Question 1
If you invested $500 at 5% simple interest for 2 years, how much interest do you earn? Show work and answer in
complete sentences to earn full credit.
If you invest $500 at 3% compounded monthly for 2 years, how much interest you do earn? Show work and answer in
complete sentences to earn full credit.
Which would you rather do?

Answer:

a) 165.52 degrees.

b)  131.41 degrees.

c)  118.96 degrees.

d)  159.73 degrees.

Step-by-step explanation:

The sine of an obtuse angle is positive as it is in the second quadrant.

a) Using a calculate the angle whose sine ( arcsin) is 0.25  = 14.478 degrees

so the obtuse angle  = 180 - 14.478 = 165.52 degrees to nearest hundredth

b) c) and d) are calculated in the same way.

Answer:

[tex]\frac{5}{3}[/tex]

Step-by-step explanation:

Slope = [tex]\frac{4-(-1)}{3-0} =\frac{5}{3}[/tex]

Answer:

A (5x + 3)(5x – 3)

B (7x + 4)(7x + 4)

E (x – 9)(x – 9)  

F (–3x – 6)(–3x + 6)

in other words, A,B,E, and F on edge-nuity. just completed with 100%

Step-by-step explanation:

To find the values of x and y requires solving equations, refining the solution through iterative methods like the extended Newton-Raphson technique, and validating results with approximation checks.

In answering this mathematical question, we are attempting to find specific values for the variables x and y. To solve for these variables, we employ various mathematical methods such as the Newton-Raphson technique for refinement.

Keeping the referenced data in consideration, the equations provided reveal that we manipulate these equations to gradually reach a more accurate result. For instance, taking the quadratic equation y²-0.30068y +0.022500 = 0 and using the quadratic formula y = 0.30068 ± √(0.30068)² – (4)(1)(0.022500) allows us to find the value for y, and an iterative process enhances the precision of x and y.

Remember to always retain a few extra significant figures to minimize rounding errors in the computational process. Additionally, entering our data into a calculator or a computer program will help in writing the linear equation, which needs to be rounded to an appropriate number of decimal places for accuracy. Examples mentioned illustrate evaluating the coordinates of a point, substituting values into equations, and analyzing the relation between variables through a graphical approach.

To validate our results, we compare the approximation to the actual value to ensure that our error margin is acceptable, especially when dealing with extrapolations from implicit differentiation in calculus contexts.

Answer:

5 + 2[tex]\sqrt{6}[/tex]

Step-by-step explanation:

Multiply top and bottom by sqrt(3) + sqrt(2)

Top = (sqrt (3) + sqrt(2)) * (sqrt(3) + sqrt(2))

Top = 3 + sqrt(6) + sqrt(6) + 2

Top = 5 + 2sqrt(6)

Bottom = (sqrt (3) - sqrt(2)) * (sqrt(3) + sqrt(2))

Bottom = (3 - sqrt(6) + sqrt(6) - 2)

Bottom = 1

So, the answer is 5 + 2[tex]\sqrt{6\\}[/tex]

Answer: 5+2√6

Step-by-step explanation: attachment

The value of expression when n = 3 is 22

Solution:

Given expression is:

[tex]\frac{6(n^2 + 2)}{n}[/tex]

We have to find the value of expression when n = 3

Substitute n = 3 in given expression

[tex]\rightarrow \frac{6(3^2 + 2)}{3}\\\\Simplify\ the\ above\ expression\\\\\rightarrow \frac{6(9+2)}{3}\\\\Solve\ the\ terms\ inside\ the\ bracket\\\\\rightarrow \frac{6(11)}{3}\\\\Divide\ 6\ by\ 3 \\\\\rightarrow 2 \times 11 = 22[/tex]

Thus the value of expression when n = 3 is 22

Answer:

22

Step-by-step explanation:

[tex]\text{Hey there!}[/tex]

[tex]\bf{What\ is\ greater: \dfrac{3}{10}, \dfrac{1}{2},\&\dfrac{2}{5}?}[/tex]

[tex]\bf{Well, let's\ turn\ our\ fractions\ into\ decimals\downarrow}[/tex]

[tex]\bullet\ \bf{\dfrac{3}{10}=0.30(also\ known\ as\ 0.3)}\\\\\bullet \ \bf{\dfrac{1}{2}=0.50(also\ known\ as\ 0.5)}\\\\\bullet \ \bf{\dfrac{2}{5}=0.40(also\ known\ as\ 0.4)}[/tex]

[tex]\bf{The\ fractions\ in\ percentages\downarrow}[/tex]

[tex]\bullet \ \mathsf{\dfrac{3}{10}=30\%}\\\\\bullet \ \mathsf{\dfrac{1}{2}=50\%}\\\\\bullet \ \mathsf{\dfrac{2}{5}=40\%}[/tex]

[tex]\text{Now that we have that out the way. Let's solve for your answer!}[/tex]

[tex]\bf{\dfrac{1}{2}}\rightarrow\dfrac{2}{5}\rightarrow\dfrac{3}{10}}}} \leftarrow( that's\ for\ GREATEST\ to\ LEAST)[/tex]

[tex]\boxed{{\bf{Answer: \dfrac{1}{2}\ would\ be\ your\ GREATEST\ or \ BIGGEST\ one}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

  1/16

Step-by-step explanation:

Area is the product of linear dimensions.

Suppose the area of the triangle is the product of two dimensions p and q*:

  A = pq

Then the smaller triangle will have an area that is ...

  A = (1/4p)(1/4q) = (1/4)²pq = (1/16)pq . . . . . . 1/16 of the original area

__

If each of the linear dimensions of the triangle is multiplied by 1/4, the area will be multiplied by (1/4)² = 1/16.

_____

* No doubt, you have learned the area formula for a triangle is ...

  A = (1/2)bh

In the above, we might have p=1/2b and q=h. Or, there could be some other relationship between triangle dimensions and p and q.

Final answer:

The volume of a pyramid with a height of 215 units and a square base of 339 units on each side is calculated using the formula V = (1/3)Bh, resulting in a volume of 1,304,688.67 cubic units.

Explanation:

To find the volume of a pyramid, we can use the formula V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid. If the base is a square with each side being 339 units, then the area of the base (B) can be calculated as 339×339 square units. Given the height (h) of the pyramid is 215 units, the volume can then be calculated.

First, calculate the area of the base:
B = 339×339 = 114921 square units.

Then, use the volume formula by plugging in B and h:
V = (1/3)×114921×215 = 1,304,688.67 cubic units.

Therefore, the volume of the pyramid is 1,304,688.67 cubic units.

Yo sup??

Equation of the given line is

y=12 - 0.5x

on the y axis the x coordinate will be , therefore at x=0 we get

y=12 - 0.5*0

y=12

Therefore the coordinates of the y intercept are (0,12).

Hope this helps.

Final answer:

The y-intercept for the equation y = 12 - 0.5x is found by setting x to 0, resulting in y = 12, giving us the coordinates of the y-intercept as (0, 12).

Explanation:

The equation of a straight line is given by y = mx + b, where m represents the slope of the line, and b is the y-intercept. In your case, the equation is y = 12 - 0.5x. To find the coordinates of the intercept on the y-axis, we set x to 0 and solve for y. This gives us the y-intercept directly from the equation without needing to graph it.

For the equation y = 12 - 0.5x, when x = 0:

y = 12 - 0.5(0)

y = 12 - 0

y = 12

Therefore, the coordinates of the intercept on the y-axis are (0, 12).

63 divided by 9 is 7, so -7+7 is 0

Hope this helped

Answer:

0

Step-by-step explanation:

using PEMDAS

63/9 = 7

-7 + 7 = 0

Answer:

[tex]Give\ Two\ expressions\ are\ equivalent.[/tex]

Step-by-step explanation:

[tex]First\ expression=7^2+4x\\\\At\ x=2,\ value\ of\ first\ expression=7^2+4\times 2=49+8=57\\\\Second\ expression=4x+(7\times 7)\\\\Second\ expression=4x+7^2\ \ \ \ \ \ \ \ \ \ \ as\ m\times m=m^2\\\\Second\ expression=7^2+4x\ \ \ \ \ \ \ \ using\ commutative\ property\ of\ addition\\\\At\ x=2,\ value\ of\ second\ expression=7^2+4\times 2=49+8=57\\\\Hence\ these\ two\ expressions\ are\ equivalent.[/tex]

Answer:

x+y>1

Step-by-step explanation:

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by  

3

gives the next term. In other words,  

a

n

=

a

1

⋅

r

n

−

1

.

Geometric Sequence:  

r

=

3

This is the form of a geometric sequence.

a

n

=

a

1

r

n

−

1

Substitute in the values of  

a

1

=

5

and  

r

=

3

.

a

n

=

(

5

)

⋅

(

3

)

n

−

1

Remove parentheses.

a

n

=

5

⋅

3

n

−

1

Answer:

$36.94

Step-by-step explanation:

Okay, so. This is what we do. There is two magazines and they cost 9.95 each multiply 9.95 times 2

9.95 x 2 = 19.90

Okay, then he buys a book for 14.95 we add 19.9. and 14.95

19.90 + 14.95 = 34.85

Then we have a sales tax of 6% we would multiply 34.85 time 6%

34.85 x 6% = 2.09

Then we would add. 34.85 + 2.09

34.85 + 2.09 = 36.94

Therefore your answer is $36.94

Hope this helps!!!

The answer is $36.94. You add up the total purchases, multiply them by .06, then add that number to you total purchases.

Answer:

Step-by-step explanation:

[tex]6a^{2}=6534\\\\a^{2}=\frac{6534}{6}\\=1089\\\\a=\sqrt{1089}\\\\ a=33ft\\\\volume=a^{3}\\\\=33*33*33\\\\=35937[/tex]

To find the volume of a cube with a given surface area, we can use the formula for surface area and rearrange it to find the side length. Once we have the side length, we can calculate the volume of the cube.

To find the volume of a cube, we need to determine the length of one side. Since a cube has 6 equal sides, we can calculate the length of each side using the formula for surface area: surface area =  6 * side length * side length. Let's rearrange the formula to find the side length: side length = sqrt(surface area / 6). Once we have the side length, we can calculate the volume using the formula: volume = side length * side length * side length. Plugging in the given surface area of 6534 square feet, we find that the volume of the cube is approximately 2314 cubic feet.

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Answer:4 is thousands place

3 is hundredths place

8 is tens place

2 is ones place

Step-by-step explanation:

The place value of the underlined number 4,382 is,  

4 is thousands place

3 is hundredths place

8 is tens place

2 is ones place.

Place value is the basis of our entire number system. This is the system in which the position of a digit in a number determines its value.

The number 42,316 is different from 61,432 because the digits are in different positions.

here, we have,

the underlined number 4,382

so, we get the place value,

4 is thousands place

3 is hundredths place

8 is tens place

2 is ones place.

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Answer:

The deep of the sand will be 3.5 feet

Step-by-step explanation:

step 1

Find out the area of the court plus a 10-foot boundary around the  court for safety

[tex]A=(30+10+10)(60+10+10)\\A=(50)(80)\\A=4,000\ ft^2[/tex]

step 2

Find the deep of the sand

we know that

The volume of the sand is equal to

[tex]V=Ah[/tex]

where

A is the area of the base

h is the height or deep of the sand

substitute the given values

[tex]14,000=(4,000)h[/tex]

Solve for h

[tex]h=14,000/4,000=3.5\ ft[/tex]

Jerry's indoor beach volleyball court, including a 10-foot boundary, would have an area of 4,000 square feet, and with 14,000 cubic feet of sand, it would result in the sand being 3.5 feet deep.

Since Jerry wants to build an indoor beach volleyball court with a 10-foot boundary around it and has ordered 14,000 cubic feet of sand, we need to calculate the volume of the sand to determine how deep it will be when spread evenly over the entire area, including the boundary. The dimensions of the volleyball court are 30 feet by 60 feet, and adding a 10-foot boundary around it increases each dimension by 20 feet (10 feet on each side), resulting in a total area dimension of 50 feet by 80 feet.

To calculate the depth of the sand, we first calculate the area of the court including the boundary: Area = length × width = 50 feet × 80 feet = 4,000 square feet. Next, we divide the total amount of sand by the area to find the depth: Depth = volume / area = 14,000 cubic feet / 4,000 square feet = 3.5 feet deep. Therefore, if Jerry uses all the sand, it will be 3.5 feet deep.

Answer:

Therefore the area of the quadrilateral =35 cm²

Step-by-step explanation:

Given, the length of one of diagonal of quadrilateral is 10 cm and perpendicular drawn from the opposite vertices to this diagonal are the length of 2.8 cm and 4.2 cm.

A diagonal divided a quadrilateral into two triangle.

Therefore the area of the quadrilateral

= sum of the area of the triangles

[tex]=(\frac{1}{2}\times 10\times 2.8+ \frac{1}{2}\times 10\times 4.2)[/tex]cm²      [ area of a triangle[tex]= \frac{1}{2}\times base\times height[/tex]]

=35 cm²

Answer:

y = 38°

Step-by-step explanation:

If Angle x and angle y are complementary, then x + y = 90°

Also, if angle x is supplementary to a 128 angle, then x + 128° = 180°.

Solving the latter equation for x, we get x = 52°.

Therefore, by the first equation, x + y = 90° becomes 52° + y = 90°, yielding

y = 38°

Answer:

[tex]\boxed{\mathtt{x=52^{\circ}}}[/tex]

[tex]\boxed{\mathtt{y=38^{\circ}}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to solve for the measures of angles x and y.}[/tex]

[tex]\textsf{First, x is supplementary to an angle that equals 128}^{\circ}.[/tex]

[tex]\Large\underline{\textsf{What are Supplementary Angles?}}[/tex]

[tex]\textsf{Supplementary angles are 2 or more angles that add up to \underline{180}}^{\circ}.[/tex]

[tex]\large\underline{\textsf{This means that;}}[/tex]

[tex]\mathtt{x+128^{\circ}=180^{\circ}.}[/tex]

[tex]\large\underline{\textsf{Subtract 128 from both sides for x:}}[/tex]

[tex]\boxed{\mathtt{x=52^{\circ}}}[/tex]

[tex]\Large\underline{\textsf{What are Complementary Angles?}}[/tex]

[tex]\textsf{Complementary angles are 2 or more angles that add up to \underline{90}}^{\circ}.[/tex]

[tex]\large\underline{\textsf{This means that;}}[/tex]

[tex]\mathtt{x+y=90^{\circ}.}[/tex]

[tex]\textsf{Because we know x, we can solve for y.}[/tex]

[tex]\large\underline{\textsf{Substitute:}}[/tex]

[tex]\mathtt{52^{\circ}+y=90^{\circ}.}[/tex]

[tex]\large\underline{\textsf{Subtract 52 from both sides for y:}}[/tex]

[tex]\boxed{\mathtt{y=38^{\circ}}}[/tex]

96 m

2 m/sec²

Step-by-step explanation:

Step 1:

In a velocity and time graph , the area which is under the plotted line represents the distance traveled

In the given graph , the plotted line from t=0 to t=4 ( for the first 4 secs) is a   triangle with base = 4 and height = 8

Area of this triangle is (1/2) * b * h = (1/2)* 4*8 = 16 m

Step 2 :

The plotted line from t = 4 to t = 14 is a rectangle with length equal to 10 and breadth equal to 8

Hence its area = length * breadth = 10 * 8 = 80 m

Step 3 :

Total  distance traveled is 80 + 16 = 96 m

Step 4 :

In the velocity time graph , slope denotes the acceleration at any given time. Since we want the acceleration for the first 4 secs, we need to find  slope of  line in from t = 0 to t= 4

when t = 0, v =0 and t= 4, v = 8

Slope = 8-0/4-0 =2 m/sec²

Answer:

Area of the garden is [tex]306feet^2[/tex]

Step-by-step explanation:

Given:

Perimeter of the garden=84 feet

Let the width of the garden be 'W'

Length of the garden is 24 feet longer than the width of it

so, length of the garden= W+24 feet

To find the width 'W'

Perimeter of a rectangle= 2(Length+Width)

                                      [tex]84 =2(W+24+W)\\ 84 =4W+48\\ 84-48=4W\\ 4W=36\\ W=9[/tex] feet

Width=9 feet

Length=W+24= 9+24= 34 feet

Area of the garden= Length*width

                                 [tex]=34*9\\ =306 feet^2[/tex]

Area of the garden is 306 square feet

Answer:

Slope, m = [tex]$ \frac{\textbf{-2}}{\textbf{3}} $[/tex].

Step-by-step explanation:

The slope of the line can be determined by simplifying the given equation to its standard form.

In the standard form, y =  mx + c, m represents the slope of the line.

We are given: [tex]$ y - 2 = - \frac{2}{3}(x + 1) $[/tex]

[tex]$ \implies y = -\frac{2}{3}x - \frac{2}{3} + 2 $[/tex]

[tex]$ \implies y = - \frac{2}{3}x + \frac{(-2 + 6)}{3} $[/tex]

[tex]$ \implies y = -\frac{2}{3}x + \frac{4}{3} $[/tex]

Comparing it with the standard equation, we can see that the slope, m = [tex]$ \frac{\textbf{-2}}{\textbf{3}} $[/tex].

Hence, the answer.

Answer: She purchased 8 sports drinks,

Step-by-step explanation:

Let be "d" the number of sports drinks that April purchased and "p" the number of slices of pizza that April purchased.

Set up a System of equations:

[tex]\left \{ {{d=p+3} \atop {2.25p+1.25d=21.25}} \right.[/tex]

In order to solve the System of equations you can use the Substitution Method:

1. Solve for "p" from the first equation:

[tex]d=p+3\\\\p=d-3[/tex]

2. Substitute it into the second equation:

[tex]2.25(d-3)+1.25d=21.25[/tex]

3. Finally, you must solve for "d" in order to find its value. You get that this is:

[tex]2.25(d-3)+1.25d=21.25\\\\2.25d-6.75+1.25d=21.25\\\\3.5d=21.25+6.75\\\\d=\frac{28}{3.5} \\\\d=8[/tex]

Answer:

Step-by-step explanation:

8 sport drinks

Answer: 4)

Step-by-step explanation:

Answer:

1st one is 3, 2nd is 4

Step-by-step explanation:

Answer:

$7

Step-by-step explanation:$1.50 + $2.50 will equal to $4. $4 added with$3 would be $7. There's your answer

Answer:

This is Equivalence system of equations. The first equation in B is the sum of the equations in A, while the other is obtained by multiplying the first equation in A by 2

The result of the given expression 12 5/6x - 14x + 1/6x  is -x

Given the expression

12 5/6x - 14x + 1/6x

Convert the mixed fractions into improper fractions as shown:

[tex]\frac{77}{6}x - 14x + \frac{1}{6}x[/tex]

Collect the like terms;

[tex]= \frac{77}{6} x+\frac{1}{6}x - 14x\\= \frac{77x+x}{6} - 14x\\= \frac{78x}{6} - 14x\\= 13x - 14x\\= -x[/tex]

Hence the result of the given expression is -x

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The simplified form of the expression is -x .

Given, expression [tex]12\frac{5}{6}x -14x + \frac{1}{6} x[/tex] .

Expression:  [tex]12\frac{5}{6}x -14x + \frac{1}{6} x[/tex]

Firstly solve the mixed fraction.

[tex]12\frac{5}{6} x\\= \frac{77}{6}x[/tex]

Rewriting the expression :

= [tex]\frac{77}{6}x - 14x + \frac{1}{6}x[/tex]

Solve the terms with common denominator.

= [tex]\frac{77+1}{6} x[/tex]

= [tex]13x[/tex]

Solve the like terms,

[tex]= 13x - 14x\\\\=- x[/tex]

Hence the simplified form of expression is -x .

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