Kim took out a $55,000 loan for college she is borrowing money from 2 banks bank a charges an interest rate of 8% and b charges an interest rate of 11% after one year Kim owes 5000 in interest how much money did she borrow from bank a.

Answer:

center (1,-3) and radius is 5

Step-by-step explanation:

We have to use completing the square here:

x^2-2x    + y^2+6y         =15  (reorder some things and added 15 on both sides)

x^2-2x+(-2/2)^2  + y^2+6y+(6/2)^2   =15+(-2/2)^2+(6/2)^2 (whatever you add on one side you also do to the other side)

x^2-2x+(-1)^2   + y^2+6y+(3)^2=15+1+9

(x-1)^2         +    (y+3)^2          =25

Center is (1,-3) and radius is 5

ANSWER

The center is (1,-3) and the radius is r=5 units.

EXPLANATION

The given equation is:

[tex] {x}^{2} + {y}^{2} - 2x + 6y - 15 = 0[/tex]

Let rearrange to get:

[tex]{x}^{2} - 2x + {y}^{2} + 6y=15[/tex]

We complete the square to get;

[tex]{x}^{2} - 2x + ( { - 1)}^{2} + {y}^{2} + 6y + {3}^{2} = 15+ ( { - 1)}^{2} + {3}^{2}[/tex]

[tex] ( {x - 1)}^{2} +( {y + 3)}^{2} = 15 + 1+ 9[/tex]

[tex] ( {x - 1)}^{2} +( {y + 3)}^{2} =25[/tex]

[tex]( {x - 1)}^{2} +( {y + 3)}^{2} = {5}^{2} [/tex]

Comparing to

[tex]( {x - h)}^{2} +( {y - h)}^{2} = {r}^{2} [/tex]

The center is (1,-3) and the radius is r=5 units.

Answer:150 square cm

Step-by-step explanation:

Answer:

"The domain of both functions is all real numbers."

Step-by-step explanation:

Given

[tex]f(x) = 5x\\and\\g(x) = 5x[/tex]

We can see that the function will have some value for any value of x and is not undefined on any value of x. So the domain of f(x) is all real numbers.

Similarly, g(x) is also not undefined on any value of x so it also has domain of all real numbers.

The range of f(x) and g(x) will be all real numbers as the functions do not produce infinity on any of the input.

Only the statement that

"The domain of both functions is all real numbers."

is true for the given functions ..

Answer:

The correct answer option is A. encryption and transfer of data.

Step-by-step explanation:

The business activities that take place through internet as the medium are referred to as electronic commerce.

The Federal Trade Commission [FCT] is one of the main functional bodies responsible for regulating such electronic commerce activities which includes encryption and transfer of data.

The risk of data theft from encryption and transfer of data is really high so FTC makes sure to prevent theft from the transaction made through e-commerce.

Answer:

Which aspect of electronic commerce does the FTC regulate?

A.  

encryption and transfer of data

B.  

disposing of credit reports

C.  

network security

D.  

antivirus software updates

Step-by-step explanation:

#platofam

Answer:

Both graphs have been shifted and flipped

Both graphs have exactly one asymptote

Step-by-step explanation:

Choice A is incorrect since both graphs are not logarithmic functions. The graph of f(x) appears to be an exponential function.

Choice B is also incorrect since both graphs are not exponential functions.  The graph of g(x) does not belong to the exponential family since y can take on negative values.

When the graph of f(x) is shifted downwards and flipped, we can obtain the graph of g(x).

Both graphs have exactly one horizontal asymptote

The potential and kinetic energy of a rock thrown into the air and falling back is misunderstood in statement 1. Voting rates are lower in the United States compared to some other democratic countries, and according to Kepler's laws, a satellite speeds up as it approaches its parent body and slows down as it moves away.

For the given set of statements:

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Answer:

  12(m -5) = 540

Step-by-step explanation:

The left side of the equation is in the form of a product. A suitable product is ...

  (calories/minute) × (minutes jogging) = (calories burned)

If m represent Anzelm's total minutes, then m-5 will represent the number of minutes actually jogging. This is what goes inside parentheses, so we have ...

  (12 calories per minute) × ((m -5) minutes) = 540 calories

Leaving off the units, which we know are consistent, we have ...

  12 (m -5) = 540

Answer:

12(m-5) = 540

Step-by-step explanation:

∵ The total calories have to burn = 540,

Also, here m represents the total time spent by Anzelm,

If he/she spent 5 minutes in rest,

Then the time he/she spent in jogging = (m - 5) minutes,

If the number of calories burnt in one minute = 12,

So, the number of calories burnt in (m-5) minutes = 12(m-5),

Therefore, for burning the whole calories,

Calories burnt by him/her = total calories

⇒ 12(m-5) = 540

Which is the required equation.

Answer:

  8 by 12 units

Step-by-step explanation:

Let w represent the width of the rectangle. Then the length is 1.5w. The perimeter is 4 more than 3 times this, so is (3(1.5w) +4) = 4.5w+4

The perimeter is given by the formula ...

  P = 2(length + width)

Filling in the given values for the variables, we have ...

  4.5w +4 = 2(w +1.5w)

  4 = 0.5w . . . . . . subtract 4.5w and collect terms

  8 = w . . . . . . . . . multiply by 2

  length = 1.5×8 = 12

The rectangle is 8 units wide and 12 units long. The perimeter is 40 units.

Answer:

Step-by-step explanation:

8x12

Answer:

To maximize the income should be 30 buses and 150 cars

Step-by-step explanation:

Let

x-----> the number of cars

y ----> the number of bus

we know that

[tex]5x+32y\leq1,710[/tex] ------> inequality A

[tex]x+y\leq 180[/tex] ----> inequality B

The function of the cost to maximize is equal to

[tex]C=2x+6y[/tex]

Solve the system of inequalities by graphing

The solution is the shaded area

see the attached figure

The vertices of the solution are

(0,0),(0,53),(150,30),(180,0)

Verify

(0,53) ---> [tex]C=2(0)+6(53)=\$318[/tex]

(150,30) ---> [tex]C=2(150)+6(30)=\$480[/tex]

therefore

To maximize the income should be 30 buses and 150 cars

Answer:

Givens

To solve this problem we need to create a table to order all this information and express it as a system of inequations.

                     Car           Bus     Total Capcity

Sq. Meters      5c           32b            1710

N° vehicles      c              b                180                

Therefore, the inequalities are

[tex]5c+32b\leq 1710\\c+b\leq 180[/tex]

The expresion which represents the income is

[tex]I=2c+6b[/tex], because a car is $2.00 and a bus is $6.00.

Now, we first need to find the critical points of the solution of the inequality system, which is attached. Observe that the only points that can be a solution is (150,30), because there can't be just car or just buses.

Then, we replace this point in the income expression

[tex]I=2c+6b\\I=2(150)+6(30)=300+180=480[/tex]

Therefore, in order to maximize incomes, we need to park 150 cars and 30 buses, to make $480 income.

Answer:

C.) y = - 8

Step-by-step explanation:

If the line has a slope of 0, it is a horizontal line.  That means y= a value

Since we have the point (0,-8)

y = -8

Final answer:

The equation of a line that goes through point (0, -8) with a slope of 0 is y = -8.(Option c)

Explanation:

We need to find the equation of a line that goes through the point (0, -8) and has a slope of 0. The general equation for a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Since the slope (m) is 0, the line is horizontal.

A horizontal line has an equation of the form y = b, where b is the y-coordinate of every point on the line. As the line goes through (0, -8), we can see that the y-coordinate is -8 for all points on this line. Therefore, the equation of this line is C) y = -8.

Answer:

21

Step-by-step explanation:

Rule of logs:

[tex] b^{\log_b x} = x [/tex]

Your problem:

[tex] 10^{\log_{10} 21} = 21 [/tex]

The value of the given logarithm expression will be 21.

Exponents can also be written as logarithms. A number base logarithm is similar to some other number. It is the exact inverse of the exponent expression.

The expression is given below.

[tex]\rightarrow 10^{\log 21}[/tex]

We know that

[tex]\rm a ^{\log_ab} = b[/tex]

Then the expression will be

⇒ 21

More about the logarithm link is given below.

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Answer:

The definition of a circle uses the undefined term  Arc

Step-by-step explanation:

There are three terms generally considered to be undefined in geometry: point, line and plane. A circle is the set of all points in a plane the same distance from a given point called the center. The only of our options that is used in this definition is plane.

Answer:

B

Step-by-step explanation:

Using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Hence

[tex]log_{5}[/tex] 9 = x ⇒ 9 = [tex]5^{x}[/tex] → B

Answer:

its d 5 < x ≤ 9 .                                                                                                                                                                                                                                                            

Answer:

93°

Step-by-step explanation:

Angle ACB is a central angle.  The theorem regarding central angles and the arcs they intercept is that the angle and the arc are congruent.  That means that arc AB is also 93°

Answer:

  about 13.8 in³

Step-by-step explanation:

The volume of air is the difference between the volume of the cylinder of radius 1.3 inches and height 7.8 inches, and that of three spheres, each with a radius of 1.3 inches.

The formula for the volume of a cylinder is ...

  V = πr²h

The formula for the volume of a sphere is ...

  V = (4/3)πr³

For h = 6r, the difference is ...

  (cylinder volume) - 3×(sphere volume) = πr²·(6r) - 3×(4/3)πr³

  = πr³(6 -4)

  = 2πr³ = 2π(1.3 in)³ = 4.394π in³

  ≈ 13.8 in³ . . . . air space in the cylinder of tennis balls

Answer:

  1/64

Step-by-step explanation:

[tex]256^{-\frac{3}{4}}=2^{8(-\frac{3}{4})}=2^{-6}=\dfrac{1}{2^6}=\dfrac{1}{64}[/tex]

256^-3/4 can be converted into a positive fraction by interpreting the negative exponent as a reciprocal and the fractional exponent as a root. It simplifies to 1/(4th root of 256^3), which equals 1/64.

To express the numeral 256^-3/4 in the form of a fraction, we first need to understand how negative and fractional exponents work. The number is in the form of a^(-m/n) which is equivalent to the nth root of a^-m or 1/(nth root of a^m). The negative sign in the exponent implies a reciprocal of the number and the fractional exponent denotes a root of the number.

Now applying this understanding to our number which is 256^-3/4. Here, the base a is 256 and the fractions -m/n is -3/4. Therefore, it is equivalent to the 4th root of 256^-3, which can also be written as 1/(4th root of 256^3).

The 4th root of 256 is 4. So, the expression now becomes 1/(4^3), which after simplifying gives us the result 1/64.

So, the expression 256^-3/4 written as a positive fraction is 1/64.

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The equation of the hyperbola is [tex]\frac{x^2}{16} - \frac{(y - 1)^2}{9} = 1[/tex]

The vertices of the hyperbola are given as:

Vertices = (±4, 1)

The foci of the hyperbola are given as:

Foci = (±5, 1)

The coordinates of the vertices is represented as::

Vertices = (±a, n)

By comparing (±a, n) and (±4, 1), we have:

a = 4

n = 1

The coordinates of the foci is represented as::

Foci = (±c, n)

By comparing (±c, n) and (±5, n), we have:

c = 5

n = 1

Calculate b using:

b = √(c² - a²)

So, we have:

b = √(5² - 4²)

Evaluate

b = 3

The equation of a hyperbola is:

[tex]\frac{x^2}{a^2} - \frac{(y - n)^2}{b^2} = 1[/tex]

So, we have:

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

Evaluate the exponent

[tex]\frac{x^2}{16} - \frac{(y - 1)^2}{9} = 1[/tex]

Hence, the equation of the hyperbola is [tex]\frac{x^2}{16} - \frac{(y - 1)^2}{9} = 1[/tex]

Read more about hyperbola at:

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Answer:

The best represents a triangle is obtuse, because 6 + 10 > 12 ⇒ answer 4

Step-by-step explanation:

* Lets talk about some facts in the triangle

- The triangle is formed when the sum of the lengths of the shortest

 two side is greater then the length of the longest side

∵ The lengths of the sides are 6 cm , 10 cm , 12 cm

∵ 6 + 10 > 12

∴ 6 , 10 , 12 are the sides of a triangle

- Two know the type of the triangle use these rules

# The three sides of the triangle have lengths a , b , c where a and b

  are the shortest sides means a , b < c, then

- If a² + b² > c² , the triangle is acute triangle (its 3 angles are acute)

- If a² + b² = c² , the triangle is right triangle (the angle opposite to c is a

 right angle and the other 2 angles are acute angles)

- If a² + b² < c² , the triangle is obtuse triangle (the angle opposite to c is an

 obtuse angle and the other 2 angles are acute angles)

∵ (6)² + (10)² = 36 + 100 = 136

∵ (12)² = 144

∵ 136 < 144

∴ (6)² + (10)² < (12)²

∴ The triangle is obtuse

* The best represents a triangle is obtuse, because 6 + 10 > 12

Answer:

theoretical probability

Step-by-step explanation:

This is theoretical probability.  The 7 pieces of paper each bear one number from {1, 2, ... , 6, 7}.  There is only one piece of paper marked 7.  So the probability of drawing a 2 is  1/7.  

Answer:

  (5, 3)

Step-by-step explanation:

Conventionally, the ordered pairs are (right, up). Then ...

Ming's = (0, 0) + (2, 5) = (2, 5)

Joe's = Ming's + (3, -2) = (2, 5) + (3, -2) = (2+3, 5-2)

Joe's = (5, 3)

Answer:

( 5,3 )

Step-by-step explanation:

i am doing this test too

Answer:

Length of side [tex]c[/tex]:

[tex]c = \rm AB \approx 115\; yds[/tex].

The distance across the canyon is approximately

[tex]\rm 113\;yds[/tex].

Step-by-step explanation:

Apply the law of sine:

[tex]\displaystyle \frac{c}{\sin{\rm A\hat{C}B} = \frac{a}{\sin{\rm B\hat{A}C}}[/tex].

In other words,

[tex]\displaystyle c = \sin{\rm B\hat{A}C} \cdot \frac{a}{\sin{\rm A\hat{C} B}}[/tex].

However, the value of the angle [tex]\rm B\hat{A}C[/tex] isn't given. Don't panic. The three interior angles of a triangle shall add up to 180°. Two of the three angles are given. The value of the third angle is implied.

[tex]\rm B\hat{A}C = 180\textdegree{} - A\hat{C}B - A\hat{B}C = 30\textdegree{}[/tex].

Apply the law of sine to find [tex]c[/tex]:

[tex]\displaystyle \begin{aligned}c &= \sin{\rm A\hat{C}B} \cdot \frac{a}{\sin{\rm B\hat{A}C}}\\ &= \sin{50\textdegree{}}\cdot \frac{\rm 75\; yds}{\sin{30\textdegree{}}}\\ &\rm = 114.907\; yds\end{aligned}[/tex].

Refer to the diagram. The distance across the canyon will be

[tex]\rm AB \cdot \sin{A\hat{B}C} = 114.907\times \sin{100\textdegree{}} \approx 113\;yds[/tex].

Answer:

  99°

Step-by-step explanation:

∠7 and ∠8 are a linear pair, so are supplementary. Numbers are assumed to be degrees.

  ∠7 + ∠8 = 180

  2x+15 + 3x = 180 . . . . . substitute given values

  5x = 165 . . . . . . . . . . . . subtract 15, collect terms

  x = 33 . . . . . . . . . . . . . . . divide by the coefficient of x

  ∠8 = 3x = 3·33 = 99 . . . . . degrees

Answer:

Explanation:

In geometry, undefined terms refer to three entities: points, lines, and planes. They are considered undefined because they are rather described than formally defined.

The reason behind this lack of definition is that they are abstractions: you cannot touch or see a real point, line or plane.

A point represents a position in the plane or the space, and it is dimensionless. Yet it is used to define a line and a plane.

Among those three terms, only line and plane meet the feature of not having begin or end. That is so because lines  and planes extend infinetly

LInes extend in two directions, in one dimension: for example, from left to right, or from east to west, or vertically.

Planes extend infinetly in two dimensions: they are flat infinite surfaces.

Answer:

D.

Step-by-step explanation:

The area formula for a circle is [tex]A=\pi r^2[/tex].

If the diameter is given, we take half of it to find the radius measure.  If d = 6, then r = 3.  Therefore, our formula can be filled in as

[tex]A=\pi (3)^2[/tex] or [tex]A=9\pi[/tex].  That is the exact area.  The approximate area is found by multiplying in 3.1415 as pi to give you that the area is approximately 28.27 square inches.  I think you meant to put pi in those answer choices instead of an underscore, so it's my belief that D. is supposed to reflect the answer of [tex]9\pi[/tex] square inches.  I'm going with D.

Answer:

D

Step-by-step explanation:

This is a vertical opening parabola, since the focus is above the vertex on the axis of symmetry x = 2

The standard form of a vertically opening parabola is

(x - h)² = 4a(y - k)

where (h,k) are the coordinates of the vertex and a is the distance from the vertex to the focus.

here (h, k) = (2, - 1) and a = 4, hence

(x - 2)² = 16(x + 1) → D

Answer:

D

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

(a)

The opposite sides of a rectangle are congruent, hence

x + 1 = 5 ( subtract 1 from both sides )

x = 4

Or

x - 1 = 3 ( add 1 to both sides )

x = 4

(b)

The sum of the 3 angles in a triangle = 180°, hence

3y + 2y + y = 180

6y = 180 ( divide both sides by 6 )

y = 30

Answer:

PART A "4"

PART B "30"

Step-by-step explanation:

PART A

If you refer to my picture below, then you will know that the sides are equal.

The x-1 side is equal to 3 and the x+1 sign is equal to 5. So it best makes sense that 4 is equal to x. That's because x-1 is 3 and x+1 is 5.

PART B

This is tricky. As you know all sides of a triangle add up to 180 degrees. I would divide by 3, but that would be incorrect. Whenever you see these y's, you have to divide by that amount. The y's are there for a reason, so that some sides are bigger than the other. Divide 180 by 6(number of y's). That is 30. This gives you the solution to one y so if it asks you for 2y or 3y, then you would multiply. But it's not. 30 is the answer

You need more input here what even is the question

Answer:

The number of tables

Step-by-step explanation:

Let

z ----> the number of tables

y-----> the number of chairs

we know that

[tex]y=2z+3[/tex]

therefore

z represent the number of tables

Answer:

the number of tables :]

Step-by-step explanation:

Answer:

  4833.33

Step-by-step explanation:

The salary of $58,000 is Alex's pre-tax income. It is presumed to be divided evenly between the 12 months of the year, so his monthly income is ...

  $58,000/12 = $4833.33

Answer:

b = 17

Step-by-step explanation:

The angle bisector of the apex angle of an isosceles triangle is also a median and altitude. PS=RS=17

b = 17

Answer:

15:20

Step-by-step explanation:

15:20 = 15/20 = .75 = 75%