Consider the diagram.

Triangles L O N and L M N share side L N. Sides O L and M L are congruent. Sides O N and N M are congruent.

The congruence theorem that can be used to prove △LON ≅ △LMN is
SSS.
ASA.
SAS.
HL

The integer represent the balance in your account is Z = + Y. The representation of integer is positive because withdrawal is always less then or equal to the amount present in the bank account.

Total rupees withdraw from saving account is $149

Let total amount in account before withdrawing is X= $500

Amount left after withdraw the money is calculated by a

AMOUNT LEFT = TOTAL AMOUNT - WITHDRAW AMOUNT

So, put the values then

Y= X($500) - $149

Y= $500 - $149

Y= $351

If we represent the balance of saving account in the integer form then it become the Z = + Y. The representation of integer is positive because withdrawal is always less then or equal to the amount present in the bank account.

So, The integer represent the balance in your account is Z = + Y. The representation of integer is positive because withdrawal is always less then or equal to the amount present in the bank account.

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The distance from Bobby to the plane is 154.7 yards.

Sine law can be used to find the distance of the plane to Bobby.

Therefore,

x / sin 40 = 240 / sin 95

cross multiply

Hence,

x sin 95 = 240 sin 40

divide both sides by sin 95

x  =  240 sin 40 / sin 95

x = 240 × 0.64278760968 / 0.99619469809

x = 154.08 / 0.9961

x = 154.683264732

x = 154.7 yards

Therefore, the distance from Bobby to the plane is 154.7 yards.

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The length of the rectangle is 8m and width of the rectangle is 7m

Given that the length and width of a rectangle are consecutive integers

Let the length of the rectangle be x+1 meter

Let the breadth of the rectangle be x meter

Also given that perimeter of the rectangle is 30 meters

To find length and breadth of the rectangle

We know that perimeter of the rectangle is P = 2 (l+b)

30 = 2 (x+x+1)

15 = 2x + 1

2x = 14

x = 7

x+1 = 8

Hence, the length of the rectangle is 8m and width of the rectangle is 7m

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The first four terms of the sequence are 6, -24, 96 and -384

How to determine the first four terms?

The sequence is given as:

an=6(-4)^n-1

When n = 1, we have:

a(1)=6(-4)^(1-1)

This gives

a(1) = 6

When n = 2, we have:

a(2)=6(-4)^(2-1)

This gives

a(2) = -24

When n = 3, we have:

a(3)=6(-4)^(3-1)

This gives

a(3)=96

When n = 4, we have:

a(4)=6(-4)^(4-1)

This gives

a(4)=-384

Hence, the first four terms of the sequence are 6, -24, 96 and -384

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Answer:

y = -x + 1

(Image of what graph looks like is attached)

Step-by-step explanation:

x = 1 - y can be rewritten into y = mx + b format.

x = 1 - y (subtract 1 from both sides)

x - 1 = -y (multiply by -1 to both sides)

y = -x + 1

Brainliest, please :)

Answer:

Complementary angles are:

∠ORS and ∠SRQ

Supplementary angles are:

∠ORP and ∠PRQ

Using the cosine ratio, the value of AD in the diagram is: 2√3π in.

If we have the following given in a right triangle like triangle ADC in the diagram:

AC = 4π (hypotenuse)

AD = ? (adjacent side)

The cosine ratio, CAH would be applied, which is:

Cos 30 = adjacent/hypotenuse

Cos 30 = AD/4π

AD = cos 30 × 4π = √3/2 × 4π [cos 30 = √3/2]

AD = 2√3π in.

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The graph has been shifted to the left and moved up and stretched as scaling is done ,

Reflecting , Rotating , Dilating a function to form a new function is called Transformation.

The graph of the function f(x) = 1/ x is given

and a transformed function is given

The graph has been shifted to the left and moved up and stretched as scaling is done ,

Therefore three types of transformation are done on the parents function.

The transformation can be seen through the graph attached.

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Answer:

x=7 and x = 1

Step-by-step explanation:

This is pretty much a quadratic in disguise.
If we multiply both sides by x, we get:
x^2-7=6x
move 6x to the left
x^2-6x-7 = 0
We can either use the quadratic formula, or we can use factoring.
with factoring*, we get:
(x-7)(x+1) = 0 , and so the solution to the equation is x=7, and x=-1

*in a equation: x^2+ax+b = (x+c)(x+d), c+d equals a, and c*d equals b

On to the quadratic formula, a=1, b=-6, and c=-7, so:
(6±sqrt(36+4*7))/2 = x
=(6±8)/2
=3±4
x=7 and x = 1

Let x = number of hours washing cars

Let y = number of hours landscaping

System of equations:

[tex]10x+8y=84\\\\x=2y[/tex]

Answer:

B. 44.93

Step-by-step explanation:

The law of sines states
[tex]\frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}[/tex]

where a, b and c are the 3 sides of the triangle and A is the angle opposite side a, B the angle opposite side b and C the angle opposite side c

In this particular problem we have

side a = 44, angle A = 46.7
side c = ? , angle C = 48

So 44/sin(46.7) = c/sin(48) or by multiplying both sides by sin(48)

c = sin(48) * 44/sin(46.7)  = 44.92937 which is 44.93 rounded to 2 decimal places

Answer:

40 people

Step-by-step explanation:

480.80 times 40 this equals 19,220

Answer:

Yes

Step-by-step explanation:

To find out whether or not a graph is a function, we can do the vertical line test. If the vertical line only touches one point, then the graph is a function. This is because in a function, an input can only have one output.

Answer:

ksb said did bud did did it did did gc victory in suf did did zudbxudng jc fn facing did fjgduf bdyrut during their fyrhfb hi f f7djdufj fhdf. Is A

Step-by-step explanation:

x + 2x + 7x

72 = 9x

72 - 9 = x

63 = x

63 ÷ 3 = 21

piece 1 = 21

piece 2 =21+2 = 23

piece 3 =21+7 = 28

21+23+28 = 72 This proves the above is correct.

Answer: No

Step-by-step explanation:

The sum of the interior angles of a polygon with n sides is given by [tex]180(n-2)[/tex]. Setting this equal to 850 degrees,

[tex]180(n-2)=850\\\\n-2=\frac{85}{18}\\\\n=\frac{121}{18}[/tex]

Since this gives n to be a non-integer value, this is an impossible situation since a polygon must have an integer number of side lengths.

Answer:

V = 343

Step-by-step explanation:

V = lwh

= 7(7)(7)

= 49(7)

= 343

The total weight of the packed box is 9 lb 6 oz

According to question:

The weight of 12 jars is 12 times the weight of one jar

The weight of jars and box together is the sum of those weights.

... 12 × (10 oz) + 1 lb + 14 oz = 1 lb + 134 oz

... = 1 lb + 8 × (16 oz) + 6 oz . . . . . . 1 lb = 16 oz

... = 9 lb 6 oz

1 ounce (oz) is equal to 0.0625 pounds (lb).

1 oz = (1/16) lb = 0.0625 lb

The mass m in pounds (lb) is equal to the mass m in ounces (oz) divided by 16:

m(lb) = m(oz) / 16

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Answer:

The new store will have a profit of $5400 after its fifth month.

(R-C)(x) = (x²+5x+14)-(x²-4x+5) = x²-x²+5x--4x+14-5 = 5x+4x+14-5=9x+9

(Use 5 for x)

(R-C)(5) = 9(5) + 9 = 45+9 = 54

Step-by-step explanation:

[tex]10x+45 > 120\\10x+45-45 > 120-45\\10x > 75\\\frac{10x}{10} > \frac{75}{10} \\x > 7.5[/tex]

Therefore, Mel has to work at least 7.5 hours or 8 total hours.

The required equation of parabola is y = (-1/4)(x-9)² +4

What is a Parabola ?

A parabola is a U shaped Curve , whose all point are at same distance from a point called as Focus and a line called as Directrix.

Let (x,y) be any point on the parabola.

the distance between (x,y) and the focus and the distance between (x,y) and directrix is equal.

The focus is at (9,0) and a directrix at y= - 4

[tex]\rm \sqrt {(x-9)^2 + (y -0)^2[/tex]  = | y +4|

[tex]\rm {(x-9)^2 + (y -0)^2 = (y-4)^2[/tex]

(x-9)²  + y² = y² +16 -4y

On solving this

4y = - (x-9)² +16

y = (-1/4)(x-9)² +4

Therefore this is the required equation of parabola .

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Answer: 9

Step-by-step explanation:

[tex](f \circ g)(0)=f(g(0))\\\\g(0)=2\\\\\implies f(g(0))=f(2)=\boxed{9}[/tex]

The graph which represents the rational function is; On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 2, and the horizontal asymptote is at y = 3.

It follows from the task content that the rational function given is; f(x) = 3x-2/x-2.

Hence, since the numerator and denominator polynomials are of the same order, it follows that the horizontal asymptote is the quotient; 3/1 = 3.

Additionally, the vertical asymptote of the function is the value of x which renders the denominator equal to 0 and consequently, the function undefined.

Hence, x -2 = 0 and x= 2.

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Answer: THE PERSON ABOVE IS CORRECT!!

The answer is D.) On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 2, and the horizontal asymptote is at y = 3.

Answer:

a = -4

b=-29

Step-by-step explanation:

First write the radicals in simplest form.

i² = -1

[tex]\sf (4 + \sqrt{-49}) -2\left(\sqrt{(-4)^2}+\sqrt{-324}\right)=4 + \sqrt{49i^2} - 2\left(\\\sqrt{16}+\sqrt{324i^2}\right)[/tex]

                                                          [tex]\sf =4 + \sqrt{7*7*i*i}-2\left(\sqrt{4*4}+\sqrt{18*18*i*i}\right)\\\\= 4 + 7i - 2(4 + 18i)\\\\= 4 + 7i - 2*4 - 2*18i\\\\= 4 + 7i -8-36i\\\\= 4 - 8 +7i - 36i\\\\= -4 - 29i[/tex]

   [tex]\sf \boxed{a = -4 }\\\\\boxed{b=-29}[/tex]

The rate charged by first mechanic is $45 per hour and the rate charged by second mechanic is $50 per hour.

Given mechanic first worked 20 hours and mechanic second worked 15 hours and they charged $1650. The sum of rates of first mechanic and second mechanic is $95 per hour.

let the rate charged by first mechanic be x .

let the rate charged by second mechanic be y.

According to question

x +y=95-----------1

20x+15y=1650----------2

Multiply equation 1 by 20 and subtract equation 2 from 1.

20x+20y-20x-15y=1900-1650

5y=250

y=50

put the value of y=50 in 1 to get the value of x.

x +y=95

x+50=95

x=95-50

x=45

Hence the rate charged by first mechanic is $45 per hour and the rate charged by second mechanic is $50 per hour.

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Question is incomplete as it should be as under:

Two mechanics worked on a car, the first mechanic worked 20 hrs. and the second mechanic worked 15 hours together. They charged a total of $ 1650.  What is the rate charged per hour for each mechanic if the sum of the two rates per hour was $95 per hour?

here u go hope this helps

Answer:

Tan p is 20/21

Tan q is 21/20

Step-by-step explanation:

Tan is short for tangeant.

tangeant means opposite/adjacent

the opposite of vertices p is 20.

the adjacent of vertices p is 21.

so tan p= 20/21

The opposite of vertices q is 21

the adjacent of vertices q is 20

so tan q is 21/20

Answer:Jared has earned 23% of the $52 he needs to buy a new jacket. Find 23% of $52.Which expression can you use to find 23% of 52? ✔ 0.23 × 5223% of $52 is $✔ 11.96.An easy way to check your answer is to use the friendly ✔ 25%and divide 52 by ✔ 4to get ✔ 13

Step-by-step explanation:

Answer:

c = 75.36 cm

Step-by-step explanation:

The equation of the circumference is:

[tex]c=\pi d[/tex]  In which "d" represents the measurement of the diameter

in this case d= 24cm, π = 3.14

Calculate the circumference:

[tex]c=\pi d=(3.14)(24)=75.36cm[/tex]

Hope this helps

A circle has a diameter of 24cm. The circumference of the circle is c = 75.36 cm.

The circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.

The circumference of the circle = 2πr

Given information;

A circle has a diameter of 24cm.

"d" represents the measurement of the diameter, so

d= 24cm, π = 3.14

Radius = d/ 2 = 12

Calculate the circumference:

The circumference of the circle = 2πr

= 2 ( 3.14 ) ( 12)

= 75.36

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The sale price of the car as a percentage of the original price is 142%

Sale price as a percentage of the original price = sale price / buying price

= 1280/900 × 100

= 1.42222222222222 × 100

= 142.22%

Approximately,

142%

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