Two drivers moving in opposite directions on an 18-mile circular racetrack cross each other at a certain point. If one of them has an average speed of 1.2 miles per minute and the other has an average speed of 1.8 miles per minute, how many minutes will it take for them to cross each other again?

Answer:

0.40x=1900

Step-by-step explanation:

Answer:

Since it's increasing add 3.5% to 100%

= 103.5% of £16470.45

= 103.5/100 × 16470.45

= 17046.92

= £17046.92

Hope this helps.

Answer:

Ratio of sandwiches with white bread and brown bread is 10:3. Of the white sandwiches 2/3 are vegetarian, of the sandwiches that are brown half are vegetarian. What fraction of the sandwiches are vegetarian?

Step-by-step explanation:

Givens

The ratio between white bread and brown bread is 10:3, that is, for every 10 white bread, there are 3 brown bread.

2/3 of white sandwiches are vegetarian.

1/2 of brown sandwiches are vegetarian.

We know that white bread is represented by 10, and brown bread is represents by 3. So, 2/3 of 10 are vegetarians, and 1/2 of 3 are vegetarians. The sum of them is

2/3 of 10 are vegetarians = [tex]\frac{2}{3} \times 10 = \frac{20}{3}[/tex]

1/2 of 3 are vegetarians = [tex]\frac{1}{2} \times 3 = \frac{3}{2}[/tex]

[tex]=\frac{20}{3}+\frac{3}{2}\\\\=\frac{40+9}{6}\\\\=\frac{49}{6}[/tex]

Therefore, 49/6 represents all the sandwiches which are vegetarian.

Answer:

1. 35 km

2. 1 cm to 5m

3. 6 cm

4. [tex]42^\circ[/tex]

5. 16.73 m

Step-by-step explanation:

Solution 1.

Reading of map scale = 1cm:5km

i.e. 1 cm is equivalent to 5 km

Measurement of map  = 7 cm

Actual distance = Measurement of map [tex]\times 5[/tex]

Actual distance = 7 [tex]\times 5[/tex] = 35 km

-------------------

Solution 2.

Length of dining hall = 35 m

Measurement of map = 7 cm

Scale = Measurement of map : Length of dining hall (i.e. ratio)

Scale = 7 cm :35 m = 1 cm : 5 m

-------------------

Solution 3.

Length of building = 30 m

Scale = 1 cm to 5m

5 m is equivalent to 1 cm on scale

1 m is equivalent to [tex]\frac{1}{5}[/tex] cm on scale

30m is equivalent to [tex]\frac{1}{5} \times 30[/tex] = 6 cm on scale

-------------------

Solution 4.

Angle of elevation of A from B = [tex]42^\circ[/tex]

Angle of depression of B from A = ?

Please refer to the image attached, we can clearly observe that both the angles (i.e. angle of elevation from A to B and angle of depression from B to A )will be equal.

Angle of depression of B from A = [tex]42^\circ[/tex]

-------------------

Solution 5.

Given that:

String length, or hypotenuse of triangle BC= 25 m

Angle of string with horizontal, [tex]\angle B = 42^\circ[/tex]

Please refer to the attached image for the clear understanding of the situation.

To find:

Height, AC = ?

We can use trigonometric identity:

[tex]sin\theta = \dfrac{Perpendicular}{Hypotenuse}[/tex]

OR

[tex]sinB = \dfrac{AC}{BC}\\\Rightarrow sin42^\circ = \dfrac{AC}{25}\\\Rightarrow AC = 25 \times 0.67\\\Rightarrow AC = 16.73 m[/tex]

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

So, the answers are:

1. 35 km

2. 1 cm to 5m

3. 6 cm

4. [tex]42^\circ[/tex]

5. 16.73 m

Answer:

8

Step-by-step explanation:

h(t) = -t + 3;

h(-5)

Let t = -5

h(-5) = - -5 +3

       = 5+3

       = 8

Answer:

8

Step-by-step explanation:

h(t) = -t + 3

Put t as -5 in the function.

h(-5) = -(-5) + 3

The negative signs cancel.

h(-5) = 5 + 3

Add both the terms.

h(-5) = 8

Answer:

150

Step-by-step explanation:

Step 1: Plug in what we know

5x + 10(5) = 800

Step 2: Solve for x (smaller cars)

5x + 50 = 800

5x = 750

x = 150

Answer:

150

Step-by-step explanation:

:)

Answer:

49

Step-by-step explanation:

Add then subtract

Answer:

$ 21

Step-by-step explanation:

Money spent = (2/5) * 60 + (1/4) * 60

                      = 2*12 + 1*15

                      = 24 + 15

                      = $ 39

Money save = 60 - 39 = $ 21

Answer:

The answer is C, 60 degrees.

Step-by-step explanation:

Answer:

apparently just label each part ( a, b, c, d, so on) and tell the order/ switch em around

Step-by-step explanation:

Answer:

area = 4cm2

Step-by-step explanation:

the area of triangle is gotten by 1/2bh

1/2 × 2 × 4 = 4.

base is 2cm because it has covered 2 grids while the height is the measure from the base to the tip of the triangle, which is 4cm.

area of square is L × L

2 by 2 = 4.

so, the two shapes have same area.

Answer:

([tex]\frac{13}{5}[/tex] , [tex]\frac{6}{5}[/tex] )

Step-by-step explanation:

Given the 2 equations

2x - y - 4 = 0 → (1)

3x + y - 9 = 0 → (2)

Adding the 2 equations term by term will eliminate the term in y, thus

5x - 13 = 0 ( add 13 to both sides )

5x = 13 ( divide both sides by 5 )

x = [tex]\frac{13}{5}[/tex]

Substitute this value into either of the 2 equations and evaluate for y

Substituting into (2)

[tex]\frac{39}{5}[/tex] + y - 9 = 0

- [tex]\frac{6}{5}[/tex] + y = 0 ( add [tex]\frac{6}{5}[/tex] to both sides )

y = [tex]\frac{6}{5}[/tex]

Solution is

([tex]\frac{13}{5}[/tex] , [tex]\frac{6}{5}[/tex] )

Answer:

$2.00

Step-by-step explanation:

The grocer bought the oranges for $15.00

15x12= 180 To find the number of oranges he bought

180-20=160 To find the rest of the remaining oranges

160/8= 20 To find how many packs he has

20x.85= 17 To find how much he made from selling the remaining oranges

17-15=2 To find the profit

Answer: (9 - 2) ⋅ 180 ° = 7 ⋅ 180 ° = 126 0 °

Step-by-step explanation:

Answer:

A=(1/2)(b)(h)

Step-by-step explanation:

The area of a triangle is 1/2(b)(h), so in this case, A=(1/2)(24)(16)=192

Answer:

91.99%

Step-by-step explanation:

To find what percentage of $7599 is $6990, we simply need to divide $7599 by $6990 and multiply by 100:

6990 / 7599 * 100 = 91.99%

Therefore, they paid 91.99% of the original price.

Answer:

dimensions are 2.19 inches by 9.14 inches

Step-by-step explanation:

Here, we are interested in knowing the dimensions of the rectangle

Now, let the width of the rectangle be x, from the question, we can write;

6x-4 as the length

Area of rectangle = l * b

x(6x-4) = 20

6x^2 - 4x = 20

divide through by 2

3x^2-2x = 10

3x^2 -2x -10 = 0

using quadratic formula;

x = -b ± √(b^2 - 4ac)/2a

From the quadratic equation, a = 3, b = -2 and c = -10

substituting these values, we have

x = 2 ± √(-2)^2 -4(3)(-10))/6

x = 2 ± √(124)/6

x = 2 + √(124)/6 or 2 - √(124)/6

x = (2+11.14)/6 or (2-11.14)/6

x = 2.19 or -1.52

Since width cannot be negative, we choose 2.19 alone

So the length is 6(2.19) -4 = 9.14

Answer:

[tex] \boxed{Number \: that \: give \: average \: of \: 27 \: with \: 12 \: is \: 42} [/tex]

Step-by-step explanation:

Let the number be 'x'

[tex] = > \frac{x + 12}{2} = 27 \\ \\ = > x + 12 = 27 \times 2 \\ \\ = > x + 12 = 54 \\ \\ = > x = 54 - 12 \\ \\ = > x = 42[/tex]

Answer:

First equation: 1/2

Second equation: -1/3

Step-by-step explanation:

We get the following equations:

[tex]\frac{1}{3}x+\frac{1}{6}y=2[/tex]          first equation

[tex]\frac{1}{2}x+\frac{3}{4}y=-3[/tex]       2nd equation

Then, to obtain opposite terms for the x variable, we need to identify the coefficient of the x for the 1st equation and the 2nd equation as:

The coefficient for x in the 1st equation is [tex]\frac{1}{3}[/tex] and the coefficient for x in the 2nd equation is [tex]\frac{1}{2}[/tex]

Finally, we need to multiply 1st equation with the coefficient of the 2nd equation and multiply the 2nd equation with the negative of the coefficient of the 1st equation.

We multiply by the negative of the coefficient of the 1st equation because we need to find opposite terms for x.

So, the first equation is equal to:

[tex](\frac{1}{3}x+\frac{1}{6}y)*\frac{1}{2} =2*\frac{1}{2} \\\frac{1}{6}x+\frac{1}{12}y=1[/tex]        

The second equation is:

[tex](\frac{1}{2}x+\frac{3}{4}y)*\frac{-1}{3} =-3*\frac{-1}{3} \\\frac{-1}{6}x+\frac{-1}{4}y=1[/tex]

Now, the coefficients for x, 1/6 and -1/6, are opposite terms.

Answer:3, -2

Step-by-step explanation:

Answer:

(2, 4)

x = 2

y = 4.

Step-by-step explanation:

To find the solution to the system of equations, we can simply set the two equations equal to each other as shown:

x + 2 = 3x - 2

Subtract 'x' from both sides:

2 = 2x - 2

Add '2' to both sides:

4 = 2x

x = 2.

Plug this value for 'x' into an equation to solve for 'y':

y = (2) + 2

y = 4.

Therefore, the solution to the system is (2, 4).

Answer:

Y=4

Step-by-step explanation:

How I did this.

y=x+2 y=3x-2

Moved around (you can do this)

y=2+2 y= 3x-x

y=4 y=2x

y=4.

Not sure if this is right. please check other answers

Answer:

B. x-intercept = 2, y-intercept = 4

Step-by-step explanation:

→The y-intercept can be found on the vertical line, while the x-intercept can be found on the horizontal line.

→Looking at the graph, you can see that the line intersects at a point on the vertical line (y-intercept), and this number is 4.

→Looking at the graph, you can see that the line intersects at a point on the horizontal line (x-intercept), and this number is 2.

Answer

Go 6 across to the right and 8 up from there

Step-by-step explanation:

Answer:

This is a coordinate, and it tells you where to plot a point on a set of axis. The first number in the coordinate tells you the x-value and the second one tells you the y-value. X-values go across the horizontal axis, known as the x-axis. Y-values go up and down the vertical axis, known as the y-axis.

In this case, to plot the point, you would start at the very center of the axis, where y and x both equal 0. You'd go 6 to the right, because they gave you a positive x-value. The you'd go up 8, because they gave you a positive y-value.

If they give you a negative x-value, you'd go to the left, and if they give you a negative y-value, you'd go down.

Hope that helped : )

Answer:

60

Step-by-step explanation:

All angles = 180

All sides are equal

Therefore, 180/3 = angle degrees = 60

x is an opposite angle of bottom right angle therfore x = 60

Answer:

(a) x = 60°

(b) Angle x is alternate to the right base angle of the equilateral triangle.

Step-by-step explanation:

(a) The triangle in the figure above is an equilateral triangle in which all sides and angles are equal. The sum of angles in a triangle is 180°. Each angle in the equilateral triangle is 60° (180°/3 = 60°)

Therefore, angle x is 60°.

(b) Alternate angles are equal. Angle x and the right base angle of the equilateral triangle are alternate angles. Therefore, angle x is 60°.

Answer:

1. $3.85 per gallon

2. $1.59

3. 7/12

Step-by-step explanation:

1. Jayden spent $46.20 on 12 gallons of gasoline. The price per gallon can be gotten by dividing the total price paid by the total number of gallons bought:

46.20 / 12 = $3.85 per gallon

The price per gallon is $3.85

2. Jayla buys 1.2 pounds of bananas and they cost $1.29 per pound. The total amount paid for the bananas is:

1.2 * 1.29 = $1.59

3. Billy ate 1/4 of a pizza, and Wi ate 1/3 of the same pizza. The total fraction of the pizza ate is:

1/4 + 1/3 = 7/12

They ate 7/12 of the pizza

Answer:

associative property with respect to addition and subtraction

3+[7+(-4)]=(3+7)+(-4)

3+[7-4]=10+(-4)

3+3=10-4

6=6

Step-by-step explanation:

i hope it will help you

Answer:

A) inside the circle

Step-by-step explanation:

equation of the circle is:

[tex](x-a)^{2} + (y-b)^{2} = r^{2}[/tex]

where (a,b) is center of the circle and r is radius so

[tex]x^{2} + y^{2} = r^{2}[/tex] now plug in given point to find the radius

[tex](6)^{2} + (-4)^{2} = r^{2}[/tex]

36 +16 = 52 so

r = [tex]\sqrt{52}[/tex]  ≈ 7.2 or  [tex]r^{2} =52[/tex]

when you plug point (√2 , -7) into equation of the circle

(√2)^2 + (-7)^2 = 2 +49 =51

51 is less than 52 so this is inside of the circle

Answer:

-44

Step-by-step explanation:

(-4+1)+(10-51)

-4+1+10-51

-3-41

-44

Answer:

x=5

Step-by-step explanation:

2(x+4)+2x+3=3x+16

One solution was found :

                  x = 5

Answer:

2x+8+2x+3=3x+16=

2x+2x-3x=-8-3+16=

4x-3x=-11+16=

x=5

Answer: See bolded below

Step-by-step explanation:

Average rate of change is the slope. To find that, we would need the equation [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].

Reminder: The scale fo the graph goes by 2. You need to make sure you are looking at the right coordinates.

1. The coordinate points are (1, 2) and (2, 4).

[tex]m=\frac{4-2}{2-1}=\frac{2}{1} =2[/tex]

The average rate of change is 2.

2. The coordinate points are (2, 4) and (3, 8).

[tex]m=\frac{8-4}{3-2} =\frac{4}{1} =4[/tex]

The average rate of change is 4.

3. The coordinates are (3, 8) and (4, 16).

[tex]m=\frac{16-8}{4-3} =\frac{8}{1} =8[/tex]

The average rate of change is 8.

Answer:

The answer would be, 2.75

Step-by-step explanation:

Add all the numbers up:

0+1+1+2+3+4+5+6=22

Divide the answer by the amount of numbers:

22÷8=2.75

Answer:

The mean of the following dot plot:

Mean: 3

Step-by-step explanation:

0 x 1 = 0

3 x 1 = 3

6 x 1 = 6

(we only add the numbers that only has a dot on the number in the dot plot)

So:

Mean: 0 + 3 + 6 = 9/3 = 3