Mr. Smith saved $15 by buying a tool at a 10% discount. What was the original price for this tool?

Answer:  ∠S corresponds to ∠V.

The solution is Option B.

The measure of angle ∠S corresponds to ∠V

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the first triangle be ΔQSR

Let the second triangle be ΔTUV

Now , the measure of ∠Q = 98°

The measure of ∠R = 37.6°

The measure of ∠U = 98°

The measure of ∠V = 37.6°

So , the measure of the third side of the triangles is

The measure of ∠S = measure of ∠T = 180 - ( 98 + 37.6 )

The measure of ∠S = measure of ∠T = 44.4°

And , ∆QRS ~ ∆TVU based on the angle-angle criterion

So , ∠Q ≅ ∠T based on the third angle theorem

And , ∆RQS ~ ∆VTU based on the angle-angle criterion

Hence , the false statement is ∠S corresponds to ∠V.

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Answer:

A =141.4875

Step-by-step explanation:

The area of a rectangle is given by

A = l*w

A = 16.17 * 8.75

A =141.4875

Answer:

x = -58.3

Step-by-step explanation:

6x - 15 + 365 - simplifly terms

6x + 350 = set to equal sides

6x = -350

x = -58.3

Answer:

D, "I will pay $25 for this book."

Step-by-step explanation

Answer:

(x-4)(x-6)

Step-by-step explanation:

By factorization, x^2-10x+24 can be written in the form (x-4)(x-6). Thus the roots of the quadratic equation are x= 4 and 6 respectively.

Answer:

25 hours

Step-by-step explanation:

$120 for every 10 hours

$12 for every hour

$300/12= 25 hours

Answer: 8

Step-by-step explanation:

Answer : The value of x and y is 8 and 10 respectively.

Step-by-step explanation :

As we known that if two parallel lines are cut by a transversal line then consecutive interior angles are supplementary.

From the given figure we conclude that:

[tex]5x-y+150=180[/tex]       ...........(1)

[tex]5x-y=180-150[/tex]

[tex]5x-y=30[/tex]      ............(2)

[tex]5x+y+130=180[/tex]       ...........(3)

[tex]5x+y=180-130[/tex]

[tex]5x+y=50[/tex]        ...........(4)

Now we adding equation 2 and 4, we get the value of x.

[tex]5x-y+5x+y=30+50[/tex]

[tex]10x=80[/tex]

[tex]x=8[/tex]

Now we are putting the value of x in 4, we get the value of y.

[tex]5x+y=50[/tex]

[tex]5(8)+y=50[/tex]

[tex]y=50-40[/tex]

[tex]y=10[/tex]

Therefore, the value of x and y is 8 and 10 respectively.

Answer:

The Answer is 2160000000

Answer:2160000000

Step-by-step explanation:

Answer:

it is D c= 180 + 50h + 20p

Step-by-step explanation:

c is the total cost and the boat is 180 but for additional hour it would be +$50

now the first four passenger is free but if another person comes on then it would be +$20 hope this help

The linear equation which describes the total cost of the rental is           c = 180 + 50h + 20p

The correct option is an option (D)

"It is an equation in which the highest power of the variable is always 1."

For given example,

The boat rental has a flat fee of $180 for up to three hours.

Fixed rental cost = 180                       ...............(1)

The boat rental has $50 per hour for each additional hour.

Let, h is each additional hour (over 3)

So, the rental cost for each additional hour = 50h               .............(2)

The first four passengers are included in this cost, but $20 is charged for each additional passenger.

Here, p is each additional passenger (over 4)

So, the rental cost for each additional passenger = 20p         ..................(3)

From (1), (2) and (3),

the required linear equation would be,

c = 180 + 50h + 20p

Therefore, the linear equation which describes the total cost of the rental is c = 180 + 50h + 20p

The correct option is an option (D).

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Answer:

C. 20

Step-by-step explanation:

105 + 9.5x = 14.75x

105 = 5.25x

20 = x

Answer:

The numbers are 19 and 71.

Step-by-step explanation:

Let x and y represent the two numbers.  Then x + y = 90.  

Also, if we assume that the larger number is y, then y = 3x + 14.

We must solve this system of linear equations.  Since we already have the result of solution for y  (y = 3x + 14), let's use the substitution method to find the solution:

x + y = 90 becomes x + 3x + 14 = 90, or:

4x = 76.  Thus, x = 76/4, or 19.       If x = 19, then y = 3(19) + 14, or y = 71.

The numbers are 19 and 71.

Note that these add up to 90, as they must, and that 71 is 14 more than 3 times 19.

Answer:

x=3

Step-by-step explanation:

If the triangles are congruent

13 = 4x+1

subtract 1 from each side

13-1 = 4x+1-1

12=4x

Divide by 4

12/4 = 4x/4

3=x

Answer:

3

Step-by-step explanation:

If the two triangles are congruent then:

13=4x+1

13-1=4x+1-1

12=4x

x=3

Hope this helps!

Answer:

m= 1/2

Step-by-step explanation:

Not sure if this is right but I hope this helps :)

Answer:

1/4

Step-by-step explanation:

We can see that two points on the line are (0, 4) and (4, 5). Using the slope formula (y₂ - y₁) / (x₂ - x₁) we get (5 - 4) / (4 - 0) = 1/4.

Step-by-step explanation:

For every 4 feet that the ladder rises, the bottom of the ladder should be 1 foot away from the wall. If you are going to climb onto a roof, the ladder should extend 3 feet higher than the roof. Also, the upper and lower sections of an extension ladder should overlap to provide stability

Solve:  2 ln 3 = ln(x - 4)

a)x = 9

b)x = 10    

c)x = 13

Answer:

x = 13

Step-by-step explanation:

To solve the problem above, we will follow the steps below;

2 ln 3 = ln(x - 4)

[using logarithm rule  aInb =  Inbᵃ]

so also our equation becomes

In 3² = In (x-4)

The In at the left-hand side of the equation will cancel-out the In at the right-hand side of the equation

Our equation becomes;

3² = x- 4

9 = x-4

add 4 to both-side of the equation in other to make x subject of the equation

9 + 4 = x-4 + 4

13 = x

x = 13

Answer:

C on Edge x = 13 x =  

-4  and x =  4

the solution is x =  4

Step-by-step explanation:

I just did the assignment on edge.

Answer:

I think that the ADA (Americans with Disabilities Act) has explicit regulations on slopes and ramps so that people with disabilities can go about their daily life easier, and to guarantee the safety and wellbeing of the disabled. If, for instance, a wheelchair ramp were too steep, there would be a danger of the wheelchair rolling down too quickly, or the person falling backward on their way up.

Answer:

$584.28

Step-by-step explanation:

first, add up the yards around the perimeter of the bakery. 10 + 10 + 17 + 17 = 54. Then, multiply 54 by 10.82 to get the cost of the shelf.

54 x 10.82 = 584.28

Answer:

1. - (C) 14

2. - (B) 4

3 - (A) 2/12

Answer:

All true

Step-by-step explanation:

By definition, an asymptote is a line at which the values of the function approach but never reach as one or both of the x or y coordinates tends to positive or negative infinity. Therefore, the graph of a rational function R never intersects any of its asymptotes.

Answer:

Below.

Step-by-step explanation:

Number is different to the other 2. Its value is +4 because negative 2 squared = + 4.

The other 2 have negative values and -2 = -(2) so they have the same value, -4.

The right answer is 280

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

Answer:

84 is 30% of 280

Step-by-step explanation:

Write and solve this equation:  84 = 0.30n, where n is the unknown number.

Then n = 84 / 0.30 = 280

84 is 30% of 280

Answer:

54

Step-by-step explanation:

90-36=54

Answer:

Angle X is 90-36 = 54 degrees

Answer: i hope this is correct take care

Step-by-step explanation:

Answer:

The three ways are;

1) Two stacks of six reams

2) Four stacks of three reams

3) Four stacks of three reams arranged two by two

Step-by-step explanation:

The parameters given are;

Dimensions of one ream of paper = 8.5 in. by 11 in. by 2 in.

The number of reams of paper = 12

The three unique ways are;

1) Two stacks of six reams

Box dimension = 6 × 2 in. by 2 × 8.5 in. by 11 in. = 12 in. by 17 in. by 11 in.

Box dimension of new box = 12 in. by 17 in. by 11 in.

2) Four stacks of three reams

Box dimension = 3 × 2 in. by 4 × 8.5 in. by 11 in. = 6 in. by 34 in. by 11 in.

Box dimension of new box = 6 in. by 34 in. by 11 in.

3) Four stacks of three reams arranged two by two

Box dimension = 3 × 2 in. by 2 × 8.5 in. by 2 × 11 in. = 6 in. by 17 in. by 22 in.

Box dimension of new box = 6 in. by 17 in. by 22 in.

Answer:

See the explanation

Step-by-step explanation:

We know that

f(x) = 2x⁶ + 3x⁴ - 4x³ + (1/x) - sin2x

Lets calculate the derivatives:

f'(x) = 6(2x⁵) + 4(3x³) - 3(4x²) -( 1/x²) - 2(cos2x)

f'(x) = 12x⁵ + 12x³ - 12x² - (1/x²) - 2cos2x

Similarly:

f''(x) = 60x⁴ + 36x² - 24x + (2/x³) + 4sin2x

f'''(x) = 240x³ + 72x - 24 - (6/x⁴) + 8cos2x

Rearrange:

f'''(x) - 240x³ +72x - (6/x⁴) + 8cos2x - 24

f''''(x) = 720x² + 72 + (24/x⁵) - 16sin2x

Rearrange:

f''''(x) = 720x² + (24/x⁵) - 16sin2x +72

Step-by-step explanation:

To find the answer, you would have to first put 2/5 in a decimal form. 2/5 in decimal form would be 40%. Now, it becomes easier to list the values.

Answer:

12.5%, 40%, 124.5%

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