Solve for m: m – 4.2 = 5.1

Answer:

  4 mph

Step-by-step explanation:

The current subtracts from the boat speed going upstream, and add going downstream. The relation between speed, distance, and time is ...

   time = distance/speed

  2 1/4 = 12/(12 -c) + 12/(12 +c) . . . . . round trip time is the sum of the trip times

  9/4(12 +c)(12 -c) = 12(12 +c) +12(12 -c) . . . . multiply by (12 +c)(12 -c)

  144 -c^2 = 128 . . . . . . multiply by 4/9 and simplify

  16 = c^2 . . . . . . . . . add c^2 -128

  c = 4 . . . . . . . . . positive square root

The current was 4 mph that day.

Answer:

15a - 12

Step-by-step explanation:

7a - 4 [ 2 - (2a - 1) ] ← distribute parenthesis inside the bracket by - 1

= 7a - 4 [ 2 - 2a + 1 ]

= 7a - 4 (- 2a + 3) ← distribute parenthesis by - 4

= 7a + 8a - 12 ← collect like terms

= 15a - 12

Answer:

  Q16a: 432 cm³

  Q16b: sides: 20 m, 6 m; height: 13 m.

Step-by-step explanation:

Each cube will have a volume ...

  V = s³

  V = (6 cm)³ = 216 cm³

The two cubes together will have a volume that is twice that.

The cuboid volume is 432 cm³.

__

Let h represent the height of the trapezium. Then its area is ...

  A = 1/2(b1 +b2)h

  169 = 1/2((h +7) +(h -7))h = 1/2(2h²) = h²

  h = √169 = 13 . . . . . distance between the parallel sides

The side lengths are h+7 = 20 m and h-7 = 6 m. The distance between them is 13 m.

The distance from the top of the mirror to the ceiling once the mirror is hung on the wall is 21 inches

The dimension of the mirror is given as:

[tex]Height = 24\ in[/tex]

[tex]Width = 28\ in[/tex]

From the center of the mirror to the floor of the wall, the distance is:

[tex]Distance =5\frac14\ ft[/tex]

So, the distance to the top of the mirror will be:

[tex]Top = 5\frac 14\ ft + \frac 12 \times Height[/tex]

Substitute 24 for height

[tex]Top = 5\frac 14\ ft+ \frac 12 \times 24\ in[/tex]

[tex]Top = 5\frac 14\ ft+ 12 \ in[/tex]

Convert feet to inches

[tex]Top = 5\frac 14\times 12\ in+ 12 \ in[/tex]

[tex]Top = 63\ in+ 12 \ in[/tex]

[tex]Top = 75 \ in[/tex]

The distance from the top of the mirror to the ceiling is the difference between the height of the wall and 75 inches.

So, we have:

[tex]Distance = 8\ ft - 75\ in[/tex]

Convert feet to inches

[tex]Distance = 8\times 12\ in - 75\ in[/tex]

[tex]Distance = 96\ in - 75\ in[/tex]

[tex]Distance = 21\ in[/tex]

Hence, the distance is 21 inches

Read more about lengths at:

https://brainly.com/question/10545161

Answer:

6.2

Step-by-step explanation: TOOK THE TEST

Answer:

4

Step-by-step explanation:

The factors of 5 and 15 are 1, 5 and 1, 3, 5, 15 respectively.

How many factors does 15 have?

4 factors

Factors of 15 are the list of integers that can be evenly divided into 15. It has a total of 4 factors of which 15 is the biggest factor and the positive factors of 15 are 1, 3, 5, and 15.

x = 9

Scale size is 3 so multiply all terms in ABC by 3.

Answer:

ya

Step-by-step explanation:

25 percent is equally to 25 over 100 which is 1over4

Answer:

Anil

Step-by-step explanation:

This is because 1/3 is greater then 1/5

Answer:

Question 2: 2/3

Question 1: 1/3

Question 3: 20

Step-by-step explanation:

Question 2: 8/4 = 2 & 12/4 = 3.

Question 1: 6/6 = 1 & 18/6 = 3.

Question 3: 10/10 = 1 & 20/10 = 2.

Answer:

$ 1.2

Step-by-step explanation:

you need to divide 6/5 and then that's the answer.

Answer:

1st

Step-by-step explanation:

1) 1m cost = $8.28/0.3=$27.60/m

2) 1m cost = $ 13.00/0.4=$32.5/m

Given :-

To Find :-

Solution :-

The equation of the line p is ,

[tex]\sf\blue{\longrightarrow}[/tex] y = 5/3x - 4

On comparing to slope intercept form of the line which is y = mx + c , we have ,

[tex]\sf\blue{\longrightarrow}[/tex] m = 5/3

Now as we know that the product of slopes of two perpendicular lines is -1 . So the slope of the perpendicular line will be ,

[tex]\sf\blue{\longrightarrow} m_{\perp} = -3/5[/tex]

Now here the line q passes through the point (-10,-3) . So on using the point slope form of the line we get ,

[tex]\sf\blue{\longrightarrow} y - y_1 = m(x-x_1)[/tex]

[tex]\sf\blue{\longrightarrow}[/tex] y - (-3) = -3/5[ x-(-10)]

[tex]\sf\blue{\longrightarrow}[/tex] y +3 = -3/5(x+10)

[tex]\sf\blue{\longrightarrow}[/tex] y+3 = -3/5x - 6

[tex]\sf\blue{\longrightarrow}[/tex] y +9 = -3/5x

[tex]\sf\blue{\longrightarrow}[/tex] y = - 3/5x - 9

Hence the required answer is y = -3/5x - 9 .

Answer:

For Perpendicular lines you have to know

Step-by-step explanation:

Slope of P ×slope of q=-1 (always since they are perpned..)

so as P has the slope 5/3 in order to optain - 1 the slope of q should be negative of the inverse of p

so q solpe =-3/5 then lets try (5/3)×(-3/5)? =-1 yes

And be aware that you have to know the formula of straight line : y-ypoint=slope(x-xpoint) or y=ax+b

so y+3=-3/5(x+10) ===> y=-3/5x - 30/5 - 3

uniting the denominater ==>y=-3/5x - 45/5

so that q equation is :y=-3/5x - 9

The answer would be 23.07/3 = 23 is $7.69

Step-by-step explanation:

5ab + 8c

Putting values of a = 3 b = 2 and c = 9

5(3)(2) + 8(9)

30 + 72

102

Answer and Explanation: We will find the area of the given shape:

To find the area, we will count the number of squares of the shaded area.

While calculating the area for a more accurate estimate, we count the square as “1” if the shaded region covers more than half of each square. By counting the squares, the area is approximately 50 square units.

Answer:

-0.048

Step-by-step explanation:

-1.2 * 0.04 = -1.2 * 4 / 100 = -4.8 / 100 = -).048

Answer:

Yes, this equation is a system of equations because the two equations do intersect at the point, (0.323529411763, -1.23529411765), making them have a solution. *Work Below*

Step-by-step explanation:

Lets use the elimination method which is ...

4x-3y=5

2x+7y=-8

Multiply the bottom part by -2

(-2)2x+(-2)7y=(-2)-8

which equals...

-4x-14y=16

Rewrite the equations

4x-3y=5

-4x-14y=16

Add and the x's cancel making..

-17y=21

Divide by -17 to isolate y

y=-1.23529411765

Replace y with -1.23529411765 on one of the equations

4x-3(-1.23529411765) =5

x=0.323529411763

solution : (0.323529411763, -1.23529411765)

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

How to get that answer:

The slope is the rate of change for any linear function.

Apply the slope formula for any two points on the diagonal line.

I'll use the points (-4, -3) and (0, 4)

[tex]m = \frac{y_2-y_1}{x_2-x_1}\\\\m = \frac{4-(-3)}{0-(-4)}\\\\m = \frac{4+3}{0+4}\\\\m = \frac{7}{4}\\\\[/tex]

The slope is m = 7/4

This indicates that each time we go up 7 (rise), we also go to the right 4 units (run)

slope = rise/run = 7/4

rise = 7, run = 4

The fraction 7/4 converts to the decimal form 1.75

We have been given that a person places $6340 in an investment account earning an annual rate of 8.4%, compounded continuously. We are asked to find amount of money in the account after 2 years.

We will use continuous compounding formula to solve our given problem as:

, where

A = Final amount after t years,

P = Principal initially invested,

e = base of a natural logarithm,

r = Rate of interest in decimal form.  

Upon substituting our given values in above formula, we will get:

Upon rounding to nearest cent, we will get:

Therefore, an amount of $7499.82 will be in account after 2 years.

Answer:

5124.83

Step-by-step explanation:

r=5.7\%=0.057

r=5.7%=0.057

Move decimal over two places

P=4080

P=4080

Given as the pricipal

t=4

t=4

Given as the time

V=Pe^{rt}

V=Pe  

rt

V=4080e^{0.057( 4)}

V=4080e  

0.057(4)

Plug in

V=4080e^{0.228}

V=4080e  

0.228

Multiply

V=5124.8281\approx 5124.83

V=5124.8281≈5124.83

Answer:

27

Step-by-step explanation:

3 * 9 = 27

Hope this helps!

Answer:

The bold word help you

Step-by-step explanation:

Consider the numbers 2, 23, 234, 2345, 23456, 234567.

Every number divisible by 9 is divisible by 3. For example, 7425 is divisible by 9, hence it is divisible by 3. However, a number divisible by 3 is not necessarily divisible by 9. For example 6, 12, 15, 21, 24, 30 are all divisible by 3 but none of them is divisible by 9.

6 is divisible by 3 but not by 9 because 6 is greater than 3 but smaller than 9

Answer:

[tex]x\approx4.5[/tex]

Step-by-step explanation:

In relation to ∠U, we are given the triangle's opposite side and adjacent side. Therefore, we should use the tangent function to determine the opposite side:

[tex]tan(\theta)=\frac{opposite}{adjacent}[/tex]

[tex]tan(34^\circ)=\frac{x}{6.7}[/tex]

[tex]6.7tan(34^\circ)=x[/tex]

[tex]x=6.7tan(34^\circ)[/tex]

[tex]x\approx4.5[/tex]

Answer:

[tex]x=-1[/tex] and [tex]x=-5[/tex]

Step-by-step explanation:

[tex]f(x)=(x+3)^2-4[/tex]

[tex]0=(x+3)^2-4[/tex]

[tex]0=(x^2+6x+9)-4[/tex]

[tex]0=x^2+6x+5[/tex]

[tex]0=(x+1)(x+5)[/tex]

[tex]x=-1[/tex] and [tex]x=-5[/tex]

Answer:

[tex]x=-1,\:x=-5[/tex]

Step-by-step explanation:

Solve the equation:

[tex]f(x)=\left(x+3\right)^2-4=0[/tex]

[tex]\left(x+3\right)^2-4=0[/tex]

[tex]\mathrm{Add\:}4\mathrm{\:to\:both\:sides}[/tex]

[tex]\left(x+3\right)^2-4+4=0+4[/tex]

[tex]\left(x+3\right)^2=4[/tex]

[tex]x+3=\sqrt{4}:x=-1[/tex]

[tex]x+3=\sqrt{2^2}[/tex]

[tex]x+3=2[/tex]

[tex]x+3-3=2-3[/tex]

[tex]x=-1[/tex]

[tex]x+3=-\sqrt{4}:x=-5[/tex]

[tex]x+3=-\sqrt{4}[/tex]

[tex]x+3=-2[/tex]

[tex]x+3-3=-2-3[/tex]

[tex]x=-5[/tex]

Now, look at the points plotted on the graph:

Answer:

≥7

Step-by-step explanation:

6x7=42

Hope that helps

Answer:

x≥7

Step-by-step explanation:

Answer:

1.6 hrs remaining, or 3.12 km/h

Step-by-step explanation:

Answer:

this is easy 100% in this case equals 100 so 15 Juveniles equals 15%

Step-by-step explanation:

Answer:

Parallel: a and c

Perpendicular: a and b, c and b

Step-by-step explanation:

Basically you would want to isolate for y.

Line a:

4y - 12x = 20

4y = 12x  + 20

y = 12x/4 + 20/4

y = 3x + 5

Line b:

3y = -x+2

y = -x/3 + 2/3

Line c:

y=3x - 1

Now look at each line and compare their slopes.

-Lines a and c have same slope., thus they are parallel.

-lines a and b are perpendicular because the slopes are negative reciprocals each other

-lines b and c are also perpendicular

Answer:

See answer below.

Step-by-step explanation:

3x - 2 =  4                Given

   +2  =  +2

  3x     =  6               Addition Property of Equality

3x/3  = 6/3

     x = 2                  Division Property of Equality

Answer:

-7 is the answer!! :) hope this helps