Create two one-step equations and explain how to solve them.

Answer:

Step-by-step explanation:

Answer:

The yield is 5.974%

Step-by-step explanation:

We proceed as follows ;

coupon rate = Annual coupon payment/bond face value.

The face value is the original amount which the bond was bought and that is $515 according to the question. While the coupon rate is 5.8%

mathematically, annual coupon payment = coupon rate * bond face value = 0.058 * 515 = $29.87

mathematically;

current yield = Annual coupon payment/bond price

current yield = 29.87/500

= 0.05974 or simply 5.974%

so the answer is c. 5.6%

Step-by-step explanation:

Answer:

A 6.0%

Step-by-step explanation:

coupon rate = Annual coupon payment/bond face value.

The face value is the original amount which the bond was bought and that is $515 according to the question. While the coupon rate is 5.8%

mathematically, annual coupon payment = coupon rate * bond face value = 0.058 * 515 = $29.87

mathematically;

current yield = Annual coupon payment/bond price

current yield = 29.87/500

= 0.05974 or simply 5.974%

5.974 rounded to 6.0 %

Answer:

3

Step-by-step explanation:

Work backwards in this problem:

(x+1)(x+2)

x^2+x+2x+2

x^2+3x+2

b=3

Answer: The answer is standard.

Step-by-step explanation: The equation for standard is ax+by+c.

Answer:

Standard Form

Step-by-step explanation:

Standard form:

ax+by=c

hope this helped and pls brainliest!

a) Factor 9x² + y² + z² - 6xy + 2yz - 6xz

This looks a lot like

(x+y+z)² = x² + y² + z²+ 2xy + 2yz + 2xz

except instead of x there's (-3x).   So this must be

(-3x+y+z)² = (-3x)² + y² + z² + 2((-3x)y + (-3x)z + yz)

= 9x² + y² + z² - 6xy + 2yz - 6xz

Looks good.

Answer: (-3x+y+z)²

Since it's a square we could also negate the inside and write this (3x-y-z)²

b) I'll guess that says we want to evaluate this when x=1, y=2, z= -1

(-3(1) + 2 -1)² = (-2)² = 4

Answer: 4

Answer:

1. 4 days

2. $1.2

3. 1 and 3 gallons

4. 15 and 10

16. 1.2 mi/h

-- Please refer to graph

-- Please refer to graph

Step-by-step explanation:

Solution 1.

Alex has $40, and Ellen has $24. Alex is saving $6 per day, and Ellen is saving $10 day.

Let x be the number of days in which they both have same money:

As per given statement:

[tex]40 + 6x=24+10x\\\Rightarrow 4x = 16\\\Rightarrow x =4[/tex]

In 4 days, they will have same money.

Solution 2:

Kendra owns a restaurant. She charges $6.00 for two eggs and one piece of toast and $3.60 for one egg and one piece of toast.

Let x be the price of one egg.

Let y be the price of one toast.

As per given statement:

[tex]2x+y=6 ...... (1)\\x+y= 3.6 ...... (2)[/tex]

Subtracting (2) from (1):

[tex]\Rightarrow x = \$2.4[/tex]

Price of toast = 3.6 - 2.4 = $1.2

Solution 3:

A restaurant has one type of lemonade that is 30% sugar and another that is 10% sugar. Resultant mixture 4 gallons of 15% sugar.

Let x be the amount of lemonade with 30% sugar.

Amount of another lemonade with 10% sugar = (4-x)

As per question statement:

[tex]x \times 30\% + (4-x) \times 10\% = 4 \times 15\%\\\Rightarrow x \times 30 + (4-x) \times 10 = 4 \times 15\\\Rightarrow 20x = 20\\\Rightarrow x = 1[/tex]

Lemonade with 30% sugar required is 1 gallon.

Lemonade with 10% sugar required is 3 gallons.

Solution 4:

A scientist has a container of 2% acid solution and a container of 5% acid solution. Resultant mixture is 25 fl oz of 3.2%.

Let x be the amount of 2% acid solution.

Amount of another lemonade with 5% acid solution = (25-x)

As per given question statement:

[tex]2\%\ of\ x + 5\% \ of\ (25-x) = 3.2\%\ of\ 25\\\Rightarrow 2x + 5(25-x)=3.2 \times 25\\\Rightarrow -3x = -1.8 \times 25\\\Rightarrow x = 15[/tex]

2% acid solution required is 15 fl oz.

5% acid solution required is 10 fl oz.

Solution 16:

Let v be the speed of river current.

Let u be the speed of kayaker.

As per question:

The speed of a kayaker is 5.75 mi/h paddling with the river current and 3.25 mi/h paddling against it.

[tex]u +v=5.75......(1)\\u-v = 3.25.....(2)[/tex]

Equation (1) - (2):

[tex]2v = 2.5\\\Rightarrow v = 1.25\ mi/h[/tex]

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

Susan make $12 per hour babysitting and $24 per hour as a lifeguard. Her goal is to make at least $420.

Let x be the number of hours for babysitting.

Let y be the number of hours as lifeguard.

As per given statement:

[tex]12x+24y > 240[/tex]

Please refer to graph attached with file name: Inequality

Three possible solutions:  (20,20), (21,21) and (22,22)

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

25. Joe wants to fence a rectangular pen for his goats. The length of the pen should be at least 40 ft, and the distance around should be no more than 150 ft

Let x be length

and y be width.

As per statement:

x > 40

And perimeter should be less than equal to 240.

2(x+y) [tex]\leq[/tex] 240

Please refer to attached graph with name: "2EquationInq"

Possible dimensions of pen can be (50,20).

Answer:

The base of the rhombus is equal to 9 centimeters.

Step-by-step explanation:

To calculate the base of the rhombus, we will follow the steps below;

write the formula for calculating the area of a rhombus

area of a rhombus = b × h

where h is the height of the rhombus and b is the base of the rhombus

From the question given,  area of the rhombus = 72 square centimeters   and height of the rhombus is 8 centimeters.

we can now proceed to insert the values into the formula and then solve for b

area of a rhombus = b × h

                72          = b × 8

Divide both-side of the equation by 8

[tex]\frac{72}{8}[/tex]  =  b × 8 /8

[tex]\frac{72}{8}[/tex]   =   b

9 = b

b = 9 centimeters

The base of the rhombus is equal to 9 centimeters.

Answer:

1) x=5 so angles are 25°, 80° and 75°

Step-by-step explanation:

The angles of a triangle should add up to 180. So e.g., for the first one, you know that

5x + 16x + 15x = 180

so

36x = 180

x = 5

Answer:

4

Step-by-step explanation:

I, m

Answer:

2/5

Step-by-step explanation:

make it reciprocal

2x/5 = 4/25

cross multiply the numbers

2x × 25 = 4×5

2x= 20/25

2x= 4/5

x = 2/5

Answer:

About 5 if your are including 6, or just 3.

Step-by-step explanation:

To find it you can just count the numbers greater than 6.

Hope this helps.

brainliest if correct

Answer:

3 Students

Step-by-step explanation:

There is only two more slots for how many candy bars each student has, in the "7" slot there is only one student that has seven candy bars and in the "8" slot there is two students that had eight candy bars.

1+2=3

I hope that helped.

Answer:

Step-by-step explanation:

I belive it is a .

Answer:

x = 2.99

Step-by-step explanation:

We can use ratios to solve

5.4            2.6

--------- = ---------

6.21         x

Using cross products

5.4x = 2.6* 6.21

5.4x =16.146

Divide each side by 5.4

5.4x = 16.146/5.4

x = 2.99

Answer:

Step-by-step explanation:

(200+30+5)(40+9)

40*200 = 8000

40*30=   1200

40*5=200

9*200= 1800

9*30=270

9*5=45

8000+1200+200+1800+270+45 =11515

The multiplication of 235 and 49 is 11515 and partial products are 8000, 1800, 1200, 270, 200, and 45.

Given that,

Multiply the numbers 235 by 49.

We have to find,

What will the partial products?

According to the question,

To determine the partial products of the given numbers following all the steps given below.

Multiplication of the numbers; 235 by 49,

           [tex]= 235 \times 49\\\\= (200+35+5) \times (40+9)\\\\[/tex]

           [tex]= (200+35+5) \times (40+9)\\\\= 200(40+9) + 35(40+9) + 5 (40+ 9)[/tex]

           [tex]= 200(40+9) + 30(40+9) + 5 (40+ 9)\\\\ = 200 \times 40 + 200 \times 9 + 30 \times 40 +30 \times 9 + 5 \times 40 + 9 \times 5\\\\= 8000 + 1800 + 1200+ 270+ 200 + 45 \\\\= 11515[/tex]

Hence, The multiplication of 235 and 49 is 11515 and partial products are 8000, 1800, 1200, 270, 200, and 45.

To know more about Partial products click the link given below.

https://brainly.com/question/16505829

Answer:

[tex]A = \dfrac{C^2}{4\pi}[/tex]

Step-by-step explanation:

Given that

Area of a circle [tex]A=\pi r^2[/tex]

Circumference of the circle [tex]C = 2 \pi r[/tex]

Let us re-write the equation of area of circle:

[tex]A=\pi r^2[/tex]

[tex]A = \pi \times r \times r[/tex]

Multiplying and dividing with 2:

[tex]A = \dfrac{2\pi r}{2} \times r\\\text{Putting }2\pi r = C:\\\Rightarrow A = \dfrac{C}{2} \times r\\\text{Multiplying and dividing by } 2\pi:\\\Rightarrow A = \dfrac{C}{2} \times \dfrac{2\pi r}{2\pi}\\\text{Putting }2\pi r = C:\\\Rightarrow A = \dfrac{C \times C}{4 \pi}\\\Rightarrow A = \dfrac{C^2}{4 \pi}[/tex]

Hence, A in terms of C can be represented as:

[tex]A = \dfrac{C^2}{4\pi}[/tex]

Start by setting up a factor tree for each number.

Factor in anyway that you'd like.

At the end, circle all prime numbers.

Remember, prime numbers are numbers

with only 2 factors, 1 and the number itself.

Now write these factors in least to greatest

multiplying them separate rows.

Circle factors they have in common.

Since 3 pairs of two's match up, multiply by 2 three times to get 8.

So the GCF is 8.

Answer:

8

Step-by-step explanation:

3 multiplied by 8 = 24

and 4 multiplied by 8 = 32

Answer:

The answer is C

Step-by-step explanation:

By using the quadratic formula, you get

a=1

b=5

c=7

so, when you substitute, you get:

-5±√5²-4(2)(7)

____________

2(1)

The next step is solving the square root and multiplying

Answer:

The area of the square is 9 cm squared

Step-by-step explanation:

I know this because the formula for a square is s squared in which s represents sides so if i substitude the known value in i would get the answer of 9 cm squared.

Solution,

Length=3m

Area of square=(l)^2

=(3)^2

=3*3

=9m^2

hope it helps

Good luck on your assignment

Answer:

[tex]1.6744809109 *10^{75}[/tex] Earths

Step-by-step explanation:

To find how many Earths are needed, take 1 googol divided by Earth's mass

[tex]\frac{\left1\times10^{100}\right}{5.972\times10^{24}}[/tex]       Divide

[tex]1.6744809109 *10^{75}[/tex] Earths are needed to have a total mass of 1 googol kilograms.

Answer:

x = 2

Step-by-step explanation:

h(x) = f(x) + g(x) = x³ + 2x² + 1 - x³ - x² - 4x + 4 ← collect like terms, thus

h(x) = f(x) + g(x) = x² - 4x + 5

Given

h(x) = 1, then

x² - 4x + 5 = 1 ( subtract 1 from both sides )

x² - 4x + 4 = 0 ← in standard form

(x - 2)² = 0 ← in factored form ( perfect square ), thus

x - 2 = 0 ⇒ x = 2

Answer:

Hope it helps

Good luck on your assignment

Answer:

Angle A: 40°

Angle B: 50°

Angle C: 90°

Side A: 14

Side B: 12

Side C: 11.2 or 11 if you round to the nearest whole number.

Step-by-step explanation:

Angle A;

Since we know angles B and C we can use those to help us find angle since all three angles should add up to 180°.

90-50=40

Angle A= 40°

Side C;

Since we know all the angles now and the other two side lengths, we will use those to help us find Side C.

cos 40°= C/14

C/14= cos 40°

C/14=  .8

C= .8 x 14

C= 11.2

Hope this helps! Have a great day! :)

Answer:

C

Step-by-step explanation:

4y=32

Taking 4 to the other side

y=32/4

y=8

Answer:

c

Step-by-step explanation:

c

Answer:

(-6,-4)

Step-by-step explanation:

Hope this helps! (:

Answer:

[tex]\sqrt[/tex]y+5x=k

Step-by-step explanation:

y=x^2-6x+k

y+6x=x^2+k

[tex]\sqrt[/tex]y+6x=x+k

[tex]\sqrt[/tex]y+5x=k

Answer:

x = 40

Step-by-step explanation:

The answer is x = 40. This is because the two angles that are x are 1. congruent and 2. supplementary with 100° (They all add up to 180°). I can show this with a simple equation.

1. 2x + 100 = 180

2. 2x = 80

3. x = 40

Hope this helps! (Please consider giving brainliest)

Answer:

304,305,306

Step-by-step explanation:

x +x+1+x+2=915

3x+3=915

3x=915-3

3x=912

x=304

The three consecutive integers are 304, 305 and 306, option D is correct.

A number system is defined as a system of writing to express numbers.

Let the three consecutive numbers be x, x+1 and x+2

Sum of three consecutive integers is 915.

x+x+1+x+2=915

3x+3=915

Subtract 3 on both sides

3x=912

Divide both sides by 3

x=304

Hence, the three consecutive integers are 304, 305 and 306, option D is correct.

To learn more on Number system click:

https://brainly.com/question/22046046

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Answer:

We can use the trigonmetry to solve for this. So first, we need to get that cos(69) = x/16. So then we multiply by 16 and get 16cos(69). Therefore if we use that as an answer approx it gives 5.734.

Answer:

-3

Step-by-step explanation:

The given equation is in slope intercept form.

The form is y=mx+b

This is where "m" is the slope, and "b" is the y intercept.

So in this equation, m=-3.

Therefore, the slope is -3.

Answer:

it is a slope intercept form