To be able to buy a new computer, kaitlin decides to save for 4 years. she opens a savings account with $500. the account pays simple interest at an annual rate of 2%. she doesn't make any more deposits. how much total interest will kaitlin earn?

Answer:

V = 343

Step-by-step explanation:

V = lwh

= 7(7)(7)

= 49(7)

= 343

The graph which represents the rational function is; On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 2, and the horizontal asymptote is at y = 3.

It follows from the task content that the rational function given is; f(x) = 3x-2/x-2.

Hence, since the numerator and denominator polynomials are of the same order, it follows that the horizontal asymptote is the quotient; 3/1 = 3.

Additionally, the vertical asymptote of the function is the value of x which renders the denominator equal to 0 and consequently, the function undefined.

Hence, x -2 = 0 and x= 2.

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Answer: THE PERSON ABOVE IS CORRECT!!

The answer is D.) On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 2, and the horizontal asymptote is at y = 3.

Answer:

Tan p is 20/21

Tan q is 21/20

Step-by-step explanation:

Tan is short for tangeant.

tangeant means opposite/adjacent

the opposite of vertices p is 20.

the adjacent of vertices p is 21.

so tan p= 20/21

The opposite of vertices q is 21

the adjacent of vertices q is 20

so tan q is 21/20

Step-by-step explanation:

x + 2x + 7x

72 = 9x

72 - 9 = x

63 = x

63 ÷ 3 = 21

piece 1 = 21

piece 2 =21+2 = 23

piece 3 =21+7 = 28

21+23+28 = 72 This proves the above is correct.

The required equation of parabola is y = (-1/4)(x-9)² +4

What is a Parabola ?

A parabola is a U shaped Curve , whose all point are at same distance from a point called as Focus and a line called as Directrix.

Let (x,y) be any point on the parabola.

the distance between (x,y) and the focus and the distance between (x,y) and directrix is equal.

The focus is at (9,0) and a directrix at y= - 4

[tex]\rm \sqrt {(x-9)^2 + (y -0)^2[/tex]  = | y +4|

[tex]\rm {(x-9)^2 + (y -0)^2 = (y-4)^2[/tex]

(x-9)²  + y² = y² +16 -4y

On solving this

4y = - (x-9)² +16

y = (-1/4)(x-9)² +4

Therefore this is the required equation of parabola .

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Answer:

B

Step-by-step explanation:

[tex]\frac{4x}{9}[/tex] - [tex]\frac{2x}{9}[/tex]

since the denominators are common , then subtract the numerators, leaving the common denominator.

= [tex]\frac{4x-2x}{9}[/tex]

= [tex]\frac{2x}{9}[/tex]

Answer:

A = 55 degrees

B = 35 degrees

C = 90 degrees

side BA = 4.8 units

side AC = 2.7 units

side BC = 3.9 units

Step-by-step explanation:

Hello!

The things we know:

A = 55 degrees

C = 90 degrees

side BA = 4.8 units

AC = adjacent side

BC = opposite side

AB = hypothenuse

B = 180 - 55 - 90 degrees

B = 35 degrees

Let's find side AC

we can use the cos of theta.

cos(55) = AC/4.8

multiply 4.8 on both sides.

4.8cos(55) = AC

AC = 2.7 units

And now we just have to find BC

to calculate BC we can either use tangent or sin.

I will just use sin

sin(55) = BC/4.8

multiply 4.8 on both sides.

4.8sin(55) = BC

BC = 3.9

And now we know everything about the triangle

Hope I Helped!

The correct statement about the matrix is B. B^-1.

From the information, it can be seen that the matrix is 2 by 2. Based on the information about the matrix, 1/3AB = 1/3BA.

From this, it can be depicted that the inverse of B illustrates that:

A(1/3B) = (1/3B)

This illustrates that the correct is B.

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Answer: y(-3y^7+18y^4+10)

Step-by-step explanation:

Answer:

Complementary angles are:

∠ORS and ∠SRQ

Supplementary angles are:

∠ORP and ∠PRQ

The value of a is -5 if the provided polynomial is divided by (3x + 2) option first -5 is correct.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a polynomial:

3x² + 5x - 3

Which is divided by (3x + 2)

= (3x² + 5x - 3) ÷ (3x + 2)

[tex]\rm = \dfrac{\left(3x^2+5x-3\right)}{\left(3x+2\right)}[/tex]

[tex]\rm =x+\dfrac{3x-3}{3x+2}[/tex]

[tex]\rm =x+1+\dfrac{-5}{3x+2}[/tex]

[tex]\rm =x+1-\dfrac{5}{3x+2}[/tex]

By comparing with the given remainder.

a = -5

Thus, the value of a is -5 if the provided polynomial is divided by (3x + 2) option first -5 is correct.

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Answer:

B and D

Step-by-step explanation:

A

[tex]\frac{5}{6}[/tex] × 13 = [tex]\frac{5(13)}{6}[/tex] = [tex]\frac{65}{6}[/tex] = 10 [tex]\frac{5}{6}[/tex] < 13

B

4 × 13 = 52 > 13

C

[tex]\frac{3}{4}[/tex] × 13 = [tex]\frac{3(13)}{4}[/tex] = [tex]\frac{39}{4}[/tex] = 4 [tex]\frac{3}{4}[/tex] < 13

D

[tex]\frac{10}{10}[/tex] × 13 = 1 × 13 = 13

Band D are equal to or greater than 13

Hello,

Answer:

for k = 4/9

Step-by-step explanation:

a = 9 ; b = 4 ; c = k

we search Δ = 0 (because 1 real root)

Δ = b² - 4ac = 4² - 4 × 9 × k = 16 - 36k

Δ = 0 ⇔  16 - 36k = 0 ⇔ 36k = 16 ⇔ k = 16/36 = (4 × 4)/(4 × 9) = 4/9

⇒ k = 4/9

Answer:

[tex]\{\frac{4}{9} \}[/tex]

Step-by-step explanation:

First off, we are given a parabola by definition:

[tex]f(x) = 9x^2 + 4x + k \\ a = 9, b = 4, c = k;[/tex]

Since [tex]a > 0[/tex], our parabola has an upward opening.

Should we think about it graphically, it will be no wonder that we should pay our attention to the points of the parabola intersecting the abscissa axis. In other words, we need our vertex to intersect the x axis only once per se.
The vertex:

[tex]V_{x} = \frac{-b}{2a} = \frac{-4}{2 * 9} = - \frac{2}{9} \\ V_{y} = 9V_{x}^2 + 4V_{x} + k = 9(- \frac{2}{9})^2 + 4(- \frac{2}{9}) + k = 9 * \frac{4}{9^2} - \frac{8}{9} + k = \frac{4}{9} - \frac{8}{9} + k = - \frac{4}{9} + k[/tex]

As a result, our [tex]V_{y}[/tex] is parametric. [tex]k = \frac{4}{9}[/tex] suits us because [tex]V_{y} = - \frac{4}{9} + \frac{4}{9} = 0[/tex]. If [tex]k > \frac{4}{9}[/tex], we do not have any roots at all. We have two roots if [tex]k < \frac{4}{9}[/tex].

The total weight of the packed box is 9 lb 6 oz

According to question:

The weight of 12 jars is 12 times the weight of one jar

The weight of jars and box together is the sum of those weights.

... 12 × (10 oz) + 1 lb + 14 oz = 1 lb + 134 oz

... = 1 lb + 8 × (16 oz) + 6 oz . . . . . . 1 lb = 16 oz

... = 9 lb 6 oz

1 ounce (oz) is equal to 0.0625 pounds (lb).

1 oz = (1/16) lb = 0.0625 lb

The mass m in pounds (lb) is equal to the mass m in ounces (oz) divided by 16:

m(lb) = m(oz) / 16

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The integer represent the balance in your account is Z = + Y. The representation of integer is positive because withdrawal is always less then or equal to the amount present in the bank account.

Total rupees withdraw from saving account is $149

Let total amount in account before withdrawing is X= $500

Amount left after withdraw the money is calculated by a

AMOUNT LEFT = TOTAL AMOUNT - WITHDRAW AMOUNT

So, put the values then

Y= X($500) - $149

Y= $500 - $149

Y= $351

If we represent the balance of saving account in the integer form then it become the Z = + Y. The representation of integer is positive because withdrawal is always less then or equal to the amount present in the bank account.

So, The integer represent the balance in your account is Z = + Y. The representation of integer is positive because withdrawal is always less then or equal to the amount present in the bank account.

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Answer:

  x = 5

Step-by-step explanation:

The equality of bases property says powers of the same base will be equal if and only if the powers are equal. This property is used to solve exponential equations.

  [tex]\dfrac{(2)^x}{2}=16\qquad\text{copy of the original equation}\\\\2\times\dfrac{(2)^x}{2}=2\times16\qquad\text{multiply by 2 to isolate the base}\\\\2^x=32\qquad\text{simplify}\\\\2^x=2^5\qquad\text{rewrite the constant as a power of 2}\\\\\boxed{x=5}\qquad\text{use the Equality of Bases Property}[/tex]

__

Additional comment

Equating the exponents is fully equivalent to taking the logarithm of both sides of the equation, to that base.

  [tex]\log_2(2^x)=\log_2(2^5)\ \Longrightarrow\ x=5[/tex]

Answer:

17 square centimeters.

Step-by-step explanation:

Divide the rectangle into a 3x5 rectangle and a 2x1 rectangle.

(3x5)+(2x1)=17

17 square centimeters.

Answer:

1±i sqrt(7/2)

Step-by-step explanation:

For this equation you would need to use quadratic formula: x=(-b+-square root b^2-4ac)/2a

Answer:the answer is option E (see pic)

Step-by-step explanation:

One root would be: x =(4-√88)/-4=1+1/2√ 22 = 1.345

The distance from Bobby to the plane is 154.7 yards.

Sine law can be used to find the distance of the plane to Bobby.

Therefore,

x / sin 40 = 240 / sin 95

cross multiply

Hence,

x sin 95 = 240 sin 40

divide both sides by sin 95

x  =  240 sin 40 / sin 95

x = 240 × 0.64278760968 / 0.99619469809

x = 154.08 / 0.9961

x = 154.683264732

x = 154.7 yards

Therefore, the distance from Bobby to the plane is 154.7 yards.

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Answer:Jared has earned 23% of the $52 he needs to buy a new jacket. Find 23% of $52.Which expression can you use to find 23% of 52? ✔ 0.23 × 5223% of $52 is $✔ 11.96.An easy way to check your answer is to use the friendly ✔ 25%and divide 52 by ✔ 4to get ✔ 13

Step-by-step explanation:

Answer:

[tex]m\angle{ABC}=144^{\circ}[/tex]

Step-by-step explanation:

By using Angle Addition Postulate, it holds:

[tex]m\angle{ABD}+m\angle{DBC}=m\angle{ABC}[/tex]

Substitute [tex]m\angle{ABD}=76^{\circ}[/tex] and [tex]m\angle{DBC}=68^{\circ}[/tex] into the equation:

[tex]76^{\circ}+68^{\circ}=m\angle{ABC}[/tex]

Add the measures:

[tex]m\angle{ABC}=144^{\circ}[/tex]

The length of the rectangle is 8m and width of the rectangle is 7m

Given that the length and width of a rectangle are consecutive integers

Let the length of the rectangle be x+1 meter

Let the breadth of the rectangle be x meter

Also given that perimeter of the rectangle is 30 meters

To find length and breadth of the rectangle

We know that perimeter of the rectangle is P = 2 (l+b)

30 = 2 (x+x+1)

15 = 2x + 1

2x = 14

x = 7

x+1 = 8

Hence, the length of the rectangle is 8m and width of the rectangle is 7m

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The solution to the value of x in the given equation is x = 0.00212658 or x = -0.00213958

The process of solving the unknown value of an algebraic equation involves equating the values of the unknown to the constant value.

Given that:

[tex]\mathbf{\dfrac{x^2}{0.35-x}= 1.3 \times 10^{-5} }[/tex]

[tex]\mathbf{x^2 = 1.3 \times 10^{-5} (0.35-x) }[/tex]

x² = 4.725 × 10⁻⁶ - 1.3 × 10⁻⁵x

= [tex]x^2 + 1.3\times10^{-5}x - 4.725 \times 10^{-6}[/tex]

= x²+0.000013x-0.000004725

x = 0.00212658 OR x = -0.00213958

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Answer:

y = -x + 1

(Image of what graph looks like is attached)

Step-by-step explanation:

x = 1 - y can be rewritten into y = mx + b format.

x = 1 - y (subtract 1 from both sides)

x - 1 = -y (multiply by -1 to both sides)

y = -x + 1

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Let x = number of hours washing cars

Let y = number of hours landscaping

System of equations:

[tex]10x+8y=84\\\\x=2y[/tex]

Answer: 1.2x

Step-by-step explanation:

Profit = Selling price - Cost

She bought the stock at a cost of x dollars

Her profit was 20% of that, which is 0.2x dollars

Selling price = Profit + Cost = x + 0.2x = 1.2x

Answer: After working for 33 [tex]\frac{1}{3}[/tex] hours a week

Step-by-step explanation:

     Let us write equations to represent these two places. Let x be hours worked and y be money earned.

   Tim Hortons:

$200 + $5x = y

    McDonalds:

$300 + $2x = y

    Now, to find the conditions of which Tim Hortons is the better employer (on the basis of money earned) we must find the interval that Tim Hortons pays more. This can be found by setting up another equation, or by graphing. I have shown both. See attached for the graph.

$200 + $5x > $300 + $2x

$5x > $100 + $2x

$3x > $100

x > [tex]\frac{100}{3}[/tex]

x > 33.3334

    Tim Hortons is the better employer after an employee has worked for 33 [tex]\frac{1}{3}[/tex] hours a week.

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Answer:

c = 75.36 cm

Step-by-step explanation:

The equation of the circumference is:

[tex]c=\pi d[/tex]  In which "d" represents the measurement of the diameter

in this case d= 24cm, π = 3.14

Calculate the circumference:

[tex]c=\pi d=(3.14)(24)=75.36cm[/tex]

Hope this helps

A circle has a diameter of 24cm. The circumference of the circle is c = 75.36 cm.

The circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.

The circumference of the circle = 2πr

Given information;

A circle has a diameter of 24cm.

"d" represents the measurement of the diameter, so

d= 24cm, π = 3.14

Radius = d/ 2 = 12

Calculate the circumference:

The circumference of the circle = 2πr

= 2 ( 3.14 ) ( 12)

= 75.36

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