Assume x > 0 and y 0.

algebra II engenuity

Answer:

(x-3)^2 + (y-1)^2 = 4

Step-by-step explanation:

The equation of a circle is usually written in the form

(x-h)^2 + (y-k)^2 = r^2

Where (h,k) is the center and r is the radius

The center is at the origin so (h,k) = (3,1) and  the radius is 2 so r=2

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

(x-3)^2 + (y-1)^2 = 4

Answer:

it's d or the fourth option

Step-by-step explanation:

Answer:

20 inch

Step-by-step explanation:

Diameter, D = 6.5in

Circumference

= π x D

= 3.142 x 6.5

= 20.42

= 20 in (rounded to nearest in)

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

Here are some reasons why

Answer:

d = 7.5t

Step-by-step explanation:

t = time

d= distance

you want to write an equation that compares time with distance.

in the question it says per hour whoch means 7.5 miles have been ran each hour. however we dont know how mmany hour lets say tom has ran. therefore, we use t instead. we got d to go behind the = sign because we are comparing. When we multiply 7.5t we are going to get the distance he ran, d.

hope this helps!

Answer:

d=7.5t

Step-by-step explanation:

Answer:

no solutions

Step-by-step explanation:

4x + 2y = –14

6x + 3y = –22

Divide the first equation by 2 and the second equation by 3

4x/2 + 2y/2 = –14/2     2x +y = -7

6x/3 + 3y/3 = –22/3    2x + y = -22/3

The left hand sides are the same but the right hand sides are different.

Multiply the second equation by -1

2x+y = -7

-2x -y = 22/3

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

0 = -7+22/3

0 = 1/3

This is never true, so there are no solutions

Answer:

B, No Solutions

Step-by-step explanation:

Answer:

25. The area of the trapezoid is 96 cm² ⇒ 2nd answer

26. The area of the kite is 40.8 feet² ⇒ 3rd answer

31. The area of the circle is 6.0025π m² ⇒ 3rd answer

Step-by-step explanation:

* Lets solve the problems

25. The figure is trapezoid

- The trapezoid has two parallel bases base 1 and base 2

- The area of the trapezoid is 1/2(base 1 + base 2) × height

- The length of base 1 is 12 cm

- The length of its height is 6 cm

- The length of the base 2 is (2 + 12 + the adjacent side to ∠45°)

- To find the missing part in the base 2 use the trigonometry

  function tan 45° = opposite/adjacent

∵ tan 45° = opposite/adjacent

∵ The opposite = 6

∵ tan 45° = 1

∴ 1 = 6/adjacent ⇒ by using cross multiplication

∴ The adjacent = 6 cm

∴ The length of base 2 = 2 + 12 + 6 = 20 cm

∵ The area of the trapezoid is 1/2(base 1 + base 2) × height

∵ The length of base 1 = 12 cm

∵ The length of base 2 = 20 cm

∵ The length of its height = 6 cm

∴ The area = 1/2(12 + 20) × 6 = 1/2(32) × 6 = 16 × 6 = 96 cm²

* The area of the trapezoid is 96 cm²

26. The figure is kite

- The kite has two diagonals

- Its diagonals perpendicular to each other

- The longest diagonal bisects the shortest diagonal

- The area of the kite is 1/2(diagonal 1 × diagonal 2)

∵ The length of diagonal 1 = 10.2 feet

∵ The length of diagonal 2 = 8 feet

∵ The area of the kite = 1/2(diagonal 1 × diagonal 2)

∴ The area = 1/2(10.2 × 8) = 1/2(81.6) = 40.8 feet²

* The area of the kite is 40.8 feet²

31. The figure is a circle

- The circle has diameter

- The radius is half the diameter

- The area of the circle is π r²

∵ The length of the diameter = 4.9 m

∵ The length of the radius 1/2 the length of the diameter

∴ The length of the radius = 1/2 (4.9) = 2.45 m

∵ The area of the circle = π r²

∴ The area = π (2.45)² = 6.0025π m²

* The area of the circle is 6.0025π m²

Answer:

25) 96 cm²

26)  40.8 ft ²

31).  6.0025π m²

Step-by-step explanation:

25) To find the area of trapezoid

Area of trapezoid = h(a + b)/2

Here a = 6 + 12 + 2 = 20 cm

b = 12 cm and h = 6

Area =  h(a + b)/2

 = 6(20 + 12)/2

 = 96 cm²

26) To find the area of kite

Area of kite = pq/2

Where p and q are the two diagonals

Here p = 10.2 ft and q = 8 ft

Area = pq/2

 = (10.2 * 8)/2 = 40.8 ft²

31) To find the area of circle

Area of circle = πr²

Here r = 4.9/2 = 2.45 m

Area = πr²    

 = π *(2.45)²

 = 6.0025π m²

Answer:

See below in BOLD.

Step-by-step explanation:

y = -3x 2 + 18x - 2

y = -3(x^2 - 6x) - 2

y = -3 [ (x - 3)^2 - 9] - 2

y = -3(x - 3)^2  + 25  is vertex form.

The  coefficient of x^2 is negative so we have a maximum  value of the function.

The maximum value is 25 and the axis of symmetry is x = 3.

Answer: The maximum value is 25 and the axis of symmetry is x = 3.

Answer:

Step-by-step explanation:

Rewrite 2x-5y< 15 as follows:  Add 5y to both sides.  Then 2x < 15 + 5y.

Next, subtract 15 from both sides:  2x - 15 < 5y.

Finally, divide all terms by 5:           (2/5)x - 3 < y

Now find the y-intercept of this line.  Let x = 0.  Then y = -3.  Plot (0, -3) on graph paper.  Now, starting at (0, -3), move your pencil point 5 spaces to the right and 2 spaces up.  Plot this new point, (5, -1).  Now draw a dashed line through both (0, -3) and (5, -1).  Shade the area ABOVE this dashed line.

Answer:

is op 4 (-3,7)

Step-by-step explanation:

Answer:

x = 5 or 25

Step-by-step explanation:

I think the method I am about to explain is slightly quicker and easier than the method in your question. This works for any 'complete the square' question.

We begin with x² - 30x = - 125.

First, we are going to factorise the left-hand side of the equation by dividing the 'b' value (-30) by 2 (you'll see why this works in a minute):

(x - 15)²

We want these brackets to multiply out to give x² - 30x, so that they equal the left-hand side of the equation. Unfortunately, if we multiply them out, we get:

(x - 15)(x - 15) =

x² - 30x + 225

There is an unwanted term (the + 225, from 15²)! We only want x² - 30x, so we have to remove this term by subtracting it from the left side of the equation. To do this, let's set up the original equation again:

(x² - 30x + 225) - 225 = - 125

Note: The reason why we don't have to subtract it from both sides is because the original equation is x² - 30x = - 125, and so we must make sure the left hand side is still equal to x² - 30x.

So now we know that (x - 15)² multiplies out to give x² - 30x +225, we can write this as (x - 15)² in our equation:

(x² - 30x + 225) - 225 = - 125

is the same as:

(x - 15)² - 225 = - 125

Now add 225 to both sides of the equation:

(x - 15)² = - 125 + 225 = 100

(x -15)² = 100

The next step is to square root both sides. Be careful here, and remember that √100 can either be 10 or -10, as (-10)² = 100. To indicate both results, write ±10 ("plus or minus 10").

√(x - 15)² = √100

x - 15 = ±10

Because, there are two possible values for the right-hand side of the equation, we need to separate our equation into two equations:

1.     x - 15 = 10

and

2.    x - 15 = -10

Now we solve these two simple linear equations for x:

1.     x = 10 + 15   <- add 15 to both sides

        x = 25 This is our first solution.

2.    x = -10 + 15  <- add 15 to both sides again

        x = 5 This is our other solution.

So our two solutions are x = 5 and x = 25!

I have attached the quick version of the working out for this question - that is what you would be expected to write down in a test.

x = 5 or 25

We begin with x² - 30x = - 125.

First, we are going to factorise the left-hand side (LHS) of the equation by dividing the 'b' value (-30) by 2 (you'll see why this works in a minute):

(x - 15)²

We need these brackets to multiply out the give x² - 30x, so that they = the left-hand side (LHS) of the equation. Unfortunately, if we multiply them out, we get:

(x - 15)(x - 15) =

x² - 30x + 225

There are an unwanted term (the + 225, from 15²)! We only need x² - 30x, so we have to remove this term by subtracting this from the left side of the equation. To do this, let's set up the original equation again:

(x² - 30x + 225) - 225 = - 125

Note: The reason why we do not have to subtract this from both sides is because original equation is x² - 30x = - 125, and so we must make sure the left hand side is = to x² - 30x.

So now we know that (x - 15)² multiplies out to give x² - 30x +225, we can write this as (x - 15)² in our equation:

(x² - 30x + 225) - 225 = - 125

as the same as:

(x - 15)² - 225 = - 125

Now add 225 to both sides by the equation:

(x - 15)² = - 125 + 225 = 100

(x -15)² = 100

The next step is to square root by both sides. Be careful here, or remember that √100 can either be 10 or -10, as (-10)² = 100. To indicate both results, write ±10 ("plus or minus 10").

√(x - 15)² = √100

x - 15 = ±10

Because, there are 2possible values for the right-hand side of the equation, we need to separate this equation into 2 equations:

1.     x - 15 = 10

and

2.    x - 15 = -10

Now we have solve these two simple linear equations for x:

1.     x = 10 + 15   <- add 15 to both sides

       x = 25 This is our first solution.

2.    x = -10 + 15  <- add 15 to both sides again

       x = 5 This is our other answer.

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Answer:

11 animals

Explanation:

-Sparkles is the first animal that is introduced, then the monkey is the second. Since there are 18 eyes, that can be divided by 2 to tell you how many of the remaining animals there are. Which would lead up to 9 and 9+2=11

Eleven (11) Animals

Based on the above given information, it can be construed that that Eleven (11) animals are in the forest.

The first mentioned animal is Sparkles the Unicorn (Animal 1) who probably might be hungry and, might have searched through the forest to get the nice big juicy apple.

She might have dodged several wild predating animals just for luck to smile on her through the discovery of a big juice apple. She plucks it, and starts eating. A nearby lurking, cunning monkey (Animal 2), snatches the fruit from Sparkles the Unicorn, due to her carelessness, and as she proceed to retrieve the fruit, she discovered that that wasn’t the only monkey around. She sees eighteen (18) pairs of eyes which means, there are nine (9) other animals i.e. 18 pairs of eyes divided by 2 (18/2 = 9) are also in the forest.

Therefore:

Animal 1 + Animal 2 + 9 other Animals = 11 Animals

This kind of question can be said to be a Mathematical Puzzle.

Mathematical puzzle is a form of recreational mathematics, which helps to enhance students’ knowledge.

Mathematical puzzle helps students to understand different concepts of mathematical problems.

This form of mathematical improve students’ learning ability

KEYWORDS:

Check the picture below.

Also check your Unit Circle for the cosine of 30°, if you don't have a Unit Circle yet, this is a good time to get one, you'll need it, you can find many online.

Answer:

4 miles

Step-by-step explanation:

6 divided by 3 = 2 = one-third of 6

--> multiply by two to get two thirds of six = 4 miles

Answer:

4 miles

Step-by-step explanation:

The probability that she will sit at either end by a window is 2/5 or 0.4.

To solve this problem, we first need to determine the total number of places Sharon could sit and then identify which of those places meet the condition of being at either end by a window.

Since the back seat is the full width of the bus and seats five students, there are a total of 5 different places Sharon could choose to sit.

Now we need to identify the places that are at either end by a window. Since it's the back seat of the bus, there would typically be a window at the far left and the far right of the seat.

So, there are two seats that meet our condition:
- One on the far left
- One on the far right

This means out of the 5 available places, there are 2 places that fulfill the condition of Sharon sitting by a window at either end of the back seat.

The probability P that Sharon will sit by a window at either end is therefore the number of favorable outcomes (sitting by a window at either end) divided by the total number of possible outcomes (any of the 5 seats).

P = (Number of favorable outcomes) / (Total number of possible outcomes)
P = 2 / 5

Therefore, the probability that Sharon will sit at either end by a window is 2/5 or 0.4 (if expressed as a decimal).

Answer:

A

Step-by-step explanation:

Given

-4x²(5[tex]x^{4}[/tex] - 3x² + x - 2)

Multiply each term in the parenthesis by - 4x²

= - 20[tex]x^{6}[/tex] + 12[tex]x^{4}[/tex] - 4x³ + 8x²

Answer:

A

Step-by-step explanation:

Answer:

   √6 + √2

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

        4

Step-by-step explanation:

15° = 45° - 30°

So

cos(15)  = cos(45 - 30)

=cos(45)  × cos(30) + sin(45) × sin(30)

= 1/√2  × (√3)/2  + 1/√2 × 1/2

    (√3) + 1

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

     2√2

    (√3) + 1              √2

= -------------- x       ---------

     2√2                  √2

   √6 + √2

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

        4

Answer:

see explanation

Step-by-step explanation:

Using the addition formula for cosine

cos(x ± y) = cosxcosy ∓ sinxsiny

and exact values

sin45° = cos45° = [tex]\frac{\sqrt{2} }{2}[/tex]

c0s30° = [tex]\frac{\sqrt{3} }{2}[/tex] , sin30° = [tex]\frac{1}{2}[/tex]

Express cos15° = cos(45 - 30 )°, then

cos(45 - 30)°

= cos45°cos30° + sin45°sin30°

= [tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex] + ( [tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{1}{2}[/tex] )

= [tex]\frac{\sqrt{6} }{4}[/tex] + [tex]\frac{\sqrt{2} }{4}[/tex]

= [tex]\frac{\sqrt{6}+\sqrt{2}  }{4}[/tex] ← exact value

Answer:

The volume of the triangular prism is [tex]595\ units^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the triangular prism is equal to

[tex]V=BH[/tex]

where

B is the area of the base

H is the height of the prism

Find the area of the triangular base B

[tex]B=(1/2)bh[/tex]

substitute the given values

[tex]B=(1/2)(14)(17)=119\ units^{2}[/tex]

Find the volume

[tex]V=(119)(5)=595\ units^{3}[/tex]

For this case, we convert the mixed numbers to fractions:

Box 1: [tex]4 \frac {2} {3} = \frac {3 * 4 + 2} {3} = \frac {14} {3}[/tex]

Box 2: [tex]5 \frac {3} {8} = \frac {8 * 5 + 3} {8} = \frac {43} {8}[/tex]

We add the fractions to find the total weight of the boxes:

[tex]\frac {14} {3} + \frac {43} {8} = \frac {8 * 14 + 43 * 4} {3 * 8} = \frac {112 + 172} {24} = \frac {284 } {24} = \frac {142} {12} = \frac {71} {6}[/tex]

Thus, between the two boxes weigh[tex]\frac {71} {6}[/tex] ounces.

In mixed number: [tex]11 \frac {5} {6}[/tex]

Answer:

[tex]11 \frac {5} {6}[/tex]ounces

The total weight of the two boxes is 10 1/24 ounces, found by converting the mixed numbers into improper fractions, finding a common denominator, and adding the fractions together.

To find the total weight of two boxes when one weighs 4 2/3 ounces and the other weighs 5 3/8 ounces, we first convert the mixed numbers into improper fractions. For 4 2/3 ounces, this would be (4 × 3) + 2 = 14/3 ounces. For 5 3/8 ounces, it is (5 × 8) + 3 = 43/8 ounces. Once in improper fraction form, we find a common denominator, which is 24, and then we add the two fractions together.

The first box in twenty-fourths is (14/3) × (8/8) = 112/24. The second box is (43/8) × (3/3) = 129/24. Adding them gives us 112/24 + 129/24 = 241/24. We divide 241 by 24, which results in 10 with a remainder of 1, giving us 10 1/24 ounces.

Therefore, the total weight of the two boxes is 10 1/24 ounces.

Answer:

Answer: f[c(p)] = 0.9265p

Step-by-step explanation:

Given: Jonah is purchasing a car that is on sale for 15% off. He knows the function that represents the sale price of his car is , where p is the original price of the car.

He also knows he has to pay 9% sale's tax on the car. The price of the car with tax is , where c is the sale price of the car.

Now, the composite function that can be used to calculate the final price of Jonah's car is given by :-

Answer:

f[c(p)] = 0.9265p

Step-by-step explanation:

c(p) = 0.85p

f(c) = 1.09c

f[c(p)] = f[0.85p] = 1.09(0.85p) = 0.9265p

Answer: f[c(p)] = 0.9265p

[tex]\bf \begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array}~\hfill \begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{\textit{we'll use this one}}{a^{log_a x}=x} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf 2\ln(3)=\ln(x-4)\implies \ln(3^2)=\ln(x-4)\implies \ln(9)=\ln(x-4) \\\\\\ \log_e(9)=\log_e(x-4)\implies e^{\log_e(9)}=e^{\log_e(x-4)}\implies 9=x-4\implies \boxed{13=x}[/tex]

Answer:

79°

Step-by-step explanation:

given both figures are congruent, and one is simply a rotation of another

m∠B corresponds to m∠k = 79°

Answer:

Given that DMKT → FCBN, B is 79°

Step-by-step explanation:

m∠D = m∠F, m∠M = m∠C, m∠K = m∠B and m∠T = m∠N

m∠K = 79° therefore m∠B = 79°.

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Answer:

[tex]\large\boxed{D.\ 168\ units^2}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a volume of a prism:}\\\\V=BH\\\\B-base\ area\\H-height\\\\\text{In the base we have the right triangle.}\\\text{The formula of an area of a right triangle:}\ A=\dfrac{ab}{2}\\\\a,b-legs\\\\\text{We have}\ a=6\ \text{and}\ b=8.\ \text{Substitute:}\\\\B=\dfrac{(6)(8)}{2}=\dfrac{48}{2}=24\\\\\text{Calculate the volume:}\\H=7\\\\V=(24)(7)=168\ units^2[/tex]

To find the volume of a triangular prism, we have to multiply the area of the base by the heigh of the prism.

Let's first identify our values:

7 = height of the prism

6 = base of triangle

8 = height of triangle

First, we have to multiply the base of the triangle by the height of the triangle. The base of the triangle is 6 and the height of the triangle is 8. Then, we have to divide it by 2.

6 × 8 = 48

48 ÷ 2 = 24

Finally, we have to multiply 24 by the height of the prism. 24 × 7 = 168

Therefore, the volume of the prism is 168 [tex]units^{2}[/tex]

Answer:C.It can be concluded, with 95% confidence, that between 81% and 85% of all employees will rate the vacation policy as "delightful."

Step-by-step explanation:

The margin of error implies that 81% to 85% of all employees will judge the vacation policy as "delightful" with 95% confidence.

The margin of error is a statistic that expresses how much random sampling error there is in a survey's results. The wider the margin of error, the less confident one should be that a poll result reflects the outcome of a population-wide survey.

Given that the organization polled a random sample of its employees regarding their new vacation policy.

Now, 83% of the workers polled assessed the vacation policy as "delightful," with a margin of error of ±2% and a confidence interval of 95%, implying that 81% to 85% of all employees will judge the vacation policy as "delightful" with 95% confidence.

Hence, the margin of error implies that 81% to 85% of all employees will judge the vacation policy as "delightful" with 95% confidence.

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Answer:

14 cm

Step-by-step explanation:

step 1

Find the actual length of the segment

we know that

The original scale is 1 cm : 4m

In the original drawing, the length of a segment is 7 cm

therefore

Let

x ----> the actual length of the segment

by proportion

1/4=7/x

x=4*7

x=28 m

step 2

Find the length of the segment in the new drawing

The new scale is 1cm : 2m

Let

x ---> the length of the segment in the new drawing

by proportion

Remember that

The actual length is 28 m

1/2=x/28

x=28/2

x=14 cm

Answer:

Step-by-step explanation:

1.) mean is 4   1,2,3,5,6,7

2.) Four students won 12, 13, 14, 15, 16, or 17 prizes.

A total of 10 prizes were won by all the students.

3.)don't know number 3

the answer for 2 is B because 4 students won 12-17 prizes. They just word it 12,13,14,15,16 or 17.

Answer:

The correct answer is [tex]9x^{2}-6x[/tex].

Step-by-step explanation:

Consider the provided division:

We need to perform the subtraction in the division:

[tex]6x^{3}+x^{2}-10x[/tex]  ......(1)

[tex]6x^{3}-8x^{2}-4x[/tex]  ......(2)

In order to perform the subtraction simply change the sign of the second expression.

  [tex]6x^{3}+x^{2}-10x[/tex]

[tex]-6x^{3}+8x^{2}+4x[/tex]

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

           [tex]9x^{2}-6x[/tex]

Therefore, the correct answer is [tex]9x^{2}-6x[/tex].

Answer:

Step-by-step explanation:

Answer:

Part 1) [tex]z=4\sqrt{2}\ units[/tex]

Part 2) [tex]x=18\ units[/tex]

Part 3) [tex]y=12\sqrt{2}\ units[/tex]

Step-by-step explanation:

step 1

Find the value of z

In the smaller right triangle IFG of the figure

Applying the Pythagoras Theorem

[tex]6^{2}=2^{2}+z^{2}[/tex]

[tex]z^{2}=6^{2}-2^{2}[/tex]

[tex]z^{2}=32[/tex]  

[tex]z=4\sqrt{2}\ units[/tex]

step 2

In the right triangle HFG

Applying the Pythagoras Theorem

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

[tex]y^{2}=x^{2}-36[/tex] -----> equation A

step 3

In the right triangle HIG

Applying the Pythagoras Theorem

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

[tex]y^{2}=32+(x-2)^{2}[/tex] -----> equation B

step 4

equate equation A and equation B

[tex]x^{2}-36=32+(x-2)^{2}\\x^{2}-36=32+x^{2}-4x+4\\4x=36+36\\4x=72\\x=18\ units[/tex]

step 5

Find the value of y

Substitute the value of x in the equation B

we have

[tex]x=18\ units[/tex]

[tex]y^{2}=32+(18-2)^{2}[/tex]

[tex]y^{2}=32+(16)^{2}[/tex]

[tex]y^{2}=288[/tex]

[tex]y=12\sqrt{2}\ units[/tex]

Answer:

B.

Step-by-step explanation:

Answer:

II

Step-by-step explanation: