be the same.

One of the sides is 24.

The other is 3 ( x + 2 )

Hence, we will get this equation.

24 = 3 ( x + 2 )

24 = 3x + 6

24 - 6 = 3x

18 = 3x

6 = x

Thus, x = 6.

I hope it helps.

Answer: 4914

Step-by-step explanation:

multiply 15 and 20 to make 300

multiply 24 and 27 to make 648

set up proportion

[tex]\frac{300}{648}[/tex] × [tex]\frac{2275}{x}[/tex]

cross multiply

300x = 648(2275)

300x = 1474200

x = 4914

Answer:

did u mean 7 minutes & 30 seconds or

do you need seperate percentage for each ???

Answer:

420 i think

Step-by-step explanation:

7 mins

7×60

=420

plus the 30sec

450 sec

450/3600×100

45000/3600

450/36

12.5

Answer:x=-3.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

First one is TRUE...you'd multiply by negative one third

Second is FALSE...no multiplication needed to get x as a positive.

3rd graph, far right on top

Step-by-step explanation:

Use the vertical line test to determine (one input for x cannot have two outputs of y)

Answer: No

Step-by-step explanation:

2 is double 1.

Because 11 is not double 9, the ratios are not equivalent.

Hope it helps :)

Answer:

6sqrt5

Step-by-step explanation:

Answer:

The solution to a system of linear equations is the ordered pair (or pairs) that satisfies all equations in the system.  The solution is the ordered pair(s) common to all lines in the system when the lines are graphed.

Lines that cross at a point (or points) are defined as a consistent system of equations. The place(s) where they cross are the solution(s) to the system.

Parallel lines do not cross. They have the same slope and different y-intercepts. They are an example of an inconsistent system of equations. An inconsistent system of equations has no solution.

Two equations that actually are the same line have an infinite number of solutions. This is an example of a dependent system of equations.

Step-by-step explanation:

Solve the system of equations graphically.

3x + 2y = 4

−x + 3y = −5

Solution

Graph each line and determine where they cross.

The lines intersect once at (2, −1).

A graphic solution to a system of equations is only as accurate as the scale of the paper or precision of the lines. At times the point of intersection will need to be estimated on the graph. When an exact solution is necessary, the system should be solved algebraically, either by substitution or by elimination.

Substitution Method

To solve a system of equations by substitution, solve one of the equations for a variable, for example x. Then replace that variable in the other equation with the terms you deemed equal and solve for the other variable, y. The solution to the system of equations is always an ordered pair.

Example

Solve the following system of equations by substitution.

x + 3y = 18

2x + y = 11

Solution

Solve for a variable in either equation. (If possible, choose a variable that does not have a coefficient to avoid working with fractions.)

In this case, it's easiest to rewrite the first equation by solving for x.

x + 3y = 18

x = −3y + 18

Next, substitute (−3y + 18) in for x into the other equation. Solve for y.

2(  3y + 12x + y = 11

2(−3y + 18) + y = 11-------Substitute -3y + 18 in for

   −6y + 36 + y = 11-------Distribute.

2(3y −5y + 36 = 11-------Combine like terms.

2(3y +  18−5y = −25-----Subtract 36 from both sides

2(3y + 18) +  y = 5----   -Divide both sides by -5.

Then, substitute y = 5 into your rewritten equation to find x.

x = −3y + 18

x = −3(5) + 18

x = −15 + 18

x = 3

Identify the solution.   A check using x = 3 and y = 5 in both equations will show that the solution is the ordered pair (3, 5).

Elimination Method

Another way to solve a system of equations is by using the elimination method.  The aim of using the elimination method is to have one variable cancel out. The resulting sum will contain a single variable that can then be identified. Once one variable is found, it can be substituted into either of the original equations to find the other variable.

Example

Find the solution to the system of equations by using the elimination method.

x − 2y = 9

3x + 2y = 11

Solution

Add the equations.

 x −  2y = 9

3x +  2y = 11

4x +  2y = 20

Isolate the variable in the new equation

4x = 20

 x = 5

Substitute x = 5 into either of the original equations to find y.

 x − 2y = 9

(5) − 2y = 9

     −2y = 4

        y = −2

Identify the ordered pair that is the solution.   A check in both equations will show that (5, −2) is a solution.

It may be necessary to multiply one or both of the equations in the system by a constant in order to obtain a variable that can be eliminated by addition. For example, consider the system of equations below:

3x + 2y = 6

 x − 5y = 8

Both sides of the second equation above could be multiplied by −3. Multiplying the equation by the same number on both sides does not change the value of the equation. It will result in an equation whereby the x values can be eliminated through addition.

Special Cases

In some circumstances, both variables will drop out when adding the equations. If the resulting expression is not true, then the system is inconsistent and has no solution.

4x + 6y = 13

6x + 9y = 17

3(4x + 6y = 13)

2(6x + 9y = 17)

12x + 18y = 39

12x + 18y = 34

             0 = 5

The equation is false.  The system has no solution.

If both variables drop out and the resulting expression is true, then the system is dependent and has infinite solutions.

6x + 15y = 24

4x + 10y = 16

2(6x + 15y = 24)

3(4x + 10y = 16)

12x + 30y = 48

12x + 30y = 48

             0 = 0

The equation is true.  The system has an infinite number of solutions.  (Notice that both of the original equations reduce to 2x + 5y = 8.  All solutions to the system lie on this line.)

Answer:

38 in

Step-by-step explanation:

114 yds divided by 3 = 38 in

Answer:

A'(-6,4) B'(2,2) C'(-2,-2)

Step-by-step explanation:

The dilation is by 2. This just means you multiply each number by two. FOr example, for point a, multiply -3 by 2 and 2 by 2 to get (-6, 4).

Step-by-step explanation:

4x×y=20

.....

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

The expression for four times the product of a number x and a number y is equal to 20 is 4xy = 20.

Given,

Four times the product of a number x and a number y is equal to 20.

We need to write the expression.

- 2 times M = 2 x M

- Product of M and N = M x N

- 3 more than M = M + 3

- 3 less than M = M - 3

Find the expression.

We have,

Four times the product of a number x and a number y is equal to 20.

Here,

The product of a number x and a number y can be written as:

= (x) x y

Four times the product of a number x and a number y can be written as:

= 4 x [ (x) x y ]

- is equal to 20 can be written as:

= 20

Now,

We get,

4xy = 20

Thus the expression for Four times the product of a number x and a number y is equal to 20 is 4xy = 20.

Learn more about how to write an expression here:

https://brainly.com/question/15284271

#SPJ2

Answer:

16x

Step-by-step explanation:

(3x + 2) (x - 6)

Multiply 3x by x and -6

3x^2 - 18x

Multiply 2 by x and -6

2x - 12

Combine like terms

3x^2 - 16x - 12

The middle term is 16x

Answer:

We want the ith row of the new matrix SijA to be the old jth row of A, so we need the ith row of Sij to extract the jth entry of column of A.

This mean the ith row of Sij must have a 1 in the jth entry and 0's everywhere else.

Similarly, the jth row of Sij must have a 1 in the ith entry and 0's everywhere else.

in the piecewise notation this is

(Sij)kl ={1 if k=i and l=j, 1 if k=k and l=i; 1 if k=l but k#i,j, 0 otherwise

Step-by-step explanation:

The number of fiction books are 7 and number of non fiction books are 3 respectively

let

number of fiction books = x

number of non fiction books = y

x = 4y - 5

Total books = z

x = 70% of z

y = 30% of z

x + y = z

4y - 5 + 30%(z) = z

4y - 5 + 0.3z = z

4y - 5 = z - 0.3z

4y - 5 = 0.7x

4y - 5 = 0.7z

4(0.3z) - 5 = 0.7z

1.2z - 5 = 0.7z

-5 = 0.7z - 1.2z

-5 = - 0.5z

z = -5/-0.5

z = 10

Therefore,

the number of non fiction = 30% of z

= 0.3 × 10

= 3

number of fiction = 70% of z

= 0.7 × 10

= 7

Learn more about equation:

https://brainly.com/question/16450098

Answer:

don't see the relationship, but if it's a proportional relationship it should have the same result every time you divide the x by the y or vice versa.

Answer:

24 adults

Step-by-step explanation:

The equation to represent the scenario is

4x + 7x = 66

Combine like terms

11x = 66

Isolate x

x = 6

To find the amount of adults attending the carnival, substitute 6 with x.

6*4 = 24 adults

7*4 = 42 children

24 + 42 = 66 people in total