Laura borrowed a total of $21,000 from two different banks to start a business. One bank charged the equivalent of 5% simple interest, and the other charged
6.5% interest. If the total interest after 3 years was $3240, determine the amount borrowed from each bank.

Let x represent the principal on the business loan at 5%.
Then, (ID is
he
remaining amount borrowed at 6.5%
X

Writing an expression consists of combining two or more variables, symbols, or numbers, with one or more mathematical operators to form a mathematical sentence that is based on a specific context

The expression for the total cost for bowling is 45·h + 5·f

The reason the above expression is correct is as follows:

The given parameters are;

The cost of shoe rentals for bowling per player = $5

The cost to book a lane per hour = $45

The number of people in the group of friends = f

The number of hours the friends go bowling = h

Required:

To write an expression for the total cost for the group of friends to go bowling

Solution:

Let the number of lanes the friends book= 1

The total cost, C, is the cost to book one lane at $45 per hour for h hours, plus the cost for the f number of friends to rent one shoe each at $5 per player (person)

Mathematically,  C = 45·h + 5·f

The expression for the total cost for the group of friends to go bowling, is therefore;

45·h + 5·f

Learn more about mathematical expressions here:

https://brainly.com/question/20596193

[tex]\\ \sf\Rrightarrow f(x)=3x-2[/tex]

[tex]\\ \sf\Rrightarrow g(x)=-4x+1[/tex]

Now

[tex]\\ \sf\Rrightarrow (f+g)(x)[/tex]

[tex]\\ \sf\Rrightarrow f(x)+g(x)[/tex]

[tex]\\ \sf\Rrightarrow 3x-2+(-4x+1)[/tex]

[tex]\\ \sf\Rrightarrow 3x-2-4x+1[/tex]

[tex]\\ \sf\Rrightarrow 3x-4x-2+1[/tex]

[tex]\\ \sf\Rrightarrow -x-1[/tex]

Answer:

(f+g)(x) = -x - 1

Step-by-step explanation:

f(x)=3x−2

g(x)=−4x+1

(f+g)(x) = 3x -2 -4x+1

= -x - 1

Answer:

X = 8

28

Step-by-step explanation:

Here Is How I did this problem:

33 - 5 = 28

X = 8

2x = 28

To Check my answer This is what I did:

28 + 5 = 33

Hope this helps! :)

Answer:

The choose D) -12

Step-by-step explanation:

[tex]3 {x}^{ - 4} \times x {y}^{2} \\ 3( { - 1}^{ - 4} ) \times ( - 1)(2)^{2} \\ \frac{3}{ - 1^{4} } \times - 1(4) \\ 3 \times - 4 \\ = - 12[/tex]

I hope I helped you^_^

Answer:

ok

Step-by-step explanation:

Answer:

ok

Step-by-step explanation:

ty for the points so very much

Answer:

26 students are good in mathematics only.

28 students are not good in any of the three courses.

Answer:

(22.5 , 1)

Step-by-step explanation:

Midpoint formula= [tex]\frac{x^1+x^{2} }{2} +\frac{y^{1} +2^{2} }{2} =Midpoint[/tex]

[tex]\frac{27+18}{2}[/tex]=22.5

3+-1=2

2/2=1

So, midpoint is (22.5 , 1)

You can also graph it out and use Pythagorean theorem but that would overcomplicate the problem.

Answer:

Step-by-step explanation:

The rotation or reflection will change the direction of the image but the translation will leave the corresponding sides parallel.

Now the answer choices:

If quadrilateral ABCD is reflected or rotated to form quadrilateral RSTU, then sides RS and TU are not necessarily parallel.

If quadrilateral ABCD is reflected or rotated to form quadrilateral RSTU, then sides AB and RS must be parallel or on the same line.

If quadrilateral ABCD is translated to form quadrilateral RSTU, then sides AB and RS are not necessarily parallel or on the same line.

If quadrilateral ABCD is reflected, rotated, or translated to form quadrilateral RSTU, then sides RS and T'U must be parallel.

Answer:

110°

Step-by-step explanation:

v is 70°, that is opposite to w. The degree of a line is 180°.

180 - 70 = 110

I hope this helps!

pls ❤ and mark brainliest pls!

Answer:

[tex] \frac{x + 11}{8} = - 3 \\ x + 11 = - 3 .8 \\ x = - 24 - 11 \\ x = - 33[/tex]

maaf jika salah

Answer:

x=-35

Step-by-step explanation:

x+11=-3*8

x+11=-24

x=-24-11

x=-35

Answer:

Both of them. This has a constant slope of -8 and technically starts off after 87.

Answer:

Area of a triangle

Step-by-step explanation:

1/2bh is used to find the area for a triangle

Answer:

16

Step-by-step explanation:

(x + 4)(x + 4) = x² + 8x + 16

The shape is 2 triangles. Find the area of each one and add them together.

1/2 x 6 x 10 = 30

1/2 x 10 x 12 = 60

30 + 60 = 90

Area = 90 square inches

Area of Trapezoid = ½ (a + b) h

= ½ (12 + 6) 10

= ½ × 18 × 10

= 1 × 9 × 10

= 9 × 10

= 90 in.²

[tex]2 {m}^{8} - 6 {m}^{2} [/tex]

Step-by-step explanation:

[tex](12 {m}^{7} - 36m) \div 6m[/tex]

➡️ [tex] \frac{1 {2m}^{7} - 36m }{6} \times m[/tex]

➡️ [tex] \frac{6(2 {m}^{7} - 6m)}{6} \times m[/tex]

➡️ [tex](2 {m}^{7} - 6m)m[/tex]

➡️ [tex]2 {m}^{8} - 6 {m}^{2} [/tex]

Answer:

8

Step-by-step explanation:

|-4-4| = |-8| = 8

Answer:

377

Step-by-step explanation:

See attached.

Step-by-step explanation:

510 (base eight)

-111 (base eight)

___

377 (base eight)

Answer:

X = 15/16

Step-by-step explanation:

2(4-8x) + 6 = -1

8 - 16x + 6 = -1

14 - 16x = -1

-16x = -1 -14

-16x = -15

X = 15/16

Answer:

[tex]2(4 - 8x) + 6 = - 1 \\ 8 - 16x + 6 = - 1 \\ - 16x = - 1 - 6 - 8 \\ - 16x = -15 \\ 16x = 15 \\ \boxed{x = \frac{15}{16} }[/tex]

y is given already

[tex]\\ \rm\Rrightarrow 2x-6=2[/tex]

[tex]\\ \rm\Rrightarrow 2x=2+6[/tex]

[tex]\\ \rm\Rrightarrow 2x=8[/tex]

[tex]\\ \rm\Rrightarrow x=\dfrac{8}{2}[/tex]

[tex]\\ \rm\Rrightarrow x=4[/tex]

Answer:

x = 4; y = 6

Step-by-step explanation:

Set the x-values equal to each other and the y-values equal to each other.

The first value in parentheses is an x-value, and the second value in parentheses is a y-value.

x - 2 = 2x - 6

Subtract x from both sides

-2 = x - 6

Add 6 to both sides to get x by itself on the right.

-2 + 6 = x

4 = x

y - 3 = 3

Add 3 to both sides

y = 6

Check answers for the x-value:

4 - 2 = 2(4) - 6

2 = 8 - 6

2 = 2

Check answers for the y-value:

6 - 3 = 3

3 = 3

Answer:

Step-by-step explanation:

we need to keep in mind that what you do to the bottom of the fraction is the same you do to the top of the fraction

Answer:

t = d/r; t = 5

Step-by-step explanation:

Hi there!

1) Isolate t

d = rt

Divide both sides by r

d/r = rt/r

d/r = t

t = d/r

2) Solve for t when distance is 40 and the rate is 8

t = d/r

Replace d with 40 and rate with 8

t = 40/8

t = 5

I hope this helps!

Answer: When used as a diacritic mark, the term dot is usually reserved for the interpunct, or to the glyphs 'combining dot above' and 'combining dot below' which may be combined with some letters of the extended Latin alphabets in use in Central European languages and Vietnamese

Answer:

the correct answer is

Line segment X Z

Answer:

Line segment X Z

Step-by-step explanation:

Step-by-step explanation:

12=-4(-6x-3)

when minus is multiplied by minus then the result is plus,

12=24x+12

Now, subtract 12 from both sides,

12-12=24x+12-12

0=24x

Now, divide both sides by 24

0/24=24x/24

0=x

Answer and Step-by-step explanation:

First, distribute the negative 4 onto the negative 6x and negative 3.

12 = 24x + 12

Subtract 12 from both sides of the equation.

0 = 24x

Divide both sides of the equation by 24.

x = 0

To check our answer:

-4(-6(0) - 3) = 12

-4(0 - 3) = 12

-4(-3) = 12

12 = 12 ✓

So, x is equal to 0.

#teamtrees #PAW (Plant And Water)

I hope this helps!

Given : The perimeter of a rectangular atrium is 64 centimeters. The length of the garden is 3 times the width. Find the length and the width.

Solution :

Let us assume the breadth be B

The length is three times the breadth So, the length be 3B

Perimeter of the rectangle = 64 cm

Perimeter = 2(Length + Breadth)

64 cm = 2(3B + B)

64 cm = 2(4B)

64 cm = 8B

B = 8 cm