Sin x + cos x = cos x/1-tanx + sin x/1-cot x. Verify the identity. Explain each step please!

Answer:

26,250

Step-by-step explanation:

25,000 + 5% = 26,250

:) please mark Brainliest

The Smiths' new car purchase price before taxes cannot exceed $23,809.52 considering they have $25,000 and need to pay a 5% sales tax on the purchase.

To calculate the maximum purchase price of the new car before taxes that the Smiths can afford, we need to account for the 5% sales tax they will have to pay on top of the purchase price. Since the Smiths have saved $25,000, this is the total amount they have available to pay for the car including the sales tax.

To find the purchase price before tax, call this price 'P'. The total cost including the sales tax will be P + 0.05P (which is the sales tax). This total cost must not exceed $25,000. Therefore, we can set up the following equation:

1.05P <= $25,000

Divide both sides of the equation by 1.05 to isolate P:

P <= $25,000 / 1.05

P <= $23,809.52

So, the purchase price of the Smiths' new car before taxes cannot exceed $23,809.52.

Answer:

The length is 16.1 ft and the width is 4.7 ft

Step-by-step explanation:

Let

x -----> the total length of the tables

y -----> the width of the tables

we know that

The area is equal to

[tex]A=xy[/tex]

[tex]A=75\ ft^{2}[/tex]

so

[tex]75=xy[/tex] -----> equation A

[tex]x=3y+2[/tex] -----> equation B

substitute equation B in equation A

[tex]75=(3y+2)y[/tex]

[tex]3y^{2} +2y-75=0[/tex]

Solve the quadratic equation by graphing

The solution is [tex]y=4.7\ ft[/tex]

Find the value of x

[tex]x=3(4.7)+2=16.1\ ft[/tex]

therefore

The length is 16.1 ft and the width is 4.7 ft

Answer:

The length and width of the serving table is 16.1 ft and 4.7 ft respectively.

Step-by-step explanation:

Consider the provided information.

Let the width of the table is x and length of the table is y.

The total length of the tables will be two more than three times the width.

This can be written as:

y = 2+3x

The area of the table is 75 ²ft

The area of rectangle is:

length × width = Area

Substitute width = x and length = 2+3x in above formula.

(x)(2+3x) = 75

2x+3x²-75 = 0

3x²+2x-75 = 0

The above equation is in the form of ax²+bx+c=0. Now use the quadratic formula to find the root of the equation.

[tex]x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Substitute a=3, b=2 and c=-75 in above formula.

[tex]x_{1,2}=\frac{-2\pm\sqrt{2^2-4(3)(-75)}}{2(3)}[/tex]

[tex]x_{1,2}=\frac{-2\pm\sqrt{904}}{6}[/tex]

[tex]x_{1,2}=\frac{-2\pm30.07}{6}[/tex]

[tex]x_{1}=\frac{-2+30.07}{6}[/tex]

Ignore the negative value of x as width should be a positive number.

[tex]x=4.7\ ft[/tex]

Now substitute the value of x in y = 2+3x.

y = 2+3(4.7)

y = 16.1 ft

Hence, the length and width of the serving table is 16.1 ft and 4.7 ft respectively.

Answer:

See explanation

Step-by-step explanation:

The distance formula is given by:

[tex]d = \sqrt{ {(x_2-x_1)}^{2} + {(y_2-y_1)}^{2} } [/tex]

We want to find the distance between (a,b) and (x,y).

The center of the habitat is missing in the question.

Assuming the center is (a,b) where a and b are real numbers, then we can use the distance formula to obtain:

[tex] d = \sqrt{(x - a)^{2} + {(y - b)}^{2} } [/tex]

For instance if the center of your habitat us (2,-1), then

[tex]d = \sqrt{(x - 2)^{2} + {(y + 1)}^{2} } [/tex]

Answer:

Part 1) The ordered pair is (0,0)

Part 2) The ordered pair is (-2,-4)

Part 3) The ordered pair is (4,8)

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem we have a direct variation

[tex]y=2x[/tex]

Complete the ordered pairs

Part 1) we have (0,?)

For x=0

Substitute in the equation and solve for y

[tex]y=2(0)=0[/tex]

therefore

The ordered pair is (0,0)

Part 2) we have (-2,?)

For x=-2

Substitute in the equation and solve for y

[tex]y=2(-2)=-4[/tex]

therefore

The ordered pair is (-2,-4)

Part 3) we have (4,?)

For x=4

Substitute in the equation and solve for y

[tex]y=2(4)=8[/tex]

therefore

The ordered pair is (4,8)

Answer:

second option

Step-by-step explanation:

We are going to use the acronym:

"Soh Cah Toa".

Why? It tells us the right-triangle definitions of sine, cosine, and tangent.

sine is opposite over hypotenuse.

cosine is adjacent over hypotenuse.

tangent is opposite over adjacent.

So looking at our triangle with respect to B tells us that 3 is the opposite measurement and 6 is the adjacent.  No matter what angle we are looking for in this triangle, the hypotenuse is constantly going to by [tex]3\sqrt{5}[/tex].

So let's look at cos(B).

[tex]\cos(B)=\frac{6}{3\sqrt{5}}[/tex]

We need to rationalize the denominator by multiplying top and bottom by sqrt(5):

[tex]\cos(B)=\frac{6\sqrt{5}}{3(5)}=\frac{2\sqrt{5}}{5}[/tex]

So now looking at sin(B).

[tex]\sin(B)=\frac{3}{3\sqrt{5}}[/tex]

We have to rationalize again by multiplying top and bottom by sqrt(5):

[tex]\sin(B)=\frac{3\sqrt{5}}{3(5)}=\frac{\sqrt{5}}{5}[/tex].

So looking at our triangle with respect to A tells us that 3 is the adjacent measurement and 6 is the opposite.  No matter what angle we are looking for in this triangle, the hypotenuse is constantly going to by [tex]3\sqrt{5}[/tex].

We don't have to use any trigonometric ratios with A.

Answer:

2 Square 5/ 5

Step-by-step explanation:

I got it right on the test

Answer:

Answer is  x=328 .

Step-by-step explanation:

solution= (4x-16)^1/2=36

squaring both sides we get

 4x-16=129

 4x=1296+16

 x=(1296+16)/4

  x=328 .

Answer:

x = 328

Step-by-step explanation:

The given equation is

[tex](4x-16)^{\frac{1}{2}}=36[/tex]

We need to find the solution of the given equation.

Taking square on both sides.

[tex]((4x-16)^{\frac{1}{2}})^2=(36)^2[/tex]

[tex](4x-16)^{\frac{2}{2}}=1296[/tex]

[tex]4x-16=1296[/tex]

Add 16 on both sides.

[tex]4x-16+16=1296+16[/tex]

[tex]4x=1312[/tex]

Divide both sides by 4.

[tex]x=\dfrac{1312}{4}[/tex]

[tex]x=328[/tex]

Therefore, the value of x is 328.

Answer:

Option B [tex]y> 0[/tex]

Step-by-step explanation:

we have

[tex]f(x)=9(2^{x})[/tex]

This is a exponential function of the form

[tex]y=a(b^{x})[/tex]

where

a is the initial value

b is the base

r is the rate

b=1+r

In this problem

a=9

b=2

r=2-1=1=100%

The domain for x is the interval ------> (-∞,∞)

All real real numbers

The range is the interval -----> (0,∞)

[tex]y> 0[/tex]

All real numbers greater than zero

see the attached figure to better understand the problem

Answer:

Option C is correct.

Step-by-step explanation:

Points given are

(1,2) and (3,8)

The formula used for slope is:

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

x₁ = 1, x₂=3, y₁=2 and y₂=8

[tex]m=\frac{8-2}{3-1}\\m=\frac{6}{2}\\m=3[/tex]

So, slope =3

Option C is correct.

Answer:

The slope of the line passing through (1,2) and (3,8) is 3.

Step-by-step explanation:

Slope formula is y2-y1/x2-x1

y2=8

y1=2

x2=3

x1=1

8-2/3-1

8-2=6

3-1=2

6/2=3

Answer:

[tex]\large\boxed{(2b+3)\times(5b-1)\times(5b+1)}[/tex]

Step-by-step explanation:

The formula of a volume of a rectangular box:

[tex]V=lwh[/tex]

l - lenght

w - width

h - height

[tex]V=50b^3+75b^2-2b-3=25b^2(2b+3)-1(2b+3)\\\\=(2b+3)(25b^2-1)=(2b+3)(5^2b^2-1^2)\\\\=(2b+3)\bigg((5b)^2-1^2\bigg)\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(2b+3)(5b-1)(5b+1)[/tex]

Therefore the dinemsions of thisp prism are:

[tex](2b+3)\times(5b-1)\times(5b+1)[/tex]

Answer:

the one with ++-

Step-by-step explanation:

Complementary angle add up to 90 degrees.

Angle A = x + 6

Angle B = x

They both add up to 90.

x + 6 + x = 90

2x + 6 = 90

2x = 90 - 6

2x = 84

x = 84/2

x = 42

Angle A = x + 6

Angle A = 42 + 6

Angle A = 48 degrees

Answer:

Step-by-step explanation:

[tex]8(x-2)=64\qquad\text{distributive property}\\8x-(8)(2)=64\\8x-16=64\qquad\text{add 16 to both sides}\\8x-16+16=64+16\qquad\text{addition property of equality}\\8x=80\qquad\text{divide both sides by 8}\\\dfrac{8x}{8}=\dfrac{80}{8}\qquad\text{division property of equality}\\x=10[/tex]

Answer:

ANSWER WOULD BE D . division property of equality

Step-by-step explanation:

Took the test the math is quite simple

Answer:

a. [tex]c(x) = 2x + 105[/tex]

b.  [tex]c(50) =\$205[/tex]

Step-by-step explanation:

The variable cost of $ 2 implies that for each manufactured calculator the total cost increases $ 2.

The fixed cost of $ 105 implies that regardless of the number of manufactured calculators there will always be a cost of $ 105.

If we call x the number of manufactured calculators then the total cost c(x) will be:

[tex]c(x) = 2x + 105[/tex]

Then, the cost of manufactured 50 calculators a day is:

[tex]c(50) = 2(50) + 105[/tex]

[tex]c(50) = 100 + 105[/tex]

[tex]c(50) =\$205[/tex]

Answer:

9 is (2/9) of the way from A = 5 to B = 23.

Step-by-step explanation:

Note that there are 23-5, or 18, units separating 5 and 23.

2/9 of that distance is (2/9)(18), or 4.

Adding 4 to 5, we get 9.

9 is (2/9) of the way from A = 5 to B = 23.

If this is not clear, I'd suggest you draw this situation and prove to yourself that 9 is (2/9) of the way from A = 5 to B = 23.

Answer:

9

Step-by-step explanation:

The equation is A+K (B-A). So 5+ 2/9 (23-5) = 9

Answer:

42.5 %

Step-by-step explanation:

You would multiply the probability of the couple having a girl and the test predicting it’s a girl.

0.85 x 0.5= 0.425 = 42.5%

Answer: C

Step-by-step explanation:

Probability: the outcome you want (2) over the total number of outcomes (6).

Probability= 2/6= 1/3.

The probability of landing on 2 is 1/6 if the total number of outcomes is 6 and favorable outcomes are 1 option (C) is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have a spinner shown in the picture.

Total number of outcomes = 6

{1, 2, 3, 4, 5, 6}

Total number of favorable outcomes = 1

{2}

P(landing on 2) = 1/6

Thus, the probability of landing on 2 is 1/6 if the total number of outcomes is 6 and favorable outcomes are 1 option (C) is correct.

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The measurement of angle RST is 105

Answer:

Option C). 105°

Step-by-step explanation:

From the figure we can see a cyclic quadrilateral QRST

To find the measure of <RST

From the figure we can see that, angle RST is an obtuse angle.

The measure of angle RST is nearer to a right angle that is nearer to 90°

From the options we get the measure of angle RST = 105°

Answer:

y = 3x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, 3)

m = [tex]\frac{3-0}{0+1}[/tex] = 3

We are given the y- intercept, that is c = 3

y = 3x + 3 ← equation of line

Answer:

C x= 0   greater than

E x= 10 greater than

Step-by-step explanation:

4(2 – x) > –2x – 3(4x + 1)

Distribute

8 –4x > –2x – 12x -3

Combine like terms

8 –4x > – 14x -3

Add 14x to each side

8 –4x+14x > – 14x+14x -3

8 +10x >  -3

Subtract 8 from each side

8-8+10x>-3-8

10x > -11

Divide each side by 10

10x/10 >-11/10

x >-1.1

Any number greater than -1.1 is a solution

A x= -1.1   not greater than

B x= -2.2   not greater than

C x= 0   greater than

D x=-10  not greater than

E x= 10 greater than

Answer:

C & E

Step-by-step explanation:

TW x WU = CW x VW

Fill in the known values:

WU = TU - TW = 21.2 - 14.6 = 6.6

14.6 x 6.6 = 6 x VW

Simplify:

96.36 = 6VW

Divide both sides by 6:

VW = 96.36 / 6

VW = 16.06

Round to one decimal place:

VW = 16.1

The answer is D>

Answer:

D.) 16.1

Step-by-step explanation:

I got it correct on founders edtell

[tex] \frac{m}{n} . \frac{n}{p} \div \frac{p}{q} \\ = \frac{m}{p} \div \frac{p}{q} \\ = \frac{m}{p} . \frac{q}{p} \\ = \frac{mq}{ {p}^{2} } [/tex]

Hope it helps...

Regards;

Leukonov/Olegion.

Answer:

The correct answer is first option

mq/p²

Step-by-step explanation:

It is given that, (m/n) * (n/p) ÷ (p/q)

To find the simplified form of given expression

Let  (m/n) * (n/p) ÷ (p/q) can be written as,

(m/n) * (n/p) ÷ (p/q) =  (m/n) * (n/p) * (q/p)

 = (m * n * q)/(n * p * q)

 = (m * q)/(p * p)

 = mq/p²

Therefore the correct answer is mq/p²

Answer:

b

Step-by-step explanation:

any set times the radius will give you the answer

Answer:

0.7557

Step-by-step explanation:

In this question use the Table of Standard Normal Probabilities for Negative z-scores and the Table of Standard Normal Probabilities for Positive z-scores

Where z=2.27 NORMDIST(2.27)=0.9884 (read from table for positive z-scores)

Where z=-0.73 NORMDIST(-0.73)=0.2327 (read from table for negative z-scores)

You know P(-0.73<z<2.27)= 0.9884-0.2327=0.7557

The probability that P(–0.73 < z < 2.27) is 0.7557.

The z score is used to determine by how many standard deviations, the raw score is above or below the mean. The z score is given by:

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} } \\\\where\ x=raw\ score,\mu=mean, \sigma=standard\ deviation,n= sample\ size\\\\\\[/tex]

From the normal distribution table, P(-0.73 ≤ z ≤ 2.27) = P(z < 2.27) - P(z<-0.73) = 0.9884 - 0.2327 = 0.7557

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Answer:C

Step-by-step explanation:4x _2y =64 because 8×8= 64

For this case we must find an equation equivalent to:

[tex]\frac {1} {4} x- \frac {1} {2} y = 8[/tex]

We add [tex]\frac {1} {2}[/tex] and on both sides of the equation:

[tex]\frac {1} {4} x = 8 + \frac {1} {2}y[/tex]

We multiply by 4 on both sides of the equation:

[tex]x = 32 + \frac {4} {2}y\\x = 32 + 2y[/tex]

Multiplying by 2 on both sides of the equation:

[tex]2x = 64 + 4y\\2x-4y = 64[/tex]

Answer:

Option B

Answer:

[tex]4x[/tex]

Step-by-step explanation:

We want to find the simplest rational exponent form of

[tex]\sqrt{x} \cdot 4\sqrt{x}[/tex]

Recall that: [tex]\sqrt{a}=a^{\frac{1}{2} }[/tex]

We rewrite the expression in the exponent form to get:

[tex]x^{\frac{1}{2}}\cdot 4x^{\frac{1}{2}[/tex]

We can regroup the product to get:

[tex]4 x^{\frac{1}{2}\cdot x^{\frac{1}{2}[/tex]

We apply the rule: [tex]a^m\cdot a^n=a6{m+n}[/tex] to get:

[tex]4 x^{\frac{1}{2}}\cdot x^{\frac{1}{2}=4 x^{\frac{1}{2}+\frac{1}{2}}[/tex]

[tex]4 x^{\frac{1}{2}}\cdot x^{\frac{1}{2}=4 x^{1}[/tex]

[tex]4 x^{\frac{1}{2}}\cdot x^{\frac{1}{2}=4x[/tex]

Answer:

Yes, it is a function.

Step-by-step explanation:

Since each x-value is used only once, the relation is a function.

Yes, The relation represented in table is a function.

A relation between a set of inputs having one output each is called a function.

Given that;

The table is,

x |  5  10  15

y | 3    8    8

Now,

Clearly, Each inputs having one output in the table as;

⇒ f (5) = 3

⇒ f (10) = 8

⇒ f (15) = 8

So, The table represent the function.

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Answer:

1180 cans

Step-by-step explanation:

Heywards collected = 980 cans

Ballards collected 200 fewer cans than Heywards.

Total cans collected by Ballard = ?

Therefore the sum of Heywards collected cans and Ballards fewer cans will give us the total cans collected by Ballard.

=980+200

=1180

Ballard collected 1180 cans....

Answer:

its 2 4/9

Step-by-step explanation:

because i did trial and error, i converted all the fractions into decimals until one of the conversions was equal to 2.444444444444...infinite

[tex]2 \frac{4}{9}[/tex] would be the correct answer.

This is not 2.4. This is "2.44444..." because of the line over the 4 after the decimal place (this applies for any decimal such as [tex]2.48\overline{47} = 2.484747474747...[/tex]).

In general, the over-lined part can be written as a fraction of 9 (99, 999, 9999, etc. if the over-lined part has more than one digit, in increasing order of digits), which is why [tex]2 \frac{4}{9}[/tex] is the correct answer.

Answer:

=20.0

Step-by-step explanation:

We can first find the value of the angle at B using the sine formula.

a/sine A=b/Sin B

9/sin 15=12/sin B

Sin B=(12 sin 15)/9

Sin B=0.345

B=20.18°

Therefore angle C =180-(15+20.18)

=144.82°

a/Sin A=c/Sin C

9/Sin 15=c/Sin 144.82

c=(9 sin 144.82)/sin15

=20.0

Answer:

The function is defined when x > 0

Step-by-step explanation:

Functions with radicals are only undefined when the value in the radical is negative, because the root of a negative number is imaginary.  

We know the function is undefined when the denominator is equal to zero.  [tex]\sqrt{2x}[/tex] is equal to zero when x=0.

We also know that functions with radicals are undefined when the value in the radicals are negative, because the root of a negative number is imaginary.  .  [tex]8x^{2}[/tex] will always be positive, but [tex]2x[/tex] is negative when x < 0.

So the function is undefined when x = 0, and when x < 0.

Therefore it is defined when x > 0

Answer:

1-4x

Step-by-step explanation:

Answer:

Step-by-step explanation:

The product of four and a number x: 4 · x = 4x

One minus the product of four and a number x: 1 - 4x