Part 2 of 2

You invested $15,000 in two accounts paying 4% and 7% annual interest, respectively. If the total interest earned for
the year was $960, how much was invested at each rate?

Answer:

Linear?

Step-by-step explanation:

its been years since I've seen this so I'm not sure

The maximum number of point of intersection of a line and circle is two

Circle:

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre. The following is the circle formula in the plane:

[tex](x-x1)^{2} +(y-y1)^{2} =r^{2}[/tex] Here,(x1,y1) are the centre of circle and r is the radius of circle.

Line:

A line has length but no breadth, making it a one-dimensional figure. A line is made up of a collection of points that may be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.

Line and Circle can intersect at two points maximum

Therefore,The maximum number of point of intersection of a line and circle is two

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Answer:

y = 8

Step-by-step explanation:

y + y + 2 = 18

2y + 2 = 18

     -2     -2    (+ 2 and - 2 cancel out each other)

   2y   = 16    

    2       2

     y = 8

You will make 1200 transactions by using the unitary method.

What is the unitary method?

Applying the unitary method to the given problem,

360 sec (three-sixty) = 360/60 = 6 min (six)

20*6(six) = 120 hr = 120*60 min

120*60/6 = 1200 transactions (answer)

You will make 1200 transactions by using the unitary method.

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The  property of equality was used to solve this equation is addition property of equality

The property states that the additive property of equality states that if we add or subtract the same number to both sides of an equation, the sides remain equal.

Given the expression

X-5=-14

Add 5 to both sides to have;

x-5 + 5 = -14 + 5

x = -14 + 4

x = -9

Hence the  property of equality was used to solve this equation is addition property of equality

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Answer:

D) Dilation and reflection.

→ The shape was dilated by -1.

→ This shape was then reflected upside down.

Dilating a shape is the act of making a shape smaller by a scaled amount. Dilation is useful in mathematics when you need to determine difference in shapes' scales factors.

Reflection is mirroring a shape to its opposite image. For instance, I have triangle ∠ABC', which is facing right. I then reflect this image, and it becomes triangle ∠ABC", which now faces left on the opposite axis.

Answer:

4    + 4√2

Step-by-step explanation:

[tex]CD=\sqrt{\left( 4-4\right)^{2} +\left( -5 - (-1)\right)^{2} } \\\\\\ =\sqrt{\left( 0\right)^{2} +(-4)^{2} }\\\\\\\ = \sqrt{16 }\\\\\\ =4[/tex]

[tex]DE=\sqrt{\left( 2-4\right)^{2} +\left( -3 - (-5)\right)^{2} } \\\\\\ =\sqrt{\left(-2\right)^{2} +(2)^{2} }\\\\\\\ = \sqrt{8 }\\\\\\ =2\sqrt{2}[/tex]

[tex]\text{\bf{EC} $=\sqrt{\left( 4-2\right)^{2} +\left( -1 - (-3)\right)^{2} } \\\\\\ =\sqrt{\left( 2\right)^{2} +(2)^{2} }\\\\\\\ = \sqrt{8 }\\\\\\ =2\sqrt{2}$}[/tex]

Perimeter (∆CDE) = CD + DE   + EC

                             = 4    + 2√2 + 2√2

                             = 4    + 4√2

                             ≈ 9.7

Answer:

Step-by-step explanation:

What is answer to X/2 - X/5 = 3

x/2 - x/5 = 3

(3/10)x = 3

x = 3 : 3/10

x = 3 * 10/3

x = 10

-------------

check

10/2 - 10/5 = 3

3 = 3

the answer is good

Answer:

B) The graph will not be symmetrical because the rates at which Jackson walks to and from his house are not equal.

Step-by-step explanation:

there you go I hope this help! :)

The graph will not be symmetrical because the rates at which Jackson walks to and from his house are not equal (option b).

Using an absolute value function to model the distance from his house would imply that the distances from his house are the same for both the outbound and return journeys, which is not the case in this scenario.

The rates at which Jackson walks to and from his house are not equal, as indicated by the different times taken for each leg of the journey (20 minutes to get away from his house and 30 minutes to return). This means the graph of the distance over time would not be symmetrical around a vertical line.

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The complete question is:

Jackson left his house and walked at a constant rate. After 20 minutes he was 2 miles from his house. Jackson then walked back towards his house at a constant rate. After another 30 minutes he arrived at his house.

Why should Jackson not use an absolute value function to model the distance from his house d after t minutes?

OA) The graph will be symmetrical because the rates at which Jackson walks to and from his house are equal.

OB) The graph will not be symmetrical because the rates at which Jackson walks to and from his house are not equal..

OC) The graph will be symmetrical because the rates at which Jackson walks to and from his house are not equal.

OD) The graph will not be symmetrical because the rates at which Jackson walks to and from his house are equal

Using it's concept, the relative frequencies are given as follows:

a) 124/639

b) 43/213

A relative frequency is given by the number of desired outcomes divided by the number of total outcomes.

For this problem, the number of students is:

583 + 620 + 187 + 163 + 558 + 645 + 439 = 3195.

620 responded study hard, hence the relative frequency is given as follows:

620/3195 (simplifying by 5)

124/639

645 responded goal in mind, hence the relative frequency is given as follows:

645/3195 (simplifying by 5)

129/639 (simplifying by 3)

43/213

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Answer:

Step-by-step explanation:

You want the dimensions of a rectangle and square such that they have the same perimeter, but the square has an area of 36 more square feet. The rectangle is twice as long as wide.

Let x represent the side length of the square. Then its area is x², and the area of the rectangle is (x² -36).

This area is the product of length and width. The expression factors as ...

  rectangle area = x² -36 = (x +6)(x -6)

If we assume these factors are the dimensions of the rectangle, then the longer dimension is twice the shorter one:

  (x +6) = 2(x -6)

  18 = x . . . . . . . . . add 12-x to both sides

This is the side length of the square. The rectangle dimensions are ...

  x+6 = 18+6 = 24 . . . . feet long

  x -6 = 18 -6 = 12 . . . . feet wide

The rectangle is 12 feet wide and 24 feet long. The square is 18 feet on a side.

__

Additional comment

The perimeter in each case is 4x = 2((x+6) +(x -6)) = 72 ft.

The area of the rectangle is (12 ft)(24 ft) = 288 ft². The area of the square is (18 ft)² = 324 ft², a value that is 36 ft² more than the rectangle area.

Alternate solution

Using x for the width of the rectangle, the length is 2x and its area is x(2x) = 2x². The perimeter is 2(x +2x) = 6x, so the side length of the square is (6x)/4 = 3/2x and its area is (3/2x)² = 9/4x².

The difference is 36 square feet, so we have ...

  9/4x² -2x² = 36 = x²/4   ⇒   x = √(36·4) = 6·2 = 12 . . . . width of rectangle

Answer:

A. A(220) = 7850; If the accountant takes 220 hours to prepare the taxes, the cost will be $7,850.

Step-by-step explanation:

Answer:

Domain: [-20, 20]

Range: [-30, 5]

Step-by-step explanation:

The domain is the set of x values and the range is the set of y values.

The coordinates of the image of the reflection of the parallelogram, HIJK, over the y-axis are;

H'(1, 3), I'(1, - 1), J'( -2, -2), K'( -2, 2)

The reflection of a pre-image, (x, y), over the y-axis gives an image at the point (-x, y), on the coordinate plane.

The given vertices of the parallelogram HIJK are;

H(-1, 3), I(-1, -1), J(2, -2), and K(2, 2)

The coordinates of the image are therefore;

[tex]H(-1, 3) \: \underrightarrow{ R_{ y-axis}} \: H ' (1, 3)[/tex]

[tex] I (-1, - 1) \: \underrightarrow{ R_{ y-axis}} \: I ' (1, - 1)[/tex]

[tex] J (2, -2) \: \underrightarrow{ R_{ y-axis}} \: J'( -2, -2)[/tex]

[tex] K (2, 2) \: \underrightarrow{ R_{ y-axis}} \: K'( -2, 2)[/tex]

The coordinates of the image, H'I'J'K' are therefore;

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hi

-(3a-3) =   -3a +3    

you cannot do much more.  

You can  rewrite it as  3 ( -a +1)   or as  -3 ( a -1)  but nothing more really.

Amelia went on a walk that was, She stopped to have lunch [tex]\frac{15}{4}[/tex] miles

when she had walked of the way [tex]\frac{12}{25}[/tex] miles. Amelia walk before lunch in

[tex]\frac{3}{25}[/tex] miles.

The mile is a customary unit of measurement in the United States and the United Kingdom that is based on the older English unit of length equal to 5,280 English feet, or 1,760 yards. It is often referred to as the international mile or statute mile to distinguish it from other miles. In 1959, the statute mile was formally redefined with respect to SI units as precisely 1,609.344 meters. This resulted in a standardization of the statute mile between the British Commonwealth and the United States.

The unqualified term "mile" is typically understood to refer to the current international mile. The international mile may also be referred to as a land mile or a statute mile when it has to be distinguished from nautical mile.

The term "statute mile" in British English can apply to either the current international mile or any other variation of the English mile since the 1593 Act of Parliament, which established it as 1,760 yards. However, in American law, a statute mile is equivalent to a US survey mile. If it is obvious from the context, as in a discussion of the 2nd-century Antonine Itinerary that the distances are described in terms of miles rather than Roman miles, the qualifier to describe the type of mile being used may be omitted. Foreign and historical units that are translated into English as miles typically employ a qualifier to describe the kind of mile being used.

Now from the above given question:

She stopped to have lunch in [tex]\frac{15}{4}[/tex] miles

She had walked of the way in [tex]\frac{12}{25}[/tex] miles

[tex]\frac{15}{4}-\frac{12}{25} = \frac{60}{100}- \frac{48}{100} = \frac{12}{100}[/tex][tex]=\frac{3}{25}[/tex].

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Answer:

The police will catch the thief in 5 minutes.

Step-by-step explanation:

Distance between thief and police after 2 minutes = 100 m

Implies, thief covers total 100 + 50t m

The police runs with the following patterns 60,65,70...

This is an Arithmetic Progression with a = 60, d = 5 & number of terms = t

t/2 (2 × 60+ (t − 1) ×5)= 50t + 100

t× (120 + 5t −5)= 100t + 200

​(−3+13)÷2= 5

So, the police will catch the thief in 5 minutes.

hmmm ok, so the advertisement says that original price is 106 and is on a 6% discount, ok, how much will that be?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6\% of 106}}{\left( \cfrac{6}{100} \right)106}\implies 6.36[/tex]

so, if the item is discounted by 6%, that'd be then 106 - 6.36 = 99.64, but they are saying they have it for 100?  something fishy is going on.

Answer:

88, 276, 192.

Step-by-step explanation:

Let the first number be x.

Then the second number is 3x.

Then the third number is (x+100).

Sum of the numbers=540

x + 3x + ( x + 100 ) = 540

5x = 440

x = 88.

The first number is 88.

The second number is 276.

The third number is 192

Answer:

0

Step-by-step explanation:

To find the slope of a line, you have to use the slope formula: [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

So, plug in the numbers: [tex]\frac{-7-(-7)}{-2-1}[/tex]

Simplifying it becomes: [tex]\frac{-7+7}{-2+-1}[/tex]. It then becomes [tex]\frac{0}{-3}[/tex].

Finally, dividing 0 by -3 gets you 0.

Answer:

18.

Step-by-step explanation:

1) formula of the perimeter given in the condition is:

p=2(VW+XV) or p=2(VY+XY).

Note, VW=XY and XV=VY;

2) if to substitute p=84, VW=2z+2 and XV=3z into the formula above, then

2(2z+2+3z)=84, ⇔ 5z+2=42; ⇒ z=8.

3) if z=8, then VW=2z+2=2*8+2=18.

Answer:

==========================

The distributive property is:

Apply this to the options:

Answer:

b) 2(x + 3) = 2x + 6

Step-by-step explanation:

The formula we refer to is,

→ a × (b + c) = (a × b) + (a × c)

The option obeys distributive law is,

→ 2 × (x + 3) = (2 × x) + (2 × 3)

→ 2(x + 3) = 2x + 6

Hence, option (b) is correct.

The simplified form of the expression (( (-2 + h)³ + 8 ) / h) is h² - 6h + 12

Given the expression in question;

( (-2 + h)³ + 8 ) / h

First, we simplify the numerator.

Lets rewrite 8 as 2³

(-2 + h)³ + 2³

Now, we can use the sum of cubes formula to factorize since both terms are perfect cubes.

a³ + b³ = ( a + b )( a² - ab + b² )

(-2 + h)³ + 2³ = ( -2 + h + 2 )( (-2 + h)² - (-2 + h)2 + 2² )

(-2 + h)³ + 2³ = h( (-2 + h)² + 4 - 2h + 4 )

(-2 + h)³ + 2³ = h( (-2 + h)²- 2h + 8 )

(-2 + h)³ + 2³ = h( (h² - 4h + 4 )- 2h + 8 )

(-2 + h)³ + 2³ = h( h² - 4h + 4 - 2h + 8 )

(-2 + h)³ + 2³ = h( h² - 6h + 12 )

Now bring back the denominator.

( h( h² - 6h + 12 ) ) / h

Cancel the common factors h

h² - 6h + 12

Therefore, the simplified form of the expression (( (-2 + h)³ + 8 ) / h) is h² - 6h + 12

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Answer:

Step-by-step explanation:

you need to turn the second y equation into the correct format, so it needs to be y=. Subtract the 1 from the left side and but it on the right side. Your equation should y=3x-1. To graph this on paper, you would go 1 down on the y axis, then rise (go up) 3 and run ( go over) one.on a calculator plug it into the y1 function and y2 function and then press graph.

Answer: 7

Step-by-step explanation: A polygon has vertices whose coordinates are A(1, 4), B(4, -1), C(-1, -4), and D(-4, 1). Use the midpoint formula to determine whether or not the diagonals

Answer:

7

Step-by-step explanation:

:D

Area of the triangle = 6x + 36

Perimeter of the rectangle = 3x + 10

Given the following parameters of a triangle as shown in the image attached below, its area and perimeter is calculated as shown below?

Area of the triangle = 1/2(base)(height) = 1/2(12)(x + 6)

Area of the triangle = 6(x + 6)

Area of the triangle = 6x + 36

The perimeter of the triangle = sum of all the three sides of the given triangle = (x - 7) + (2x + 5) + (12)

Perimeter= x - 7 + 2x + 5 + 12

Add like terms

Perimeter= x + 2x  - 7 + 5 + 12

Perimeter= 3x + 10

Therefore, we have:

Area of the triangle = 6x + 36

Perimeter of the rectangle = 3x + 10

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Step-by-step explanation:

There are 3 terms. A term is either a single number or variable or numbers and variables multiplies together

Answer:

Step-by-step explanation:

there are 3 terms

Answer:

193 and 194

Step-by-step explanation:

Left page = X

Right page = X + 1

You know the total sum.

X + (X + 1) = 387

2X + 1 = 387

2X = 387 - 1

2X = 386

X = 193

When you plug X in you get the following;

Left page = 193

Right page = 193 + 1 = 194