This sequence represents the diameters of circles used to create an art project: 2.5 cm, 3.1 cm, 3.7 cm, 4.3 cm Let f(n) represent diameter in centimeters and n the term number in the sequence. Which equation represents the sequence of diameters? f(n) = 0.6n + 1.9 f(n) = 0.6n + 2.5 f(n + 1) = f(n) + 1.9 f(n + 1) = f(n) – 0.6

Answer:

k= l/3 - 14/3j

Step-by-step explanation:

l = 14j + 3k

Solve for k

l = 14j + 3k

Subtract 14j from both sides

l - 14j =14j + 3k - 14j

l - 14j = 3k

Divide both sides by 3

l - 14j / 3=3k / 3

k= l/3 - 14/3j

Or

1/3(l - 14j) = k

Answer:

Which expression is equivalent to ‐10

k

‐

10

?

Step-by-step explanation:

Answer:

  60°

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relation between sides of a right triangle and angles.

  Tan = Opposite/Adjacent

  tan(T) = SU/ST

  tan(T) = (5√51)/(5√17) = √3

Now, the arctangent function is used to find the angle whose tangent is √3.

 T = arctan(√3) = 60°

Answer:

23/30

Step-by-step explanation:

x/y

(3 5/6)/(3 3/4)

((3*6)+5/6)/((3*4)+ 3/4)

(18+5/6)/(12+3/4)

(23/6)/(15/4)

(23/6)*(4/15)

(23*3)/(6*15)

(69/90)

23/30

Answer:

1 1/45

Step-by-step explanation:

Answer:

[tex]\boxed{ x = 23}[/tex]

Step-by-step explanation:

=> x - 15 = 8

Adding 15 to both sides

=> x - 15 + 15 = 8 + 15

=> x = 23

Answer:

A. x = 23

Step-by-step explanation:

Step 1: Write out equation

x - 15 = 8

Step 2: Add 15 to both sides (Addition Equality)

x - 15 + 15 = 8 + 15

x = 23

Answer:

The answer is option A.

Step-by-step explanation:

The steps are :

[tex]x + y = 8 - - - (1)[/tex]

[tex]x - y = 6 - - - (2)[/tex]

[tex](1) - (2)[/tex]

[tex]x + y - x - ( - y) = 8 - 6[/tex]

[tex]2y = 2[/tex]

[tex]y = 1[/tex]

[tex]substitute \: y = 1 \: into \: (1)[/tex]

[tex]x + 1 = 8[/tex]

[tex]x = 7[/tex]

Answer:

88

Step-by-step explanation:

The original number ⇒ 100

100 is increased by 10%

The result is 20% reduced.

Calculate increase.

100 × (1 + 10%)

100 × (1.1)

= 110

Calculate decrease.

110 × (1 - 20%)

110 × 0.8

= 88

Answer:

15.5mi

Step-by-step explanation:

S refers to the distance covered

Given:

Last week Perry ran 24.9 miles more than Mike. Perry ran 40.5 miles.

Required:

How many miles did Mike run=?

Formula:

40.5mi-S(Perry)=S(Mike)

Solution:

40.5mi-S(Perry)=S(Mike)

40.5mi-24.9mi=S(Mike)

15.6mi=S(Mike)

Hope this helps.

Answer:

15.6 miles

Step-by-step explanation:

40.5 mi - 24.9 = 15.6 mi

Mike ran 15.6 miles

Answer: B

Step-by-step explanation:

Option A simplifies to 7/15

Option B simplifies to 11/21

If 1/2 is equal to .50, then when subtracted 7/15 would be equal to 0.46666667 and 11/21 would be equal to 0.52380952... meaning that 11/21 would be closer to 1/2 (or .50).

Hope this helps!

Answer:

32

Step-by-step explanation:

P=2(l+w)

so 2(11+5)=P

2(11+5)=32

Answer:

Step-by-step explanation:

Tom wanted to find the inverse of f(x)= 4x - 2 using the steps in the attached image.

Tom's first mistake was in Step 3.

To correct the mistake, he should not switch the variables.

The correct procedure is:

Step 1 : Given

f(x) = 4x - 2

Step 2 : Change f(x) to y

y = 4x - 2

Step 3 : Add 2 to both sides

[tex]4x=y+ 2[/tex]

Step 4:  Divide each side by 4

[tex]x=\dfrac{y+2}{4}[/tex]

Step 5: Change x to [tex]f^{-1}(x)[/tex]

[tex]f^{-1}(x)=\dfrac{y+2}{4}[/tex]

Answer:

1) [tex]\boxed{Option \ 3}[/tex]

2) [tex]\boxed{Option \ 2}[/tex]

Step-by-step explanation:

A) [tex]x^2-5x+6[/tex]

Using mid term break formula

[tex]x^2-6x+x-6\\x(x-6)+1(x-6)\\Taking \ (x+6) \ as \ common\\(x-6)(x+1)[/tex]

B) [tex]\frac{-20p^{-5}qr^6}{16p^{-2}q^{-3}r^4}[/tex]

Solving it using the two rules: => [tex]\frac{a^m}{a^n} = a^{m-n} \ and \ a^m * a^n = a^{m+n}[/tex]

=> [tex]\frac{-5p^{-3}q^4r^2}{4}[/tex]

We need to put p in the denominator to cancel its negative sign

=> [tex]\frac{-5q^4r^2}{4p^3}[/tex]

Answer:

C and b

Step-by-step explanation:

First question:

The polynomial expression we want to factor is x^2-5x-6

Let's calculate the discriminant to find the roots. The discrminant is b^2-4ac

● b= -5

● a = 1

● c = -6

b^2-4ac= (-5)^2-4*1*(-6) = 25+24 = 49>0

So this polynomial expression has two roots since the discriminant is positive

Let x" and x' be the roots:

● x'= (-b-7)/2a = (5-7)/2= -1

● x"= (-b+7)/2a = (5+7)/2 =6

7 is the root square of the discrminant

The factorization of this pulynomial is:

● a(x - x') (x-x")

● 1*(x-(-1)) (x-6)

● (x+1)(x-6)

So the right answer is c

■■■■■■■■■■■■■■■■■■■■■■■■

Second question:

The expression is: (-20*p^(-5)*q*r^(6))/(16*p^(-2)*q^(-3)*r^3)

To make it easier we will simplify the similar terms one by one.

● Constant terms

-20/16 = (-5*4)/(4*4) = -5/4

● terms containing p

-p^(-5)/p^(-2) = p^(-5-(-2)) = p^(-3) =1/p^3

● terms containg q

q/q^(-3)= q(1-(-3)) = q^4

● terms containg r

r^6/r^4 = r^(6-4) = r^2

Multiply all terms together:

● -5/4 *1/p^3 *q^4 *r^2

● (-5*q^4*r^2)/(4p^3)

The right answer is b

Answer:

(C) 1809 in.2

Step-by-step explanation:

Took the test on edg :3

Answer:

(b) 0

Step-by-step explanation:

Assuming a typo in the last term:

5 (1728)^(1/3) + 100(81)^(1/4) - ( 6(10)^(1/2) )^2

=5(12) + 100(3) -36(10)

=60+300-360

=0

Answer:

[tex]\boxed{\sf (b) \ 0}[/tex]

Step-by-step explanation:

[tex]\sf 5\sqrt[3]{1728} +100\sqrt[4]{81} -(6\sqrt{10} )^2[/tex]

[tex]\sf Evaluate.[/tex]

[tex]\sf 5(12)+100(3) -((6)^2 (\sqrt{10})^2)[/tex]

[tex]\sf 60+300 -(36(10))[/tex]

[tex]\sf 360-360[/tex]

[tex]\sf 0[/tex]

Answer: A) 18(1.15)x

Step-by-step explanation:

18 was the original cost, so the price will always be determined with this starting point. Sice there is an increasing value, that makes it 1.15 instead of .15. And it goes up by 15%, making it the coefficient.

Answer:

A) y = 18(1.15)x

Step-by-step explanation:

Answer:  A) 3.2 ft

Step-by-step explanation:

f(4) = -0.3(4)² + 2(4)

     = -4.8 + 8

     =  3.2

Answer:

3.2 feet

Step-by-step explanation:

Answer: [tex]x=0\text{ and }x=e^4[/tex]

Step-by-step explanation:

Given function: [tex]f(x) = \ln(4 - \ln(x))[/tex]

Since, [tex]\ln 0=\infty[/tex]

Here, if

[tex]f(x)\to \infty\\\Rightarrow\ 4-\ln x=0\Rightarrow\ln x=4\Rightarrow\ x=e^4\\\text{OR}\ln x=\infty\Rightarrow\ x=0[/tex]

Hence, the vertical asymptotes of f(x) are:

[tex]x=0\text{ and }x=e^4[/tex].

Using it's concept, it is found that the vertical asymptotes of the function are: [tex]\mathbf{x = 0, x = e^4}[/tex]

A vertical asymptote of a function f(x) are the values of x for which the function is outside it's domain.

For the ln function, that is, [tex]\ln{g(x)}[/tex], they are the values of x for which:

[tex]g(x) = 0[/tex]

In this problem, the function is:

[tex]f(x) = \ln{(4 - \ln{(x)})}[/tex]

For the inner function, x = 0 is a vertical asymptote, as [tex]\ln{0}[/tex] is outside the domain.

For the outer function:

[tex]4 - \ln{(x)} = 0[/tex]

[tex]\ln{(x)} = 4[/tex]

[tex]e^{\ln{(x)}} = e^4[/tex]

[tex]x = e^4[/tex]

A similar problem is given at https://brainly.com/question/23535769

Answer:

a) Multiplica la variable independiente por -7 y luego resta 7

Step-by-step explanation:

Sea [tex]f(x) = -7\cdot x - 7[/tex], las acciones realizadas por la función sobre la variable independiente, esto es, [tex]x[/tex], son:

1) Multiplica la variable por 7.

2) Refleja el resultado anterior con eje de simetría en el eje x. (Multiplicación por -1).

3) Traslada vertical el resultado de 2) siete unidades en la dirección -y.

Por ende, la opción correcta es a).

Answer:

Slope = m = -5/2

Y-intercept = b = -3

Step-by-step explanation:

[tex]-5x-2y = -6[/tex]

Getting it in a slope - intercept form:

[tex]-2y = 5x+6\\Dividing \ both \ sides \ by \ -2\\y = \frac{-5x}{2} + (-3)\\y = \frac{-5x}{2} -3\\[/tex]

Comparing it wit the slope intercept equation [tex]y = mx+b[/tex] we get

Slope = m = -5/2

Y-intercept = b = -3

Answer:

she works 50 hours for that week

Step-by-step explanation:

She is paid $18 per hour and received a bonus of $125 per bonus for the first week . she claims her compensation for the first week should be $1025 . The number of hour she worked base on her claim can be calculated below.

Let

the number of hours she worked = a. Therefore,

18a + 125 = 1025

18a = 1025 - 125

18a = 900

divide both sides by 18

a = 900/18

a = 50

she works 50 hours for that week

Answer:

a

Step-by-step explanation:

there are 4 quarts in a gallon.

4 times $0.79 =$3.16

Answer:

The answer is: 13 minutes

Step-by-step explanation:

First Let us form equations with the statements in the two scenario

[tex]time=\frac{distance}{speed}[/tex]

Let the time in which the bell rings be 'x'

1. If Andrew walks (50 meters/minute), he arrives 3 minutes after the bell rings. Therefore the time of arrival at this speed = (3 + x) minutes

[tex]3 + x =\frac{distance}{50}\\distance = 50(3+x) - - - - - (1)[/tex]

2. If Andrew runs (80 meters/minute), he arrives 3 minutes before the bell rings. Therefore the time taken to travel the distance = (x - 3) minutes

[tex]x - 3 = \frac{distance}{80} \\distance = 80(x-3) - - - - - (2)[/tex]

In both cases, the same distance is travelled, therefore, equation (1) = equation (2)

[tex]50(3+x)=80(x-3)[/tex]

[tex]150 +50x=80x-240\\[/tex]

Next, collecting like terms:

[tex]150 + 240 = 80x - 50x\\390 = 30x\\30x = 390\\[/tex]

dividing both sides by 3:

x =  390÷30 = 13

∴ x = 13 minutes

Answer:

The bigger avocado will be a better deal if the ratio of the sizes of the bigger one to the smaller one is less than the ratio of the prices of the bigger one to the smaller one.

Step-by-step explanation:

Given that two sizea of avocados are being sold, since the regular size is being sold for $0.84 each, let the price for the bigger avocado be $x.

Then note the following:

1. How bigger than the smaller avocado is the bigger one?

This would determine if the price for the bigger one is a bargain, or a mistake.

If for instance, the bigger avocado is double the size of the smaller one, then for any price, $x less that $1.68 (twice of $0.84), it is a bargain.

The bigger avocado will be a better deal if the ratio of the sizes bigger one to the smaller one is less than the ratio of the prices of the bigger one to the smaller one.

Answer:

The better deal cannot be decided as we were not the weights of the 2 avocados. However, we assume they are x is the price of the larger avocado and y the weight of the larger avocado. Therefore we calculate the price per pound of the larger avocado which is x/y. The weight of the smaller avocado is called z while the price od the smaller / regular avocado is $0.84.The price per pound of the smaller / regular avocado is calculated as 0.84/z. Therefore x/y<0.84/z will make buying the longer avocado a better deal. Also, x/y>0.84/z will make buying the smaller/ regular avocado a better deal.

Step-by-step explanation:

The better deal cannot be decided as we were not the weights of the 2 avocados. However, we assume they are x is the price of the larger avocado and y the weight of the larger avocado. Therefore we calculate the price per pound of the larger avocado which is x/y. The weight of the smaller avocado is called z while the price od the smaller / regular avocado is $0.84.The price per pound of the smaller / regular avocado is calculated as 0.84/z. Therefore x/y<0.84/z will make buying the longer avocado a better deal. Also, x/y>0.84/z will make buying the smaller/ regular avocado a better deal.

Answer: THE ANSWER IS A

Step-by-step explanation:

5-(3/2)^3

=13/8

im a math god

Answer:

7.8

Step-by-step explanation:

because if you square 5 and 6 you get 25 and 36. Add them together and you get 61. Square 61 to get 7.8102... which you can round to 7.8

The equation to find the hypotenuse of a right triangle is a^2+b^2=c^2

Answer:

1/4

Step-by-step explanation:

Well see how far each points are from each other.

Start at the red triangle and go up 1, go to the right 4.

Thus,

the rise/run is 1/4.

Hope this helps :)

Answer:

1/4

Step-by-step explanation:

To find the rise/run, you first need to pick two points from the line.  You can pick whichever points you want, and you will get the right answer.  I will pick (-8, -3) and (8, 1).

Divide the difference of the y's by the difference of the x's.

-3 - 1 = -4

-8 - 8 = -16

-4/-16 = 1/4

The rise/run is 1/4.

Answer: C: 60 ft

Step-by-step explanation:

Her pencil is 12 inches and its shadow is 4 inches. Her pencil is 3 times longer than its shadow, so using that logic we can conclude that the tower is 3 times longer than its shadow as well.

[tex]20*3=60[/tex]

The tower is 60 feet tall.

Answer: (1) 2p: 5q.

(2) 3:10.

(3) 5:6.

Step-by-step explanation:

To find : Ratio

(1) 4p²q : 10pq²

[tex]=\dfrac{4p^2q}{10pq^2}\\\\=\dfrac{2p^{2-1}}{5q^{2-1}}\\\\=\dfrac{2p}{5q}[/tex]

i.e. Simplified ratio of 4p²q : 10pq²  is 2p: 5q.

(2) 9 months : 2½ years

1 year = 12 months

[tex]2\dfrac{1}{2}\text{years}=\dfrac{5}{2}\text{years}\\\\=\dfrac{5}{2}\times12=30\text{ months}[/tex]

Now, 9 months : 2½ years = [tex]\dfrac{9\text{ months}}{30\text{ months}}=\dfrac{3}{10}[/tex]

Hence, Simplified ratio of 9 months : 2½ years is 3:10.

(3) 5 m : 600 cm

1 m = 100 cm

So, 5m = 500 cm

Now, 5 m : 600 cm = [tex]\dfrac{500\ cm}{600\ cm}=\dfrac{5}{6}[/tex]

Hence, Simplified ratio of  5 m : 600 cm  is 5:6.

Answer:

Area of the triangle = 0

Step-by-step explanation:

We are given the vertices of a triangle as: (- 8,4 ), (- 6,6), (- 3,9)​

The formula to find the Area of the triangle =

1/2[ x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)]

Where :

(x₁, y₁) =  (- 8,4 )

(x₂, y₂) = (- 6,6)

(x₃, y₃) =  (- 3,9)

Area of the triangle = 1/2[-8(6 - 9) + -6(9 - 4) + -3(4 - 6)]

= 1/2[ (-8 × -3) +( -6 × 5) +( -3× -2)]

= 1/2[ 24 - 30 + 6)

= 1/2[ 24 + 6 - 30]

= 1/2 [30 - 30]

=1/2[ 0 ]

= 0

Therefore, the area of triangle whose vertices are (- 8,4 ), (- 6,6) and (- 3,9)​ is ZERO( = 0 )

Answer:

a

Step-by-step explanation:

The standard form of the equation of a circle is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k) = (0, 0), thus

(x - 0)² + (y - 0)² = r², that is

x² + y² = r² → a

Answer:

72%

Step-by-step explanation:

First find the number of mangoes

200 -56 = 144

Take the number of mangoes over the total

144/200

.72

Change to percent by multiplying by 100

72%

Answer:

72%

Step-by-step explanation:

If 56 of the 200 fruits were durians, then [tex]200-56[/tex] of the fruits were mangoes. Therefore, 144 of the fruits were mangoes.

Now we can set up a percentage proportion to find what percent of 200 144 is.

[tex]\frac{144}{200} = \frac{x}{100}[/tex]

Multiply the cross values and divide by the value thats diagonal to the variable.

[tex]144\cdot100=14400\\14400\div200=72[/tex]

So, the answer is 72%

Hope this helped!