Utilize graphing to find the solution to
the following system of equations.
y = 2x 1 AND y = x - 3
-
([?], [])

Answer:

Step-by-step explanation:

Remark

A good thing to understand is that when a whole number and a fraction are multiplied, the method is the same as multiplying 2 fractions. What that means is make the whole number into the numerator of a fraction and put a 1 where the denominator should be.

Solution

4/1 * 2/3 = 4*2 / 1 * 3 = 8/3

A) If the current market interest rate is 6.5%, you should not buy the bond because the present value of the bond is $905.97, which is less than the current price of $940.

B) Assuming you buy and hold this bond for 5 years, the price you must sell the bond to earn a 7% rate of return on this investment is $938.50.

The price of a bond can be determined by calculating the present value of the cash flows till maturity through discounting.

The present value can be computed using the present value formula or table.  It can also be determined using an online finance calculator as follows:

a. If the current market interest rate is 6.5%. Should you buy the bond? Why or why not?

N (# of periods) = 15 years

I/Y (Interest per year) = 6.5%

Coupon interest rate = 5.5%

PMT (Periodic Payment) = $55

FV (Future Value) = $1,000

Results:

PV = $905.97

Sum of all periodic payments = $825 ($55 x 15)

Total Interest = $919.03

b. Assuming you buy and hold this bond for 5 years. What price must you sell the bond for if you want to earn a 7% rate of return on this investment?

N (# of periods) = 5 years

I/Y (Desired Interest per year) = 7%

Coupon interest rate = 5.5%

PMT (Periodic Payment) = $55

FV (Future Value) = $1,000

Results:

PV = $938.50

Sum of all periodic payments = $275 ($55 x 5)

Total Interest = $336.50

Learn more about calculating the present values at https://brainly.com/question/20813161

Answer:a minimum of 15 weeks to about 30 weeks.

Step-by-step explanation:

Step-by-step explanation:

In the given figure,

Base(b)= 6cm

Height (h)= 8 cm

We know that,

[tex]area \: of \: a \: triangle \\ = \frac{1}{2} \times b \times h \\ = \frac{1}{2} \times 6 \times 8 \\ = \frac{48}{2} \\ = 24 \: cm ^{2} [/tex]

Hence, the are of the given figure is 24 cm².

Answer:

Good morning! Number of trials are 250.

Step-by-step explanation:

A researcher finds 50% of all commuters in a metropolitan area take the train to work.

The researcher polls 250 people in the area to ask them whether they take the train to work or not.

We have tell the number of trials for this binomial experiment.

Researcher will do 250 trials to confirm whether they take the train work and this irrespective of their response.

_AnnieTheDreamGirl, 3/8/2022

Answer:

7.75 is the the correct answer

Answer:

c. The solution to a system of equations is the point or points where they intersect

Answer:

(B) 0.9688

Step-by-step explanation:

mark me brainliest!!

Answer:

this expression is true for all values of a.

Step-by-step explanation:

So if the expression is:

a - 5 = 5 - a

For this reason:

2a = 10

a = 5

a - 5 = -5 + a

0 = 0

Answer:

x = 2•sqroot(5)

x ~= 4.47

Step-by-step explanation:

Draw a line to make the "top" part be a

4 × 3 rectangle. see image.

Then you will have a right triangle on the bottom. It has legs 2 and 4 units long. Use the Pythagorean theorem to solve for x. see image.

Answer:

4.5

Step-by-step explanation:

Answer:

49 ft.

Step-by-step explanation:

Since the figure is a rectangle, the length of the top of the figure is the same as that of the bottom. Thus, we can form an equation which we can later use to find the value of x.

4x +3= 16

Minus 3 on both sides:

4x= 16 -3

4x= 13

Divide by 4 on both sides:

x= 13 ÷4

x= 3.25

Breadth of rectangle

= 2x +2

= 2(3.25) +2

= 6.5 +2

= 8.5

Perimeter of rectangle

= 2(length +breadth)

= 2(16 +8.5)

= 2(24.5)

= 49 ft.

Answer:

The numbers that are greater than - 2 qnd less than 3 are:

-1,0,1&2

Answer:

Percentage of Money Zack receives =

[tex]\bold{\frac{the \:share \:he\: gets \:in\: ratio \:form}{Total \:share \:in\: ratio \:form} \times 100}\\[/tex]

[tex] \bold{\frac{9}{11 + 9} \times 100} \\ \\\bold{ ⇢ \frac{9}{\cancel{20}} \times\cancel{ 100} }\\ \\ \bold\blue{ ⇢ 45\%}[/tex]

hope helpful~

Step-by-step explanation:

we want to find the hypotenuse

soh cah toa

he have hypotenuse and opposite

soh

sin 20 = H/4

can u do the rest and put answer in comments please mark brainest

Answer:

HJ

Step-by-step explanation:

For a line to be perpendicular to another line, you must find the negative reciprocal.

The negative reciprocal of 1/2 is -2.

The only line with a slope of -2 is line HJ because it goes down 2 for every 1 to the right.

Answer:

line HJ on edge

Step-by-step explanation:

The significance level shows that z approximately equals 1.41 for a p-value of 0.078642.

Based on the complete question, the sample proportion for city A will be:

= 54/90 = 0.60

The sample proportion for city B will be:

= 63/90 = 0.70

Using the table given, it can be deduced that the test statistic value will be 1.41. Therefore, the p-value will be 0.078652 in the Excel function.

Since the p-value is greater than 0.05, then we fail to reject the null hypothesis that there is no difference in the commute time.

Learn more about significance level on:

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The distance from building A to building C is 433m

Therefore,

sin 60° = opposite / hypotenuse

sin 60° = b / 500

cross multiply

b = 500 sin 60°

b = 500 × 0.86602540378

b = 433.0127

b = 433 meters

learn more on right angle triangle here: https://brainly.com/question/20795478

[tex]\frac{1}{2}[/tex] of the water takes [tex]\frac{1}{2}[/tex] of the fuel and empty tank takes [tex]\frac{1}{6}[/tex] of the fuel, the

fraction that would will be spent if there was no leak is [tex]\underline{\dfrac{11}{18}}[/tex] of the fuel

The given parameters are;

The volume of oil consumed = [tex]\mathbf{\dfrac{1}{2}}[/tex] of the fuel tank

Volume consumed if the water tank was empty = [tex]\dfrac{1}{6}[/tex] of the fuel tank

Let w represent the weight of the water that fills the tank.

Therefore;

[tex]The \ average \ weight \ carried \ by \ oil = \dfrac{w + \dfrac{w}{2} }{2} = \mathbf{\dfrac{3 \cdot w}{4}}[/tex]

The amount of fuel consumed by the water that leaked = [tex]\dfrac{1}{2} - \dfrac{1}{6} = \dfrac{1}{3}[/tex]

Let x represent the amount of oil used to carry only the water if there

was no leak, therefore;

[tex]\mathbf{\dfrac{\frac{3 \cdot w}{4} }{w} }= \dfrac{\frac{1}{3} }{x}[/tex]

Which gives;

[tex]\mathbf{\dfrac{3 \cdot w}{4} \times x}} = \dfrac{1}{3} \times w }[/tex]

[tex]x = \dfrac{4}{3 \times 3} = \dfrac{4}{9}[/tex]

The total amount of fuel that will be consumed without leakage is

therefore;

[tex]Total \ amount \ of \ fuel = \dfrac{4}{9} + \dfrac{1}{6} = \mathbf{ \dfrac{11}{18}}[/tex]

The amount of oil consumed if there was no leakage is therefore;

Learn more about averages here;

https://brainly.com/question/24398353

Answer: 285.7L

Step-by-step explanation:

Tank initially had 500L of water.

On Monday a third leaked out, therefore:

Amount of water that leaked = 500L x 1/3 = 166.6667 = 166.7L

Remaining water after Monday leak = 500-166.7 = 333.3333 = 333.3L

On Tuesday a seventh of the remaining water (333.3L) leaked out, therefore:

Amount of water that leaked: (333.3333) x 1/7 = 47.6190 =47.6L

Water left after both leaks =500L - (166.6667 + 47.6190)L = 500L - 214.2857L = 285.7143L = 285.7L.

OR Water left = 333.3333L - 47.6190L = 285.7143L = 285.7L

Answer:

# of reserved seats = R;  # of general admission seats = G

                                                    G - R = 85

                                         $18R + $9G =$3600

Multiply 1st equation by 18:  18G - 18R = 1530

Rearrange 2nd equation:   $9G + $18R =$3600

Combine the equations:               27 G  =   5130

                                                       G  =  190

                                                       R  =  105

Step-by-step explanation:

Answer:

(x - 2)² + (y - 2)² = 4

Step-by-step explanation:

The circle is tangent to both axes, so the radius = x = y

Center is on 2x + 3y = 0, so 2x + 3x = 1-

x = 2 = y

center: (2, 2)

radius = 2

equation: (x - 2)² + (y - 2)² = 2²

(x - 2)² + (y - 2)² = 4

Answer:

Mary climbed higher

Step-by-step explanation:

think of it like this a wall is four feet and you climb 3 feet up. You are closer to the top than if you climbed 3 feet up a 8 wall.

Answer:

  B. X=0.02

Step-by-step explanation:

The solution to the natural log equation is found by taking antilogs.

  ln(x) = -4 . . . . . . . given equation

  x = e^-4 . . . . . . . take antilogs

  x ≈ 0.0183156

  x ≈ 0.02 . . . . rounded to 2 decimal places

_____

Additional comment

Essentially, we use each side of the equation as a power of e.

  e^ln(x) = e^(-4)

  x = e^-4 . . . . . . . simplified

Choices C and D can be eliminated by the fact that ln(x) for x < 0 is undefined. x cannot be negative.

Answer: 25%

Step-by-step explanation:

As you can see 8/32 simplified would be 1/4 which would be 1/4 and 1/4 is equal to 25%!

Answer:

You started with 32.00

Step-by-step explanation:

47 minus 15 is 32

Answer:

X=48

Step-by-step explanation:

100 = 2x+4

100-4 = 2x

96 = 2x

96/2 = x

x = 48

Answer:

  c║d by Converse of Corresponding Angles postulate

Step-by-step explanation:

Line 'a' is not shown as having any relationship to anything. It can be removed from the picture, and all answer choices involving line 'a' can be ignored.

Line 'b' crosses two lines (c and d), so can be considered their transversal. The marked angles are not all between c and d, nor are they all outside of c and d, so they are neither "interior" nor "exterior." Eliminating the obviously incorrect choices leaves only c║d and the choice of the Corresponding Angles postulate or its Converse.

The Corresponding Angles postulate tells you that corresponding angles are congruent where a transversal crosses parallel lines. Its Converse tells you the lines are parallel if the corresponding angles are congruent. Here, we're given angles and asked about the lines being parallel. Clearly, the applicable postulate is ...

  c║d by Converse of Corresponding Angles Postulate

Answer:

$41 cents

Step-by-step explanation:

$8 divided by $3.35 equals $0.41 cents

[tex]\underline{\underline{\large\bf{Given:-}}}[/tex]

[tex]\red{\leadsto}\:[/tex][tex]\textsf{} [/tex][tex]\sf Endpoints \:of \: line \: segment \:are \:(-8,7) [/tex]

[tex]\sf and \:(6,4) [/tex]

[tex]\underline{\underline{\large\bf{To Find:-}}}[/tex]

[tex]\orange{\leadsto}\:[/tex][tex]\textsf{Length of the line} [/tex][tex]\sf [/tex]

[tex]\\[/tex]

[tex]\underline{\underline{\large\bf{Solution:-}}}\\[/tex]

>>Let us consider these points on a line segment AB such that point A and B lies on opposite ends

[tex] \\A( - 8,7) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: B(6,4)\\ \bull \frac{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{} \bull \\[/tex]

We will find distance between points by distance formula-

[tex]\red{\underline{\boxed{\sf{Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}}}}[/tex]

Here-

Putting Values:-

[tex]\begin{gathered}\\\longrightarrow\quad \sf AB = \sqrt{(6 - (-8)) ^{2} + (4-7) ^{2} } \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\longrightarrow\quad \sf \sqrt{(6+8)^2 + (-3)^2} \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\longrightarrow\quad \sf \sqrt{14^2+ (-3)^2 } \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\longrightarrow\quad \sf \sqrt{196+ 9 } \\\end{gathered} [/tex]

[tex]\begin{gathered}\\\longrightarrow\quad \sf \sqrt{205} \\\end{gathered} [/tex]

[tex]\longrightarrow \sf length \:of \: the \: line \:segment \:whose \: \: [/tex]

[tex]\sf endpoints \;are \: (-8,7) \:and \:(6,4) \:is \: \sqrt{205} \;units [/tex]