A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km down-stream. Determine the speed of the stream and that of the boat in still water.

Answer:

To eliminate y- terms

Multiply equ(1) by 3 and equ(2) by -4

To eliminate y- terms

Multiply (1) by 3 and (2) by -5

Step-by-step explanation:

5x - 4y = 28 (1)

3x - 3y = 30 (2)

To eliminate y- terms

Multiply equ(1) by 3 and equ(2) by -4

15x-12y=84

-12x+12y= -120

Add equ (3) and (4)

3x=84-120

3x=-36

x=-36/3

= -12

x=-12

To eliminate x- terms

5x-4y=28

3x-3y=30

Multiply (1) by 3 and (2) by -5

15x-12y=84

-15x+15y=-150

Add the new equation

3y= -66

y= -22

Answer:

[tex]-\frac{16}{17}\\-0.94117[/tex]

Step-by-step explanation:

[tex]\frac{-\frac{1}{2}}{\frac{2\left(9+3\right)-4-3}{4\left(8\right)}}\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=\frac{-\frac{1}{2}}{\frac{2\left(9+3\right)-4-3}{4\cdot \:8}}\\\frac{2\left(9+3\right)-4-3}{4\cdot \:8}=\frac{17}{32}\\\frac{2\left(9+3\right)-4-3}{4\cdot \:8}\\2\left(9+3\right)-4-3=17\\2\left(9+3\right)-4-3\\2\left(9+3\right)=24\\2\left(9+3\right)\\\mathrm{Add\:the\:numbers:}\:9+3=12\\=2\cdot \:12\\\mathrm{Multiply\:the\:numbers:}\:2\cdot \:12=24\\=24-4-3[/tex]

[tex]\mathrm{Subtract\:the\:numbers:}\:24-4-3=17\\=\frac{17}{4\cdot \:8}\\\mathrm{Multiply\:the\:numbers:}\:4\cdot \:8=32\\=\frac{17}{32}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}\\=-\frac{\frac{1}{2}}{\frac{17}{32}}\\\mathrm{Divide\:fractions}:\quad \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c}\\=-\frac{1\cdot \:32}{2\cdot \:17}\\Refine\\=-\frac{32}{2\cdot \:17}\\\mathrm{Multiply\:the\:numbers:}\:2\cdot \:17=34\\=-\frac{32}{34}[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:2\\=-\frac{16}{17}\\\mathrm{Decimal:\quad }\:-0.94117[/tex]

Answer:

b

Step-by-step explanation:

Because y increases by a factor of 2 every time x goes up by 1, the opposite happens when x decreases by 1. This means that when x = 0, y = 5 so the answer is b.

Applying the points and finding the equation, it is found that point (0,5) is also on the graph, option b.

The exponential equation has the following format:

[tex]y = ab^x[/tex]

Point (1,10) means that when [tex]x = 1, y = 10[/tex], thus:

[tex]ab = 10[/tex]

Point (2,20) means that when [tex]x = 2, y = 20[/tex], thus:

[tex]ab^2 = 20[/tex]

From the first equation:

[tex]a = \frac{10}{b}[/tex]

Replacing on the second:

[tex]\frac{10}{b}b^2 = 20[/tex]

[tex]10b = 20[/tex]

[tex]b = \frac{20}{10}[/tex]

[tex]b = 2[/tex]

So

[tex]a = \frac{10}{b} = \frac{10}{2} = 5[/tex]

Then, the equation is:

[tex]y = 5(2)^x[/tex]

When [tex]x = 0, y = 5(2)^0 = 5[/tex], thus point (0,5) is also on the graph, which means that option b is correct.

A similar problem is given at https://brainly.com/question/14773454

Answer:

t= -105

Step-by-step explanation:

To solve the equation, we want to find out what t is. In order to do this, we have to get t by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.

-1/15t=7

t is being multiplied by -1/15. The opposite of multiplication is division. Divide both sides by -1/15.

-1/15t/-1/15=7/ -1/15

t=7/ -1/15

Instead of dividing a number by a fraction, you can multiply the number by the reciprocal of the fraction.

To find the reciprocal, flip the numerator (top number) and denominator (bottom number).

-1/15--flip--> -15/1=-15

Substitute -15 in for -1/15, and switch the division sign to a multiplication sign.

t= 7* -15

t=-105

Let's check out solution. Plug -105 back in for t in the original equation.

-1/15t=7

-1/15*-105=7

7=7

Both sides are the same, so we know that t=-105.

Answer:

t=-105

Step-by-step explanation:

[tex]-\frac{1}{15} t =7[/tex]

What we need to do here is to isolate t.

Let's multiply both sides by -15.

[tex]-\frac{1}{15}t * -15 = 1t[/tex]

7*-15= -105

t=-105

Answer:

60

Step-by-step explanation:

60 times 2 is 120 plus 24 is 144

Answer:

D. Cubic meters

Explanation:

Anytime you see a question asking about volume, the units will always have cubic in it.

Answer:

D

Step-by-step explanation:

For the volume of a sphere with radius of 2 meters, Since here, the unit is "meters", so the volume of this sphere would be in cubic metres.

Answer:

1

Step-by-step explanation:

Since you are going for the largest value of x that satisfies the equation, you don't need to worry about negative numbers, and therefore don't need to worry about the absolute value.

5x-1=x+3

5x=x+4

4x=4

x=1

Hope this helps!

Given that a rectangle has an area of 345 square millimeters and a base of 15 millimeters, find the height.

Area of a Rectangle = b x h

So, to find the height, we would reverse it by dividing the area by the base.

Work:

345/15 = 23

So, 23 would be our height.

Thus, the height of the rectangle is 23 millimeters.

Answer:

23 millimeters

Step-by-step explanation:

The area of a rectangle can be found using the following formula.

a=b*h

We know that the area is 345 square millimeters and the base is 15 millimeters, but we don't know that the height is.

a=345

b=15

Substitute these variables into the formula.

345=15*h

We want to find out what the height, or h is.  In order to do this, we have to get h by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.

h is being multiplied by 15. The opposite of multiplication is division, so divide both sides by 15.

345/15=15*h/15

345/15=h

23=h

Add appropriate units. In this case, the units are millimeters.

h=23 millimeters

The height of the rectangle is 23 millimeters.

Answer:

i) 2x² + 4x + 7x + 14

= 2x² + 11x + 14

ii) 2x² - 5x - 12x + 30

= 2x² - 17x + 30

Answer:

The triangle's area is 12 square units.

Step-by-step explanation:

We start by drawing the requested points A = (-4, -3) and B = (0, -3), which we notice are located horizontally on the line of y = -3 and separated 4 units from each other (see red dots in the attached image).

Then we look for a point over the line y = 3 that is equidistant from points A and B (so we place it at the point (-2, 3)) and name it "C".

Now, the triangle ABC defined by the three points has base = 4 units, and height = 6 units (from the line y = -3 to the line y = 3).

Then recall that the area of a triangle is defined by the product of the triangle's base times its height, divided by two:

[tex]Area=\frac{base\,*\,height}{2} \\Area=\frac{4\,*\,6}{2} \\Area = 12[/tex]

So the triangle's area is 12 square units.

Answer:

200g of sugar, 600g of flour, 400g of butter

Step-by-step explanation:

50g sugar = 15 biscuits

3 x 50g = flour --) 150g = flour

2 x 50g = butter --) 100g = butter

60/15 = 4; 4 times as much

4 x 50g = 200g of sugar

4 x 150g = 600g of flour

4 x 100g = 400g of butter

Answer:

-5/3

Step-by-step explanation:

Answer:

Step-by-step explanation:

The first two steps are for the purpose of eliminating fractions.  Doing so results in 4(2x - 5) = 9(x - 2), which is to be solved for x.

Perform the indicated multiplication, obtaining:

8x - 20 = 9x - 18.

Then combine like terms:  -2 = x, or

x = -2.

To complete the formal check, substitute -2 for x in the first equation.  This results in:

(1/3)(-4 - 5) = (3/4)(-2 -2), or

        -3       =        -3

... which is obviously true.  

Answer:

See explanation

Step-by-step explanation:

Line A

gradient = 4

x-intercept = -1

y-intercept = 4

Line B

gradient = -3

x-intercept = -1

y-intercept = -3

y + 8x = - 72

x-intercept = -9

y-intercept = -72

Answer:

x=6

Step-by-step explanation:

Because of the Pythagorean theorem, you know that the square of the two legs of a right triangle will be equal to the square of the hypotenuse. Conversely, the square of one of the legs will be equal to the square of the other leg subtracted from the square of the hypotenuse. Therefore:

[tex]x^2=10^2-8^2 \\\\x^2=100-64\\\\x^2=36\\\\x=6[/tex]

Hope this helps!

Answer:

6

Step-by-step explanation:

By Pythagoras theorem

10^2 = 8^2 + x^2

100= 64 + x^2

X^2 =100-64

X^2= 36

[tex]x = \sqrt{36} \\ x = 6[/tex]

Hope this helps..

Answer:

[tex]6a^3+45b[/tex]

Step-by-step explanation:

[tex]2a\times a\times 3a+b\times 45[/tex]

[tex]2a\times 1a\times 3a+b\times 45[/tex]

[tex]2\times 1\times 3 \times a \times a \times a+b\times 45[/tex]

[tex]6a^3+b \times45[/tex]

[tex]=6a^3+45b[/tex]

Answer:

6a^3 + 45b

Step-by-step explanation:

=2a × a × 3a + b × 45

=2a × 1a × 3a + b × 45

=2 × 1 × 3 × a × a × a + b × 45

=6a^3 + b × 45

= 6a^3 + 45b

Answer:

x< -8

Step-by-step explanation:

To solve the inequality, we must get x isolated.

-1/2x>4

We have to perform the inverse operation to both sides. x is being multiplied by -1/2. The inverse of multiplication is division. Divide both sides by -1/2.

-1/2x / -1/2 > 4/ -1/2

When dividing by fraction, you can also multiply by the reciprocal.

To find the reciprocal, flip the numerator and the denominator.

-1/2–> -2/1

-2/1 *-1/2x > 4* -2/1

x> 4* -2/1

When multiplying or dividing by a negative number in an inequality, you must flip the inequality sign.

x < 4* -2/1

x < 4*-2

x< -8

Answer:

14

Step-by-step explanation:

look at the other answer as the person is taking a very long time to write it

Answer: radius = 14.01 m

Step-by-step explanation:

Circumference = 2πr

88 = 2πr

r = 88/2π = 14.01m

Answer:

o7 fy hk hpxi oyli ifuod pir8

Answer:

13 = 15(x) - 23

x = 12/5 or 2 2/5

Answer:

1/3

Step-by-step explanation:

plug in 0 for x

0 * anything = 0 (cancels out the -2/9) and you're left with 1/3

Answer:

(-3.5,2.5)

Step-by-step explanation:

[tex]m=\left( \dfrac{-6+-1}{2},\dfrac{-2+5}{2} \right)=\left( \dfrac{-7}{2},\dfrac{3}{2}\right)=\left( -3.5,2.5 \right)[/tex]

Hope this helps!

Answer:

0< h ≤ 15

Step-by-step explanation:

A = 1/2 * base * height = 1/2*16*h = 8h

A no more is ≤.

A ≤ 120

8h ≤ 120

h ≤ 15

0< h ≤ 15

Height should be  more than 0 feet and no more than 15 feet.

Answer:

p: 42

a: 82.16

Step-by-step explanation:

For perimeter, add all the sides together

For area, multiple the longer side by the shorter side

Answer:

-2/3

Step-by-step explanation:

Perpendicular slopes have lines that multiply to -1

m* 3/2 = -1

Multiply each side by 2/3

m* 3/2 * 2/3 = -1 * 2/3

m = -2/3

The slope of the perpendicular line is -2/3

Answer:

The answer is B

I use an online graphing calculator called Desmos. You should check it out some time :)

Answer:

B

Step-by-step explanation:

The x term is 1 in all the pairs this would form a horizontal line (x=1)

Answer: C) ((-2,7), (0,12), (1,4), (1,5)

Step-by-step explanation: An ordered pair will usually have a pattern that'll repersent a linear function. Out of all of the options only C as a constant pattern.

I hope this helps!

Which question are you talking about? I mean that why is there no attachment / image of your question? How do we know what is the question?So could you pls complete your question? :)

Answer:

(1, - 12 )

Step-by-step explanation:

Given the graph of f(x) then f(x) + c represents a vertical translation of f(x)

• If c > 0 then a shift up of c units

• If c < 0 then a shift down of c units

Thus f(x) - 4 represents a shift down of 4 units, that is

(1, - -8 ) → (1, - 8 - 4 ) → (1, - 12 )

Answer:

Option (2).

Step-by-step explanation:

This question is incomplete; here is the complete question and find the figure attached.

In the diagram of a circle O, what is the measure of ∠ABC?

27°

54°

108°

120°

m(minor arc [tex]\widehat {AC}[/tex]) = 126°

m(major arc [tex]\widehat {AC}[/tex]) = 234°

By the intersecting tangents theorem,

If the two tangents of a circle intersect each other outside the circle, measure of angle formed between them is half the difference of the measures of the intercepted arcs.

m∠ABC = [tex]\frac{1}{2}[m(\text {major arc{AC})}-m(\text{minor arc} {AC})][/tex]

             = [tex]\frac{1}{2}(234-126)[/tex]

             = 54°

Therefore, Option (2) will be the answer.

Answer:

B.

Step-by-step explanation:

Step-by-step explanation:

I think A

I hope it will help