simplify the expressions by applying the properties of potentiation...​

Answer:

$1,041.69

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 5/100

r = 0.05 rate per year,

Then solve the equation:

Forumla; P(1 + r/n)nt

700.00(1 + 0.05/4)(4)(8)

700.00(1 + 0.0125)(32)

$1,041.69

hope this helps!

Answer:

$1,041.69

Step-by-step explanation:

Compound interest formula: [tex]A=P(1+\frac{r}{n})^{nt[/tex]

A = amount (future value ($))

P = principal (orignal amount - $700)

R = rate (written as a decimal - 5%/100= 0.05)

N = compound (quarterly - 4) 4 quarters in 1 yr.

T = number of years (8)

[tex]A=P(1+\frac{r}{n})^{nt[/tex]

[tex]A=P(1+\frac{r}{n})^{nt}\\\\A=700(1+\frac{0.05}{4})^{4*8} < == start\ from\ the\ parenthesis\ and\ divide\ first\\\\A=700(1+0.0125)^{4*8} < == add\ the\ \#s\ in\ the\ parenthesis\\\\A=700(1.0125)^{4*8} < == multiply\ the\ exponents\\\\A=700(1.0125)^{32} < ==multiply\\\\A=700(1.488131) < ==multiply\\\\A=1041.691\\\\A=$1,041.69[/tex]

Hope this helps!

Answer:There are 7 daises

Step-by-step explanation: half of 16 roses is 8 and half of 14 daises is 7. given the ratios from roses to daises is 8:7

Answer:

10 daisies

Step-by-step explanation:

Answer:

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relation between the cosine of an angle and the sides of the triangle.

  Cos = Adjacent/Hypotenuse

__

In the given triangle, the hypotenuse is AC. The side adjacent to angle A is AB, so its cosine is ...

  cos(A) = AB/AC

  cos(A) = 3/5

__

The right angle in the triangle is angle B. The cosine of a right angle is 0.

  cos(B) = 0

__

The side adjacent to angle C is CB, so its cosine is ...

  cos(C) = CB/AC

  cos(C) = 4/5

Answer:

cos <ABC=0

cos <BAC=3/5

cos<ACB=4/5

GIVE 5 STARS IF YOU DO RSM!!!

Answer:

5.5

3y = x

Step-by-step explanation:

→ Find the scale factor enlargement

12 ÷ 4 = 3

→ Divide 16.5 by 3

5.5

→ Write SF in terms of x and y

3y = x

The Length of BC is 5.5 cm and equation for y in terms of x is y = 3x

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures.

According to question

Triangle ABC ≅ triangle PQR  

where,

AB = 4cm

PQ=12cm

RQ= 16.5 cm

AC = xcm

PR= ycm

According to the similarity rule

the same ratio of corresponding sides

therefore,

[tex]\frac{AB}{PQ} = \frac{BC}{QR} = \frac{AC}{PR} \\[/tex]

(a) Calculate the length of BC

[tex]\frac{AB}{PQ} = \frac{BC}{QR}[/tex]

⇒ [tex]\frac{4}{12} = \frac{BC}{16.5}[/tex]

⇒ [tex]\frac{1}{3} = \frac{BC}{16.5}[/tex]

⇒ BC = 5.5 cm

 (b) Write down an expression for y in terms of x

we know  ,  [tex]\frac{AB}{PQ} = \frac{AC}{PR} \\[/tex]

⇒ [tex]\frac{4}{12} = \frac{x}{y} \\[/tex]

⇒ [tex]\frac{1}{3} = \frac{x}{y} \\[/tex]

⇒ [tex]y=3x[/tex]

Hence, Length of BC is 5.5 cm and equation for y = 3x

To know more about similarity in triangles  here :

https://brainly.com/question/20502441

# SPJ2

Answer:

x=15 inches

Step-by-step explanation:

Area of ∆ is 27sq inches

Height is 4.5 inches

base is (x-3) inches

Area of ∆= ½×b×h

27= ½×(x-3)×4.5

27=2.25×(x-3)

27=2.25x-6.75

2.25x=27+6.75

2.25x=33.75

x=33.75/2.25

x=15 inches

Answer:

He sold 38 cars

Step-by-step explanation:

first we subtract his base salary from how much he made, 9,220.11 - 1,137.80 = 8,082.22

then we divide that by the commission he gets from selling 1 car which is 212.29, the equation looks like: 8,082.22 / 212.69 and that equals 38 which means he sold 38 cars.

Answer:

m∠O=67

Step-by-step explanation:

m∠O=180-m∠R-the other angle since it is not given we can assume that the other angle is the same as m∠O so you divide 134 by 2 to get 67 therefore m∠O=67

Answer:

15% off

Step-by-step explanation:

28-23.80 = 4.2$

23.8/28 = 0.85

100-85 = 15

15%

Answer:

Area = 201.1

Cicumference = 50.27

Your answers are correct

Step-by-step explanation:

A = Area = ?

C = Circumference = ?

SInce both the "Area" and "Circumference" are unknown, we use the formula:

[tex]\mathrm{A = \dfrac{ 1 }{ 4 } \pi { d }^{ 2 }}[/tex]

Remember that:

The diameter is the length of the line through the center

and

The radius is half the diameter

Given:

Diameter = 16

Now we substitute "16" for "d" into the formula and solve

[tex]\mathrm{A = \dfrac{ 1 }{ 4 } \pi {( 16) }^{ 2 }}[/tex]

Calculate 16 to the power of 2 and get 256

[tex]\mathrm{A = \dfrac{ 1 }{ 4 } \pi \times 256}[/tex]

Multiply [tex]\frac{1}{4}[/tex] and 256 to get  [tex]\frac{256}{4}[/tex]

[tex]\mathrm{A = \dfrac{ 256 }{ 4 } \pi}[/tex]

Divide 256 by 4 to get 64

[tex]\mathrm{A=64\pi }[/tex]

Multiply 64 and π to get 201.06192983

[tex]\mathrm{A=201.06192983}[/tex]

Round to the nearest tenth and get 201.1

[tex]\mathrm{A=201.1}[/tex]

Next we need to find the "Circumference"

Formula for finding circumference is:

C = πd

Given:

Diameter = 16

Now we substitute "16" for "d" into the formula and solve

C = π(16)

Multiply 16 and π to get 50.265482457

C = 50.265482457

Round to the nearest hundreth and get 50.27

C = 50.27

So, your answers are correct.

The only mistake that could happen is whether you need to round to the nearest hundreth or tenth.

Answer:

both weigh the same.

Step-by-step explanation:

you have 5kg of steel and 5kg feathers.

The weight is the same so both weigh the same.

Answer: 33

To maximize the length of the third side, which I'll call x, it needs to be the longest side.

So by the triangle inequality theorem, 19+15>x, meaning the maximum whole number value of x is 33.

Answer:

dimensions are 51x91

Step-by-step explanation:

Assuming that the gym is rectangular in shape, then...

l*w=4641

and 2l+2w=284

We have two variables and two equations so to solve this we plug one equation into another.

Solve for one variable:

l*w=4641

w=4641/l

Plug into the other equation...

2l+2(4641/l)=284

Solve

l*(2l+9282/l)=284

2l^2+9282=284l

2l^2-284l+9282=0

Factor the trinomial:

2(l−51)(l−91)=0

l−51=0 or l−91=0(Set factors equal to 0)

l=51 or l=91

now, lets plug it into one of the equations to find w

51*w=4641

w=91, l=51

or...

91*w=4641

w=51, l=91

Answer:

91 ft × 51 ft

Step-by-step explanation:

while the other answer is basically correct, it makes a to at the beginning of the calculation (but the continues correctly).

and it assumes you can find the right factoring of the expression.

so, I will show you here how to generally solve this, even if you cannot find the right factorization :

l×w = 4,641 ft²

w = 4641/l

2l + 2w = 284

2l + 2(4641/l) = 284

2l + 9282/l = 284

2l² + 9282 = 284l

2l² - 284l + 9282 = 0

to make things easier let's divide everything by 2

l² - 142l + 4641 = 0

the general solution to a squared equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = l

a = 1

b = -142

c = 4641

l = (142 ± sqrt((-142)² - 4×1×4641))/(2×1) =

= (142 ± sqrt(20,164 - 18,564))/2 =

= (142 ± sqrt(1600))/2 = (142 ± 40)/2 = 71 ± 20

l1 = 71 + 20 = 91

l2 = 71 - 20 = 51

w1 = 4641/91 = 51

w2 = 4641/51 = 91

so, they are interchangeable (it does not matter which we call length and which width).

the dimensions are 91 ft × 51 ft

Answer:

x = 16.71m

Step-by-step explanation:

KL² = KX² + LX² - 2KX × LX × cos(KXL)

x² = 26² + 20² - 2 × 26 × 20 × cos(40°)

x = 16.713m ≈ 16.71m

PLEASE MARK ME AS BRAINLIEST AND HAVE A NICE DAY :)

Answer:

B: Frequency of Foreign-Language Studies by Row

Answer:

Improper Fraction:
933/100

Mixed Number:
9 33/100

Step-by-step explanation:

Have a great rest of your day
#TheWizzer

Answer :-

Explanation :-

As per the provided information in the given question, we have been given that the Length of Rectangle is 11.2 cm . Its Breadth is given as 5.1 cm . And, we have been asked to calculate the Area of Rectangle .

For calculating the Area , we will use the Formula :-

[tex] \bigstar \: \: \: \boxed {\sf { \: Area \: of \: Rectangle \: = \: Lenght \: \times \: Breadth \: }} [/tex]

Therefore , by Substituting the given values in the above Formula :-

[tex] \dag \: \: \: \sf {Area \: of \: Rectangle \: = \: Lenght \: \times \: Breadth} [/tex]

[tex] \longmapsto \: \: \: \sf {Area \: of \: Rectangle \: = \: 11.2 \: \times \: 5.1} [/tex]

[tex] \longmapsto \: \: \: \textbf {\textsf {Area \: of \: Rectangle \: = \: 57.12 }} [/tex]

Hence :-

[tex] \underline {\rule {205pt} {4pt}} [/tex]

Additional Information :-

[tex] \begin{gathered} \begin{gathered} \begin{gathered}\begin{gathered}\boxed{\begin{array}{c} \\ \underline{ { \textbf {\textsf \red{ \dag \: \: More \: Formulas \: \: \dag}}}} \\ \\ \\ \footnotesize \bigstar \: \bf{Area \: _{Square} = Side \times Side} \\ \\ \\ \footnotesize\bigstar \: \bf{Area \: _{Rectangle} = Lenght \times Breadth} \\ \\ \\ \footnotesize \bigstar \: \bf{Area \: _{Triangle} = \frac{1}{2} \times Base \times Height } \\ \\ \\ \footnotesize \bigstar \: \bf{Area \: _{Parallelogram} = Base \times Height} \\ \\ \\ \footnotesize \bigstar \: \bf{Area \: _{Trapezium} = \frac{1}{2} \times [ \: A + B \: ] \times Height } \\ \\ \\ \footnotesize \bigstar \: \bf {Area \: _{Rhombus} = \frac{1}{2} \times Diagonal \: 1 \times Diagonal \: 2}\end{array}}\end{gathered}\end{gathered} \end{gathered} \end{gathered} [/tex]

[tex] \underline {\rule {205pt} {4pt}} [/tex]

Note :-

The area of the given rectangle.

[tex]a = length \times width[/tex]

[tex]a = 11.2 \times 5.1[/tex]

[tex]a = 57.12 \: {cm}^{2} [/tex]

Therefore, the area of the given rectangle is 57.12 square centimeters.

Answer:

2 and 3

Step-by-step explanation:

prime numbers=2,3,4,5,...

taking 2 and 3

2+3=5

5²=25

hence the different prime numbers are 2 and 3

The numbers can be (2, 7), (2, 23), (3, 13), (5, 11)

A prime number is a whole number greater than 1 whose only factors are 1 and itself.

Given that, Nidah writes down two different prime numbers.

She adds together her two numbers.

Her answer is a square number less than 30

Square numbers less than 30 are = 1, 4, 9, 16, 25

The pairs of numbers that can satisfy the given condition are;

2 + 7 = 9

2 +23 = 25

3 + 13 = 16

5 + 11 = 16

Hence, Nidah could have chosen from these numbers (2, 7), (2, 23), (3, 13), (5, 11)

For more reference on Prime numbers, click;

https://brainly.com/question/15048606

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Answer:

Its 3 because the radius if half of the diameter

Step-by-step explanation:

Answer:

Q15: A

Q12: A,C,D

Q13: B

Q14: C

Answer:

1) Left 5, Down 1

2) A, C, D

3) B

4) D

Step-by-step explanation:

Desmos graphing calculator will help you with all of these.

The system of equations that represent the situation are 1.20R + 2B = 70, and R + B = 90.

The system of equations are sets of equations that have to be solved simultaneously in order to determine their required values. They are often referred to as simultaneous equations.

To learn more about simultaneous equations, please check: https://brainly.com/question/25875552

Answer:

84.2%

Step-by-step explanation:

420 + 380 = 800

800 / 950 = .842

.842 * 100 = 84.2

84.2 = 84.2%

Answer:

C is the answer

Good luck! :)

Answer/Step-by-step explanation:

Given:

Seven more than the quotient of a number b and 45 is greater than 5

So:

Seven more than the quotient of a number b and 45 is greater than 5

=

7 + b/45 > 5

Solve if needed:

[tex]\begin{bmatrix}\mathrm{Solution:}\:&\:b > -90\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-90,\:\infty \:\right)\end{bmatrix}[/tex]

[tex]\mathrm{Subtract\:}7\mathrm{\:from\:both\:sides}[/tex]

[tex]7+\frac{b}{45}-7 > 5-7[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]\frac{b}{45} > -2[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:}45[/tex]

[tex]\frac{45b}{45} > 45\left(-2\right)[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]b > -90[/tex]

~Lenvy~

Answer:

55.9 m

Step-by-step explanation:

If you swam from one cornee to the other, you divide the rectangle into 2 right triangles

the diagonal is a common hypothenus of the triangles

applying pytha

C² = A² + B²

C² = 25² + 50²

C² = 625 + 2500

C² = 3125

C = sqrt 3125

C = 55.9 m

Answer:

105 cubic meters

Step-by-step explanation:

w = won game

l = lost game

w + l = 15

and

w = I + 3

so

l + 3 + l = 15

2l = 12

l = 6

lost = 6

won = 9

Answer:

The ratio of wins to losses is 3 to 1, out of 32 total games. 3:1 has a total of 4 parts (3+1).

Total games divided by total parts is 32/4 = 8.

Now multiplying number of parts to divisor gives us 3x8 : 1x8 or 24:8. Therefore they won 24 games, lost 8.

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

12 divided by 1/2 = 24

Hope this helped! :)

Answer:

here my answer

Step-by-step explanation:

hope this helps