What is the complete solution to the following
equation?
ew
25 - 5x = 5(-x+5)

Answer: I believe

M = 80

Step-by-step explanation:

100 - 20 = 80

The distance between Ray-Ann and Steve, using the law of cosines, is given as follows:

11.5 feet.

The law of cosines states that we can find the length of the missing side c of a triangle as follows:

c² = a² + b² - 2abcos(C)

The parameters of the equation are given as follows:

In the context of this problem, the values of these parameters are given as follows:

Hence the distance between Ray-Ann and Steve is obtained as follows:

c² = 6²+ 7² - 2 x 6 x 7 x cos(124)º

c² = 132

c = square root of 132

c = 11.5 feet.

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The measure of angle MTU m∠MTU is 114 degree.

From the figure in the diagram:

Measure of angle STU is 145 degrees and measure of angle STM is 31 degree.

Since, angle STU composes or is the sum of angle STM and angle MTU.

To find angle MTU, simply subract angle STM from angle STU.

m∠STU = m∠STM + m∠MTU

Hence:

m∠MTU = m∠STU - m∠STM

Plug in the given values and simplify

m∠MTU = 145° - 31°

Subtract 31 from 145

m∠MTU = 114°

Therefore, angle MTU measure 114°.

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Given:

Price of car = $32,000

Sales tax = 8%

To find:

The price of car including sales tax.

Solution:

We have,

Price of car = $32,000

Salas tax = 8%

Amount of sales tax = 8% of price of car

\(\text{ Sales Tax}=\dfrac{8}{100}\times 32000\)

\(\text{Sales Tax}=2560\)

Now,

Total price of car including tax = Price of car + Sales tax

\(\text{Total price of car including tax}=32000+2560\)

\(\text{Total price of car including tax}=34560\)

Therefore, the price of car including tax is $34560.

The values of the six trignometric functions for the angle are

The above sketch an angle θ in standard position such that θ has the least possible positive measure, and the point (0,-2) is on the terminal side of θ. We have to determine the value of six

triganomertric functions at angle θ. As we see at terminal side point (0,-2) the value of angle θ = 3π/2. The six trigonometric functions are sine, cosine , secant , cosecant , tangent , cotangent .

= Sin ( 180° + π/2) = - sin(π/2) ( since, 180° + θ represents 3rd quadrant where sinθ is negative)

=> Sinθ = - 1

= Cos( 180° + π/2) = - Cos(π/2) ( since, 180° + θ represents 3rd quadrant where cosθ is negative)

=> Cosθ = Cos(π/2) = 0

= tan( 180° + π/2) = - tan(π/2) ( since, 180° + θ represents 3rd quadrant where tanθ is positive)

=> tanθ = - sin(π/2)/cos(π/2) = 1/0

= undefined

= Csc( 180° + π/2) = - Csc(π/2) ( since, 180° + θ represents 3rd quadrant where cscθ is negative)

=> Cscθ = - Csc (π/2) = - 1/sin(π/2) = 1

= Sec( 180° + π/2) = - Sec(π/2) ( since, 180° + θ represents 3rd quadrant where secθ is negative)

=> Secθ = -Sec(π/2) = -1/cos(π/2) = - 1/0

= undefined

= Cot( 180° + π/2) = Cot(π/2) ( since, 180° + θ represents 3rd quadrant where cotθ is positive)

=> Cotθ = cot(π/2) = Cos(π/2)/sin(π/2) = 0

Hence, we determined all required triganomertric functions value for θ=3π/2.

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The six trignometric functions' values for the angle are

Tan = tan(3/2) = undefined, Sin = Sin(3/2) = -1, Cos = Cos(3/2) = 0, and vice versa.

Cot = Cot(3/2), Csc = Csc(3/2), and Sec = Sec(3/2), respectively.

The above drawing shows an angle in standard position with the point (0,-2) on the angle's terminal side and the smallest positive measure achievable. We must calculate the value of six.

Triganomertric operates at an angle. As can be seen, the angle's value is 3/2 at the terminal side point (0,-2). In trigonometry, there are six different functions: sine, cosine, secant, cosecant, tangent, and cotangent.

At this point, Sin = Sin(3/2) = Sin( + /2)

= Sin ( 180° + π/2) Since 180° + denotes the third quadrant, where sin is negative, the expression is equal to - sin(/2).

=> Sinθ = - 1

Cos is equal to Cos(3/2) = Cos(+/2)

because 180 degrees, = Cos(180° + /2) = - Cos(/2)

Since 180° + denotes the third quadrant, where cos is negative, the equation is Cos(180° + /2) = - Cos(/2).

Hence, Cos = Cos(/2) = 0.

Tan is equal to Tan (3/2) = Tan (+/2)

= tan( 180° + π/2) Since 180° + denotes the third quadrant, where tan is positive, the expression is = - tan(/2).

Consequently, tan = - sin(/2)/cos(/2) = 1/0

not defined

Csc is equal to Csc(3/2) = Csc(+/2)

Since 180° + represents the third quadrant, where csc is negative, Csc(180° + /2) = - Csc(/2)

=> 1/sin(/2) = 1 = Csc = - Csc (/2)

Se( + /2) = Se( = Sec(3/2)

Since 180° + represents the third quadrant, where sec is negative, sec(180° + /2) = - Sec(/2)

The formula is: Sec = -Sec(/2) = -1/cos(/2) = -1/0.

not defined

Cot = Cot(3/2), which equals Cot(+/2)

Since 180° + denotes the third quadrant, where cot is positive, the equation is Cot(180° + /2) = Cot(/2).

Consequently, Cot = Cot(2/2) = Cos(2/2)/sin(2/2) = 0

As a result, we calculated the values for all necessary triganomertric functions for 3/2.

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Using the Charles law, the following are the solutions to the problems;

1) 16 dm3

2) 170 K

3) 2.4 L

Charles law states that, the volume of a given mass of gas is directly proportional to the temperature at constant pressure.

For problem 1;

T1 = 20 + 273 = 293 K

V1 = 15 dm3

T2 = 318 K

V2 = ?

V1/T1 = V2/T2

V1T2 =V2T1

V2 = V1T2/T1

V2 = 15 dm3 * 318 K/293 K

V2 = 16 dm3

Problem 2

V1 = 250cm3

T1 = 10 + 273 = 283 K

V2 = 150cm3

T2= ?

T2 = V2T1/ V1

T2 =  150cm3 *  283 K/250cm3

T2 = 170 K

Problem 3

V1 = 2.3 L

T1 = 25 + 273 = 298K

V2 = ?

T2 = 40 + 273 = 313 K

V2 = V1T2/T1

V2 = 2.3 L * 313 K/298K

V2 = 2.4 L

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Answer:

1st angle is 28° and the 2nd angle is 62°

Step-by-step explanation:

Complementary angles mean that the angles add up to 90 so:

2x - 2 + 5x - 13 = 90

7x - 15 = 90

7x = 90 + 15

7x = 105

x = 15

Plugging in:

2x - 2

2(15) - 2

30 - 2

28

5x - 13

5(15) - 13

75 - 13

62

Answer:12x+8y

Step-by-step explanation:Simplify the expression

The expression equivalent to 4(3x+2y) is 12x +8y.

Equivalent expressions are expressions that have similar value or worth but do not look the same.

Create an expression equivalent to 4(3x+2y).

The equivalent expression is determined in the following steps given below.

\(\rm =4(3x+2y)\\\\=4 \times 3x+4\times 2y\\\\=12x+8y\)

Hence, the expression equivalent to 4(3x+2y) is 12x +8y.

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step by step explanation

\( \binom{10\%}{100\%} \times \frac{76.50}{1} \)

Answer

10×76.50

100×1

765÷ 100 = 7.65

answer =7.65

Answer:

36 green apples

Step-by-step explanation:

Red=40%

Green =x%

40/100 × 60apples

0.4×60

24red apples

so 60-24

36green apples

Answer:

b) 36.

Step-by-step explanation:

Justicemoya35 has an excellent answer, but I will provide a slightly different approach!

According to the word problem, the box contains 60 apples.

If 40% of the apples are red, then 60% of the apples are green.

As I mentioned before, there are 60 apples; 60% of the 60 apples are green.

This means we have the find 60% of 60.

We can find the percentage of a number by using this formula:

60% OF 60

\(\frac{is}{of} =\frac{percent}{100}\)

\(\frac{x}{60} =\frac{60}{100}\)

Now that I've correctly set up the problem, we cross multiply, then divide the products.

\(60*60=3600\)

\(100*x=100x\)

\(3600/100x=36\)

\(x=36.\)

Therefore, 36 apples are red.

Answer:

B.  -414,720 x⁷y⁶

Step-by-step explanation:

To find the 4th term of the expansion of (2x - 3y²)¹⁰, we can use the binomial theorem.

The binomial theorem states that for an expression of the form (a + b)ⁿ:

\(\displaystyle (a+b)^n=\binom{n}{0}a^{n-0}b^0+\binom{n}{1}a^{n-1}b^1+...+\binom{n}{r}a^{n-r}b^r+...+\binom{n}{n}a^{n-n}b^n\\\\\\\textsf{where }\displaystyle \rm \binom{n}{r} \: = \:^{n}C_{r} = \frac{n!}{r!(n-r)!}\)

For the expression (2x - 3y²)¹⁰:

Therefore, each term in the expression can be calculated using:

\(\displaystyle \boxed{\binom{n}{r}(2x)^{10-r}(-3y^2)^r}\quad \textsf{where $r = 0$ is the first term.}\)

The 4th term is when r = 3. Therefore:

\(\begin{aligned}\displaystyle &\;\;\;\;\:\binom{10}{3}(2x)^{10-3}(-3y^2)^3\\\\&=\frac{10!}{3!(10-3)!}(2x)^7(-3y^2)^3\\\\&=\frac{10!}{3!\:7!}\cdot2^7x^7(-3)^3y^6\\\\&=120\cdot 128x^7 \cdot (-27)y^6\\\\&=-414720\:x^7y^6\\\\ \end{aligned}\)

So the 4th term of the given expansion is:

\(\boxed{-414720\:x^7y^6}\)

Answer: {...-3, -1, 1, 3, 5...}

Step-by-step explanation:

For a point to be discontinuous, the graph doesn't exist at that point. This means, it is represented with an open circle. All we have to do is to list out all the open circles on the graph.

{-3, -1, 1, 3, 5}

Answer:

b. {... –3, –1, 1, 3, ...}

Step-by-step explanation:

so basically it's b. the person above me is right they just added a 5 to the end

Given, Option A: Hourly wage is $19 and the salesperson works 40 hours per week. So, he will earn in a week \(\sf = 19 \times 40 = \$760\)

Now, according to option b, he will get 8% commission on weekly sales.

Let. x = the amount of weekly sales.

To earn the same amount of option A, he will have to equal the 8% of x to $760

So, \(\sf \dfrac{8x}{100}=760\)

Or, \(\sf 8x= 76000\)

Or, \(\sf x= \dfrac{76000}{8}=9500\)

the salesman needs to make a weekly sales of $9,500 to earn the same amount with two options.

Answer:

a), y=62       b.) c=1 3/5 or 8/5

Step-by-step explanation:

Okay so these are fairly simple lets start with A

4y=248, all we have to do is divide 4 on both sides

4y/4=y

248/4=62

Pretty Simple

For b just subtract 2/5 from both sides

(c+2/5)-2/5=c

2-2/5=1 3/5 or 8/5

Each number should be dragged to a box to complete the table as follows;

Kilometers     Meters

1                        1,000

2                       2,000

3                       3,000

5                       5,000

8                       8,000

In Science and Mathematics, a conversion factor can be defined as a number that is used to convert a number in one set of units to another, either by dividing or multiplying.

Generally speaking, there are one (1) kilometer in one thousand (1,000) meters. This ultimately implies that, a proportion or ratio for the conversion of kilometer to meters would be written as follows;

Conversion:

1 kilometer = 1,000 meters

2 kilometer = 2,000 meters

3 kilometer = 3,000 meters

4 kilometer = 4,000 meters

5 kilometer = 5,000 meters

6 kilometer = 6,000 meters

7 kilometer = 7,000 meters

8 kilometer = 8,000 meters

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2

Step-by-step explanation:

a recursive formula in a geometric sequence allows a term to be found by multiplying the preceding term by the common ratio r

here r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{-16}{-2}\) = 8 , then

\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2

Step-by-step explanation:

The Rule: If you are multiplying by a value less than one, your product will decrease. If you are multiplying by 1, the product will be equal and if you are multiplying by a value greater than 1, the product will increase.

Answer: 24 inches

Step-by-step explanation:

First, remember that 1 ft is equal to 12 in

Then, if 1 ft = 12 in

1 = 12in/1ft

this means that we can write a constant:

C = 12in/1 in

and C = 1, then we can write the width 2ft as:

2ft = 2ft*C = 2ft*12in/1ft = 24in

Answer:

r(-1) = 15

Step-by-step explanation:

3 * (-1)^2 - 9 (-1) + 3

3 * 1 +9 + 3

3+9+3

15

Answer:

d=-6.5

Step-by-step explanation:

2d+13=0

2d=-13

d= -13/2

d=-6.5

Answer:

Step-by-step explanation:

Graph 1 shows the correct representation the solution of the system.

For the given question;

The system of linear equation are given as;

x + 2y ≤ 16  .......eq 1

4x + y > 6    ......eq 2

Consider equation 1;

x + 2y = 16

For x = 0; y = 8 , Point = (0, 8)

For y = 0, x = 16, Point = (16, 0)

As the inequality of the eq 1 is less than equal to, the shaded region will lies below the line with solid lines.

Consider equation 2;

4x + y = 6

For x = 0; y = 6 , Point = (0, 6)

For y = 0, x = 1.5, Point = (1.5, 0)

As the inequality of the eq 2 is greater than, the shaded region will lies above the line with doted lines.

Thus, graph 1 shows the correct representation the solution of the system.

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Answer:

26÷2=13 so if the longer one is 2 cm longer so 13+1 =14. the shorter one is going to be 13-1=12 so 12+14 =26 and the shorter one is 2 cm smaller then the longer one

Answer:

Step-by-step explanation:

a. In interval notation, Increasing intervals: (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm). Decreasing intervals: (8am, 9am) U (11am, 12pm). Constant intervals: (9am, 10am) U (10am, 11am)

b. The increase in cost between 12 noon and 3 pm is $2.

c. Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

Interval notation is used to represent continuous intervals of numbers or values, like ranges on a number line.

The graph shows that from 8-9am, and 11-12pm, the cost from Swift Ride decreases.

We can represent it as (8am, 9am) U (11am, 12pm).

It increases at these times (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm).

And stays constant at : (9am, 10am) U (10am, 11am)

We simply deduct the 12pm's cost from 3pm's cost.

So, we have

Cost increase = $3.5 - $1.5

Evaluate the difference

Cost increase = $2

Hence, the cost increase is $2

When you plot the points provided for Yellow cab, you'll notice that Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

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The expression r + 12 is converted into a word that will be the sum of the number 'r' and twelve. Then the correct option is D.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The act of converting a specified statement into an expression or equation is known as a sentence-to-equation transformation.

The algebraic expression is given below.

⇒ r + 12

The plus sign represents the addition, sum, or summation between the numbers.

The expression r + 12 is converted into a word that will be the sum of the number 'r' and twelve. Then the correct option is D.

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Answer:

(3x+2)(x-5)

Step-by-step explanation:

Factor by grouping

\(3x^2-13x-10\\=3x^2-15x+2x-10\\=3x(x-5)+2(x-5)\\=(3x+2)(x-5)\)

Answer:

237.65 feet

Step-by-step explanation:

From the diagram attached,

Let the height of the blimp above the ground be h

From triangle A of the diagram,

tan18° = (360-y)/h

h = (360-y)/tan18°..................... Equation 1

Also

From triangle B in the diagram,

tan50° = y/h

h = y/tan50°.............................. Equation 2

Equation equation 1 and equation 2

(360-y)/tan18° = y/tan50°

tan50°(360-y) = tan18°(y)

1.19(360-y) = 0.325(y)

428.4-1.19y = 0.325y

428.4 = 0.325y+1.19y

1.515y = 428.4

y = 428.4/1.515

y = 282.8

Substituting the value of y into equation 2

h = 282.8/tan50°

h = 282.8/1.19

h = 237.65 feet.

Answer:

Step-by-step explanation:

1/10 is one tenth

Answer:

Roots: x = 5; x = 4

Step-by-step explanation:

Given the quadratic equation, x² -9x + 20 = 0

where a = 1, b = -9, and c = 20

Determine the nature and number of solutions based on the discriminant, b² - 4ac:  

b² - 4ac = (-9)² - 4(1)(20) = 1

Since b² - 4ac > 0, then it means that the equation will have two real roots.

Use the Quadratic Formula:

\(x = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}\)

\(x = \frac{-(-9) +/- \sqrt{(-9)^{2} - 4(1)(20)} }{2(1)}\)

\(x = \frac{9 +/- \sqrt{1}}{2}\)

\(x = \frac{9 + 1}{2}; x = \frac{9 - 1}{2}\)

\(x = \frac{10}{2}; x = \frac{8}{2}\)

x = 5; x = 4

Therefore, the roots of the quadratic equation are: x = 5; x = 4.