Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A (4, 5), B (12,9); 3 to 1 The coordinates of P are:

Answer:

x=172°

Step-by-step explanation:

5x-11=3x-5

2x-11=5

2x=16

x=8

180-8=172

Answer: y = -4 + x/2

Step-by-step explanation:

The theorem that justifies that the pair of triangles are congruent is: AAS.

The AAS is known as the angle-angle-side congruence theorem, which justifies why two triangles that have a pair of non-included congruent side and two pairs of corresponding congruent sides.

The diagram shows that the two triangles have two corresponding congruent angels that are marked, and they share a common side, which means they have a pair of non-included congruent sides.

This goes to show that the criterion for proving that the two triangles are congruent by the AAS are already given and known.

Therefore, the triangles are congruent to each other by the AAS congruence theorem.

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Answer: 4 gallons

Step-by-step explanation:

The boat can travel 228 miles on 19 gallons of gasoline. We can divide 228 by 19 to find out how many miles the boat can travel on 1 gallon of gasoline, which is 12. For the boat to go 48 miles, we can divide 48 by 12 to get the answer, which is 4. The boat can travel 48 miles with 4 gallons of gasoline.

a) (2, -2)

answer: the ordered pair is not a solution of the given system

b) ( -1, 5)

answer: the ordered pair is a solution of the given system

Answer:

============================

The total deposit over 12 weeks:

Equation in general form:

Answer:

Step-by-step explanation:

Find the number that makes the ratio equivalent to 3:5

6:10

9:15

12:20

In linear equation, If the person doesn't attend any events, n = 0, and the price stays at 10, therefore f(n) = 10 + 2n.

What in mathematics is a linear equation?

To describe the cost of attending n events, create an equation using function notation.

A 10 dollar entrance fee is required each time, and a further 2 dollars must be paid for each unique exhibit that a visitor chooses to visit.

The function, which would depend on n events, is

If the person doesn't attend any events, n = 0, and the price stays at 10, therefore f(n) = 10 + 2n.

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The unknown value from the given linear expression is 1/4

Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5.

When an equation is given in this format, finding both intercepts is rather simple (x and y).

Given the equation below;

6 = 12k * 2

6 = 24k

Divide both sides by 24

24k = 6

k = 6/24

k = 1/4

Hence the value of k from the given expression is 1/4

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The total cost of fencing the garden will be 3x+200 where x is the perimeter of garden that is variable according to the length and breadth of the garden.

Distance is measured in length. Length has the dimension of distance in the International System of Quantities. The majority of measurement systems choose a base unit for length from which all other units are derived. The metre serves as the foundational unit of length in the International System of Units.

A closed path that encompasses, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations.

Here,

Let x be the perimeter to be fenced.

the cost is 3 rupees per meter.

so the equation will be= 3x+200

The total cost of fencing the garden will be 3x+200, where x is the garden's perimeter and is dependent on the garden's length and width.

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Answer:

92

Step-by-step explanation:

  1

 46

x  2

 92

Answer:

A: A unique triangle

B: A unique triangle

C: More than a triangle

Answer:

2[tex]\sqrt{3}[/tex]

Step-by-step explanation:

[tex]\frac{6}{\sqrt{3} }[/tex]  They do not want a radical in the denominator.  So you need to multiple the numerators and the denominator by [tex]\sqrt{3}[/tex]

[tex]\frac{6}{\sqrt{3} }[/tex]  x  [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex]  = [tex]\frac{6\sqrt{3} }{3}[/tex] = 2[tex]\sqrt{3}[/tex]

[tex] \frac{6}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } = \frac{6 \sqrt{3} }{3} = 2 \sqrt{3} [/tex]

hope it will work

The length of the diagonal of the Triangle is 14.86 units

What is Diagonal?

When two polygonal vertices are not on the same edge, a diagonal is a line segment connecting them. Any sloping line is known as a diagonal informally.

Given,

Area of Rectangle = 110square units

Length = 11units

Breadth = ?

Area of Rectangle = length x breadth

Breadth = Area of Rectangle / length

Breadth = 110 / 11

Breadth = 10units

Length of diagonal (Pythagoras Theorem)

H^2 = P^2 + B^2

H^2 = (11)^2 + (10)^2

H^2 = 121 + 100

H^2 = 221

H = [tex]\sqrt{221}[/tex]

H = 14.86 units

Hence, The length of its diagonal is 14.86 units

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Answer:

7.3units

Step-by-step explanation:

[tex] \sqrt{(x2 - x1) {}^{2} + (y2 -y1) {}^{2} } [/tex]

[tex] \sqrt{ (- 1 - 6) { \\ }^{2} + (14 - 16) {}^{2} } [/tex]

[tex] = 7.3[/tex]

The amount of water left in the bathroom is 0.93 gallons

From the question, the given parameters are:

The amount of water left is the difference between the total amount of water in the bathroom  and the amount of eater drained out

This is represenetd as

Amount left = Total amount of water in the bathroom - Amount of eater drained out

Substitute the known values in the above equation

Amount left = 7.2 - 6.27

Evaluate

Amount left = 0.93

Hence, the amount left is 0.93 gallons

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The required measure of the volume of water left in the bathtub is 0.93 gallons.

As per the given data, There were 7.2 gallons of water in Sandra's bathtub. Then 6.27 gallons drained out. How much water is left in the bathtub is to be determined.

Here,
According to the question, the water left after the 6.27 gallons of draining out can be evaluated by the arithmetic subtraction of the initial volume to the volume that drained out, that is,
The volume of water left in the tub  = 7.2 - 6.27 = 0.93.

Thus, the required measure of the volume of water left in the bathtub is 0.93 gallons.

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Answer:x-intercepts (5,0)

y-intercepts (0,-5)

Step-by-step explanation: To find the x-intercept substitute in 0 for y and solve for x. to find the y-intercept subsitute 0 for x and solve for y

In the absence of ATC restriction on climb or descent, and aircraft are within 1,000 feet of assigned altitude. pilots should attempt to both climb and descend at a rate of between 500 fpm and 15000 fpm. (Option A)

An Air Traffic Controller (ATC) clearance refers to an authorization by ATC for the purpose of preventing known aircraft collision. The rate of climb or descend expected by ATV is when an aircraft is within 1000 feet of assigned altitude, descend, or climb at an optimum rate consistent with the operating characteristics of the aircraft to 1,000 feet above or below the assigned altitude, and then attempt to descend or climb at a rate of between 500 and 1,500 fpm until the assigned altitude is reached.

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Answer:

I think it's 4 on the left and 5 on the right side

Step-by-step explanation:

4*4*4=64

and

5*5*5=125

Given that April has 30 days, Luke used, on average, 20.05 kilowatt-hours of electricity per day during April.

The average is the mean value obtained by dividing the total value of a data set by the number of items.

In this situation, we can divide the total electric bill for April by 30 to obtain the average daily charge.

In addition, we can divide the average charge per day by the cost per kilowatt-hour to obtain the number of kilowatt-hours used per day.

The total electric bill for April = $84.21

The charge per kilowatt-hour (kWh) = $0.14

The number of days in April = 30

The bill per day = $2.807 ($84.21/30)

The kilowatt-hours per day = 20.05 kWh ($2.807/$0.14)

Thus, Luke used an average of 20.05 kilowatt-hours per day in April.

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Take into account that the slope of a line is given by the following formula:

where (x1,y1) and (x2,y2) are two points on the line.

In this case:

(x1,y1) = (p,3)

(x2,y2) = (6,p)

By replacing the previous values into the formula for m, we get:

Now, by making m = 2 and solving for p, we obtain:

Hence, the value of p is p = 5

Answer:

2,500

Step-by-step explanation:

1cm=50km

50cm*50km=2500km

Answer:

2500 km

Step-by-step explanation:

If 1 cm is equal to 50 km, we can multiply the 1 cm by 50 to get 50 cm. In order to do this, we also have to multiply the 50 km (which was equal to the 1 cm) by 50 as well.

50 x 50 = 2500

Whatever we do to one side, we have to do to the other to make it equivalent.

The pre-tax subtotal was $171.00.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that:

After-tax total = $1,656.99

Tax rate in the area = 8.396%

The pre-tax price would be 100% and this tax rate is an addition.

Total percent = (100+8.396)% = 108.3%

Consider x be the pre-tax amount.

The total bill=  (after-tax total) = (pre-tax subtotal) + 8.3% · (pre-tax subtotal)

 (after-tax total) = (pre-tax subtotal) 108.3

Divide by the coefficient on the right;

 (pre-tax subtotal) = (after-tax total)/108.3

= $1,656.99/108.3

= $171.00

Therefore, The pre-tax subtotal was $171.00.

The pre-tax amount was $130.

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The equation of the line is y = x - 8 which passes through the point  (13,5) with slope 1.

We have to determine the equation of a line that passes through the point (13,5) with slope 1.

The slope of a line is defined as the angle of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

Let the required line would be as

⇒ y - y₁ = m (x - x₁ )

The required line passes through the point (13, 5)

Here x₁ = 13 and y₁ = 5 and m = 1

Substituting these inputs into the above equation obtains the line equation.

⇒ y - 5 = (1)(x - 13)

⇒ y - 5 = (x - 13)

⇒ y = x - 13 + 5

⇒ y = x - 8

Thus, the equation of the line is y = x - 8 which passes through the point (13,5) with slope 1.

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Answer:B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Least number (sample size) of viewers that should be randomly selected to ensure that a 95% confidence interval for the true proportion of viewers will have a width of 0.06 or less is 225.

E = 0.06,

P = 0.30

c= 95%

& = 1 - 0. 95

To x/2 = 0-025

21096*/ 2 = 0-025

Margin of error

P ( 1 - P )

To ac / 2 ) 2 P ( 1 - P )

E= ( 1. 96* 0 . 30 x ( 1 - 0 - 30 )0-06

=224.09 ~ 225

round to next number

225

In order to guarantee that a 95% confidence interval for the true proportion of viewers would have a width of 0.06 or less, the minimum number of viewers (sample size) that should be chosen at random is 225.

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Answer:

Step-by-step explanation: f(x) =2-5x

2-5(-2)=12

2-5(-1)=7

2-5(0)=2

2-5(1)= -3

2-5(2)-8

I hope this helps. All you have to do is plug in the numbers in the equation for x and then solve!