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Answer:

Option C. 4 units

Step-by-step explanation:

As we know median of a triangle intersect each other at a point in the ratio of 2.01.

Therefore, in Δ QNL,

[tex]\frac{NS}{SR}[/tex] = [tex]\frac{2}{1}[/tex]

[tex]\frac{(7x-3)}{(5x-3)}[/tex] = [tex]\frac{2}{1}[/tex]

By cross multiplication

(7x - 3) = 2(5x -3)

7x - 3 = 10x - 6

6 - 3 = 10x - 7x

3 = 3x

x = 1

Now length of NS

= (7x - 3)

= (7 × 1 - 3)

= (7 - 3)

= 4 units

Option C. 4 units is the answer.

To compute for distance from a to b:

Distance A = 4 miles, base of triangle formed between a and b

Distance B = 3 miles, height of triangle formed between a and b

Distance AB = (A^2 + B^2)^0.5    hypotenuse of triangle formed between a and b, or square root of (A^2 + B^2)

Distance AB = ((4)^2 + (3)^2)^0.5

Distance AB = (16 + 9)^0.5

Distance AB = (25)^0.5

Distance AB = 5 miles

To compute for distance from b to where bank employee got stuck

BC = distance from b to c

BC  = 4 miles

Total distance driven by bank employee

= AB + 0.5(BC)

= 5 + 0.5(4)

= 5 + 2

= 7 miles, total distance driven by the bank employee

Answer:

The minimum total distance the employee may have driven before getting stuck in traffic is 9.0 miles.

Step-by-step explanation:

Given information: a(−3, 1), b(2, 4), and c(4, −2).

On a town map, each unit of the coordinate plane represents 1 mile.

Distance formula:

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

Distance between bank a and bank b is

[tex]ab=\sqrt{(2-(-3))^2+(4-1)^2}[/tex]

[tex]ab=\sqrt{(5))^2+(3)^2}[/tex]

[tex]ab=\sqrt{25+9}[/tex]

[tex]ab=\sqrt{34}[/tex]

Distance between bank b and bank c is

[tex]bc=\sqrt{(4-2)^2+(-2-4)^2}[/tex]

[tex]bc=\sqrt{(2)^2+(-6)^2}[/tex]

[tex]bc=\sqrt{4+36}[/tex]

[tex]bc=\sqrt{40}[/tex]

[tex]bc=2\sqrt{10}[/tex]

A bank employee drives from branch a to branch b and then drives halfway to branch c before getting stuck in traffic. It means total distance employee may have driven before getting stuck in traffic is

[tex]Distance=ab+\frac{1}{2}bc[/tex]

[tex]Distance=\sqrt{34}+\frac{1}{2}(2\sqrt{10})[/tex]

[tex]Distance=\sqrt{34}+\sqrt{10}[/tex]

[tex]Distance=8.99323[/tex]

[tex]Distance\approx 9.0[/tex]

Therefore the minimum total distance the employee may have driven before getting stuck in traffic is 9.0 miles.

Answer:

{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)}

Step-by-step explanation:

{(2, –2), (1, 5), (–2, 2), (1, –3), (8, –1)} is not a function because 1 have two different images.

{(6, 8), (5, 2), (–2, –5), (1, –3), (–2, 9)} is not a function because -2 have two different images.

{(–3, 1), (6, 3), (–3, 2), (–3, –3), (1, –1)}  is not a function because -3 have two different images.

{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)} is a function because all x values has one only image value.

In the stated experiment, the weight gain of the ten-year-old boys is the dependent variable. It is expected to change based on the consumption of doughnuts, which is the independent variable.

In the study described, where a group of ten-year-old boys are fed doughnuts every morning for a week and then weighed to see how much weight they gained, the dependent variable is the weight gain of the boys. The dependent variable is the outcome that is measured in an experiment or study. It is the factor that is expected to change as a result of changes to the independent variable, which in this case is the eating of doughnuts.

The dependent variable depends on the independent variable. For example, if the independent variable is the number of doughnuts eaten, the dependent variable (body weight) would likely change in response to the number of doughnuts consumed.

To illustrate this further, if we were to create a graph with the number of doughnuts eaten (independent variable) on the x-axis and the weight gained (dependent variable) on the y-axis, we could see if there is an exponential relationship or a different kind of correlation between these two variables. By understanding the dependent and independent variables, we can better interpret the results of studies and experiments.

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The equation of the circle is: is (x - 4)² + (y - 4)² = 16 Option A

To find the equation of a circle tangent to the x-axis at (4, 0) and tangent to the y-axis at (0, 4)

Let's use the general form of the equation for a circle:

(x - h)² + (y - k)² = r²

Where (h, k) is the center of the circle, and r is the radius.

The center of the circle is (4, 4) because it's tangent to both the x-axis and y-axis at 4.

The radius can be found by the distance from the center to the point (4, 0) (which is on the x-axis):

r = √((4 - 4)² + (0 - 4)²) = √(0 + 16) = √16 = 4

So the equation of the circle is:

(x - 4)² + (y - 4)² = 4²

(x - 4)² + (y - 4)²= 16

The correct option is: a) (x - 4)² + (y - 4)² = 16

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Answer:

The equation that represents the relationship between the number of tigers and the total number of square feet of space is f = 1,000t.

Step-by-step explanation:

add the 2 numbers together

40 + 90 = 130 degree range

The quadratic equation x^2 - 4x + 4 = 0 has one real number solution, x = 2, which is a repeated solution since the discriminant of the equation is zero.

To determine the number of real number solutions for the equation x2
- 4x + 4 = 0, we can use the discriminant method. The discriminant D of a quadratic equation ax2 + bx + c = 0 is given by b2 - 4ac. For our equation, a = 1, b = -4, and c = 4.

Calculating the discriminant gives us D = (-4)2 - 4(1)(4) = 16 - 16 = 0. Since the discriminant is equal to zero, it indicates that there is exactly one real number solution, which means the quadratic has a perfect square trinomial, or the two real solutions are identical.

In this case, the solution to the equation can be found by factoring the quadratic as (x - 2)2 = 0, which implies that x = 2. Therefore, the equation x2 - 4x + 4 = 0 has one real solution, x = 2, which is repeated.

The coordinates of the point are x=3 / 4, y = 3 / 4, and z = 3 for the plane.

A plane is a two-dimensional Euclidean surface that extends indefinitely in mathematics. A plane is the two-dimensional equivalent of a point, a line, and space.

Given that the points are x = 3t, y = 3t and z = 4t. The equation of the plane is 6x + 6y -8z = 1.

Substitute the value of x,y, and z in the equation and solve for the value of 't'.

6x + 6y -8z = 1.

6 x 3t + 6 x 3t - 8 x 4t = 1

18t + 18t - 32t = 1

4t = 1

t = 1 / 4

The coordinates will be calculated as,

x = 3t = 3 x 1 / 4= 3 / 4

y = 3t = 3 x 1 / 4= 3 / 4

z = 4t = 4 x 3 / 4 = 3

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Answer:

The answer is 1.

Step-by-step explanation:

Took the test.

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 

                     3/x-1-5*x/x+2-(1/4)=0 

 4.1   Subtracting a whole from a fraction 

Rewrite the whole as a fraction using  x  as the denominator :

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole 

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

 4.2       Adding up the two equivalent fractions 
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 5.1   Subtracting a whole from a fraction 

Rewrite the whole as a fraction using  x  as the denominator :

 5.2       Adding up the two equivalent fractions 

 6.1   Adding a whole to a fraction 

Rewrite the whole as a fraction using  x  as the denominator :

 7.1     Pull out like factors :

   3 - 6x  =   -3 • (2x - 1) 

 7.2       Adding up the two equivalent fractions 

 8.1    Find the Least Common Multiple 

      The left denominator is :       x 

      The right denominator is :       4 

      Least Common Multiple: 
      4x 

 8.2    Calculate multipliers for the two fractions 


    Denote the Least Common Multiple by  L.C.M 
    Denote the Left Multiplier by  Left_M 
    Denote the Right Multiplier by  Right_M 
    Denote the Left Deniminator by  L_Deno 
    Denote the Right Multiplier by  R_Deno 

   Left_M = L.C.M / L_Deno = 4

   Right_M = L.C.M / R_Deno = x

 8.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)2   and  (y2+y)/(y+1)3  are equivalent as well. 

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

 8.4       Adding up the two equivalent fractions 

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

Now, on the left hand side, the  4x  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   12-17x  = 0

 9.2      Solve  :    -17x+12 = 0 

 Subtract  12  from both sides of the equation : 
                      -17x = -12 
Multiply both sides of the equation by (-1) :  17x = 12 


Divide both sides of the equation by 17:
                     x = 12/17 = 0.706 

The inequality 5x-(x+2)>-5(1+x)+3 simplifies to x>5/9 after combining like terms and isolating x. Therefore, any x greater than 5/9 is a solution, including x=1, which satisfies the inequality.

To find a particular solution to the inequality 5x-(x+2)>-5(1+x)+3, we first simplify both sides of the inequality:

5x - x - 2 > -5 - 5x + 3

This further simplifies to:

4x - 2 > -5x + 3

Next, we add 5x to both sides and add 2 to both sides to get:

9x > 5

Now, we divide both sides by 9 to isolate x:

x >  5/9

Therefore, any x greater than 5/9 is a particular solution to the original inequality. For example, x=1 is such a solution, as it satisfies the inequality:

5(1) - ((1)+2) > -5(1+(1)) + 3

That simplifies to:

5 - 3 > -5(2) + 3

2 > -10 + 3

2 > -7, which is true, thus confirming x=1 is a solution.

Answer:

x = 2.7

Step-by-step explanation:

To find x

1) 1.89 ÷ 0.7 = 2.7

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