Using the linear equation 3x+2y=6, express x in terms of y

Answer:

C.15+25y

Step-by-step explanation:

5(3+5y) solved via distribution is 15+25y

Happy to help :D

C. Because 5(3+5y) is the same as 5x3 plus 5x5y which is 15 + 25y

Answer:

The total interest paid by Nell in 20 years is $3,724.80

C is correct

Step-by-step explanation:

Nell took out a subsidized student loan of $6000 at a 4.8% APR, compounded  monthly.

First we find total amount in 10 months

[tex]A=6000(1+\frac{0.048}{12})^{10}[/tex]

[tex]A=6244.37[/tex]

Now, He has to pay loan off on 6244.37 for 20 years at 4.8% APR

Loan Formula:

[tex]P=\dfrac{PV\cdot r}{1-(1+r)^{-n}}[/tex]

PV=6244.37

r=0.048/12

n=240

[tex]P=\dfrac{6244.37\times \frac{0.048}{12}}{1-(1+\frac{0.048}{12})^{-240}}[/tex]

[tex]P=40.52[/tex]

Total pay in 20 years = 40.52 x 20 = 9724.80

Total amount took loan = $6000

Interest = 9724.80 - 6000

             = $3,724.80

Hence, The total interest paid by Nell in 20 years is $3,724.80

Answer: $3345.60

Step-by-step explanation:

Apex - Took one for the team on the quiz because I forgot to check the rating on the other answer </3

Answer:

x = 4.  x = 64, d = 0.60.

Step-by-step explanation:

a. 256 /x = 64

64x = 256

x = 256/64

x = 4.

b.  256/x = 4

4x = 256

x = 256/4

x = 64.

c.  36/d = 60

60d = 36

d = 36/60

d = 0.60.

Answer:

Those are trigonometric identities. and tan is just a shortened version of tangent, same for cos is means cosine

   The sine/sin of the angle = the length of the opposite side divided by the length of the hypotenuse.

   The cosine/cos of the angle = the length of the adjacent side divided by the length of the hypotenuse.

   The tangent/tan of the angle = the length of the opposite side divided by the length of the adjacent side.

Answer:

63,960 possibilities in total.

Step-by-step explanation:

For the first number, you can choose from 41 different numbers, so there are 41 possibilities.

For the second number, you cannot choose the same as the first one, so you are now limited to 40 possibilities.

For the third number, you are down to 39 possibilities since you cannot pick the same as the first two ones.

So, you have 41 * 40 * 39 = 63,960 possibilities in total.

Picking a new combination is easy... remembering it is the hard part :-)

If you want to calculate it from a formula standpoint, the base formula would be:

[tex]P(n,r) = \frac{n!}{(n-r)!} = \frac{41!}{(41-3)!} = 63960[/tex]

Where n is the total numbers possible and r is the quantity of numbers you have to pick.

729. multiple 9 times 9 then 81 times 9 and you get D

Answer:

Final answer is $4440.

Step-by-step explanation:

Let amount of money invested in 8% stock = x

Let amount of money invested in 6% stock = y

then total money invested $325.6 gives equation

8% of x + 6% of y = 325.6

0.08x + 0.06y = 325.6

8x + 6y = 32560...(i)

other equation will be x=2y...(ii)

plug (ii) into (i)

8x + 6y = 32560

8(2y) + 6y = 32560

16y+ 6y = 32560

22y = 32560

[tex]y=\frac{32560}{22}[/tex]

y=1480

plug y=1480 into (ii)

x=2y=2(1480)=2960

Then total money invested in stocks = x+y= 1480+2960=4440

Hence final answer is $4440.

Answer:

Step-by-step explanation:

Note that the reciprocal of tan B is by definition the cotangent (cot) of B:

   1                        adjacent side           BC

---------- = cot B = ----------------------- =  ---------

 tan B                   opposite side            AC

Answer:

Hence, The reciprocal of tan B is tan A

B is correct.

Step-by-step explanation:

We are given a right angle triangle. Right angle at ∠C

We need to find the reciprocal of tan B

First we write the formula of tan B using trigonometry identity.

[tex]\tan\theta=\dfrac{\text{Opposite}}{\text{Base}}[/tex]

In ΔABC, ∠C=90°

[tex]\tan B=\dfrac{AC}{BC}[/tex]

Now we reciprocal it.

[tex]\dfrac{1}{\tan B}=\dfrac{BC}{AC}[/tex]

[tex]\tan A=\dfrac{BC}{AC}[/tex]

Comparing both equation ( Right sides equal )

[tex]\dfrac{1}{\tan B}=\dfrac{BC}{AC}=\tan A[/tex]

[tex]\dfrac{1}{\tan B}=\tan A[/tex]

Hence, The reciprocal of tan B is tan A.

Answer:

28.26 cm²

Step-by-step explanation:

It's not the point O, but the circle O.

The area of a circle is given by the formula A = π r²

We already have r (3cm)... so we can plug it directly into the equation:

A = π r² = π 3² = 9π = 28.26 cm²

Answer:

A = 28.27

Step-by-step explanation:

A = π r^2

A = π 3^2

A= π (9)

A = 28.27433

Answer: Obtion B

[tex]P = 1.3e ^ {-0.038t}\\\\P = 2.1e ^ {-0.046t}[/tex]

Step-by-step explanation:

The equation for exponential decay has the following form:

[tex]y = pe ^{-rt}[/tex]

Where

p is the initial population  

r is the rate of decrease

t is time.

In this problem we have to:

The current population of insect A to be 1.3 million and the current population of insect B to be 2.1 million.

So

[tex]p_1 = 1.3[/tex]  in millions

[tex]p_2 = 2.1[/tex]  in millions

We also need the populations of insect to be reduced at a rate of 3.8% and insect to be reduced at a rate of 4.6%.

so:

[tex]r_1 = 0.038\\\\r_2 = 0.046[/tex]

then the exponential decay equation for insect A is:

[tex]P = 1.3e ^ {-0.038t}[/tex]

the exponential decay equation for insect B is:

[tex]P = 2.1e ^ {-0.046t}[/tex]

Finally, the system of equations is:

[tex]P = 1.3e ^ {-0.038t}\\\\P = 2.1e ^ {-0.046t}[/tex]

The answer is the Option B

Answer:

(7x-5)(7x+5)

Step-by-step explanation:

Answer:

(7x + 5)(7x - 5)

Step-by-step explanation:

49x² - 25 ← is a difference of squares and factors in general as

a² - b² = (a + b)(a - b)

49x² = (7x)² ⇒ a = 7x

25 = 5² ⇒ b = 5

49x² - 25

= (7x)² - 5² = (7x + 5)(7x - 5)

Answer:

B. 1184

Step-by-step explanation:

Answer is B

See photo

Answer:

The answer is 18.2.

Hope this helps!

Answer: 18.2

Step-by-step explanation:

you would round to 18.2 because with 5 and above, you give it a shove, 4 and below let it go

Answer:

Step-by-step explanation:

Convert the inequality to the form y > mx + b:

3x + y > -8           subtract 3x from both sides

y > -3x - 8

Put the coordinates of the points to the inequality and check:

for (-3, 0)

0 > -3(-3) - 8 → 0 > 9 - 8 → 0 > 1   FALSE

for (-2, -1)

-1 > -3(-2) - 8 → -1 > 6 - 8 → -1 > -2   TRUE

for (0, -10)

-10 > -3(0) - 8 → -10 > 0 - 8 → -10 > -8  FALSE

for (2, -16)

-16 > -3(2) - 8 → -16 > -6 - 8 → -16 > -14  FALSE

Answer:

[tex]\frac{4}{5}[/tex]

Step-by-step explanation:

Given

sinΘ = [tex]\frac{3}{5}[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]

Then the hypotenuse = 5 and one leg of the right triangle is 3

Using Pythagoras' identity to find the second leg (x)

x² + 3² = 5²

x² + 9 = 25 ( subtract 9 from both sides )

x² = 16 ⇒ x = 4

cosΘ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4}{5}[/tex]

The expression sin x / csc x + cos x / sec x simplifies to sin^2 x + cos^2 x by using the reciprocal identities of the trigonometric functions csc x and sec x.

The expression sin x / csc x + cos x / sec x can be simplified by substituting the reciprocal identities for the trigonometric functions csc x and sec x. The reciprocal of csc x is sin x and the reciprocal of sec x is cos x. Thus, sin x / csc x becomes sin x / (1/sin x) which simplifies to sin^2 x. Similarly, cos x / sec x becomes cos x / (1/cos x) or cos^2 x. Therefore, the simplified form of the expression is sin^2 x + cos^2 x.

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Answer:

Step-by-step explanation:

Here's how I would do it (not necessarily the only way or best way).

Draw an imaginary line from A to C.  This splits the kite into two triangles: ABC and ADC.  Since AB ≅ AD, CB ≅ CD, and AC ≅ AC, the two triangles must be congruent by SSS.  Therefore, ∠B ≅ ∠D.

Answer:

Step-by-step explanation:

Rent, wages and car insurance don't vary much.  Grocery expenses depend upon the particular groceries purchased each time one goes to the grocery store, and are least likely to be steady / constant from week to week.

Answer:

5.4 ft²

Step-by-step explanation:

Since the circle is inscribed in the square then radius r = 2.5

Area of yellow = area of square - area of circle

A = (5 × 5) - (π × 2.5²)

  = 25 - 6.25π ≈ 5.4 ft²

Answer:

Area of the Yellow Region is 5.4 ft²

Step-by-step explanation:

Given:

Length of the side of the square = 5 ft

Diameter of the Circle = Length of the side = 5 ft

⇒ Radius of the circle, r = 5/2 = 2.5 ft

To find: Area of the Yellow region from the figure.

Area of the Yellow Region = Area of the Square - Area of the Circle

                                            = Side × Side - πr²

                                            = 5 × 5 - 3.14 × (2.5)²

                                            = 25 - 3.14 × 6.25

                                            = 25 - 19.625

                                            = 5.375

                                            ≈ 5.4 ft²   (nearest tenth)

Therefore, Area of the Yellow Region is 5.4 ft²

There are 11 letters in "probability"

There are two B's and two I's

11!/(2!2!) = 9,979,200

hope that helps. please name me brainliest

Answer:

8

6

Using all the letters of the word ARRANGEMENT how many different words using all letters at a time can be made such that both A, both E, both R both N occur together .

Hope this helps <3<3<3 Aaliyah

Step-by-step explanation:

Answer:

The answer is option C. rectangle, parallelogram, rhombus

Step-by-step explanation:

The set of quadrilaterals that must have opposite sides that are congruent and parallel are - rectangle, parallelogram, rhombus.

These three quadrilaterals have opposite sides congruent. Kites and trapezoids does not have opposite sides congruent.

The required set of quadrilaterals that satisfy these conditions is a rectangle, parallelogram, and rhombus. Option C is correct.

The set of quadrilaterals that must have opposite sides that are congruent and parallel is option C: rectangle, parallelogram, rhombus.

In a rectangle, opposite sides are congruent and parallel.

In a parallelogram, opposite sides are congruent and parallel.

In a rhombus, opposite sides are congruent and parallel.

Therefore, the set of quadrilaterals that satisfy these conditions is a rectangle, parallelogram, and rhombus. Option C is correct.

Learn  more about quadrilaterals here:

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Answer:

Step-by-step explanation:

The percent of 64 which that is 16 is 25% because, to find what percent a number y is of a number x, you have to follow the steps: Divide y by x.

Answer:

25%

Step-by-step explanation:

The question aks: What percentage of 64 is 16?

Let that percentage be x,

[tex]\frac{x}{100}[/tex] of 64 = 16

We multiply both sides by 100 then divide by 64 to get:

x = [tex]\frac{1600}{64}[/tex] = 25%

Answer:

-3/5

Step-by-step explanation:

you can use the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] to find the slope of a line when given two points.

we are given both the x and y intercepts, and we can use those in the formula.

the x intercept is (5,0) and the y intercept is (0,3)

i will treat (5,0) as my x1 and y1, and (0,3) as my x2 and y2

[tex]\frac{3-0}{0-5}[/tex] = -3/5

the slope is -3/5

The slope of the line is -3/5 if the line p has an x-intercept of 5 and a y-intercept of 3.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have a line p:

The x-intercept of line p is 5 or (5, 0)

The y-intercept of line p is 3 or (0, 3)

The slope m can be evaluated:

[tex]\rm m =\dfrac{3-0}{0-5}[/tex]

m = -3/5

Thus, the slope of the line is -3/5 if the line p has an x-intercept of 5 and a y-intercept of 3.

Learn more about the slope of the straight line here:

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Answer:

16

Step-by-step explanation:

h(x) × h(x) = (6 - x)²

(h × h)(10) = (6 - 10)² = (- 4)² = 16

For this case we have by definition, that given two functions, then:

[tex](f * g) (x) = f (x) + g (x)[/tex]

Here, we want to find ([tex](h * h) (x):[/tex]

[tex](h * h) (x) = (6-x) (6-x)\\(h * h) (x) = 36-6x-6x + x ^ 2\\(h * h) (x) = 36-12x + x ^ 2[/tex]

We want to find the value of the function when [tex]x = 10[/tex].

[tex](h * h) (10) = 36-12 (10) + (10) ^ 2\\(h * h) (10) = 36-120 + 100\\(h * h) (x) = 16[/tex]

Answer:

[tex](h * h) (x) = 16[/tex]

Answer:

56.5 inches

Step-by-step explanation:

We are given the area of a circle and we are to find the circumference of the same circle.

We know that the area of a circle is given by [tex]\pi r^2[/tex] so equating the given value to get.

[tex]\pi r^2=254.47[/tex]

[tex]r^2=\frac{254.47}{\pi }[/tex]

[tex]r=\sqrt{81.00}[/tex]

r = 9 inches

Since we now know the radius of the circle so we can find its circumference.

Circumference of circle = [tex]2\pi r[/tex] = [tex]2\pi (9)[/tex] = 56.5 inches

Answer: 56.54 in

Step-by-step explanation:

The area can be calculated with this formula:

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

Where r is the radius

And the circumference can be calculated with this formula:

[tex]C=2\pi r[/tex]

 Where r is the radius

Solve for the radius from  [tex]A=\pi r^2[/tex]. Then, tha radius is:

[tex]r=\sqrt{\frac{A}{\pi }}=\sqrt{\frac{254.47in^2}{\pi }} =9in[/tex]

Then, the circumference is:

 [tex]C=2\pi (9in)=56.54in[/tex]

Answer:

Step-by-step explanation:

[tex]5+(-3)(6x-5)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=5+(-3)(6x)+(-3)(-5)\\\\=5-18x+15\qquad\text{combine like terms}\\\\=-18x+(5+15)\\\\=-18x+20[/tex]

Answer:

none of the above

Step-by-step explanation:

just for people who dont want one

The answer is D. you would do 0.25 x 6.5. you add 2 to the original needed batches of 4.5.

Answer:

1.125 (A)

Step-by-step explanation:

First you multiply 0.25 x 4.5=1.125

The domain of a function is the complete set of possible values of the independent variable.

The cosine function is represented by the expression: y=cos(x), where "x" is the independent function, and "y" the dependent function. So the domain comes to be all the values that "x" can take.

The domain of the cosine function is all the real numbers. All this can be verified by looking at its graph (attached)

Answer:

2.11 ft

Step-by-step explanation:

Given in the question,

number of revolution a wheel make = 32

distance that wheel traveled while rotating  = 425ft

Step 1

Find the circumference of the wheel

circumference = total distance covered / number of revolution

                        = 425 / 32

                        = 13.28 ft

Step 2

Formula of circumference  

2πr = 13.28 ft

r  = 13.28/2π

r = 2.11 ft

Answer:

Have the same vertex , and be congruent.

Step-by-step explanation:

Answer:Have the same vertex , and be congruent.

Step-by-step explanation: