It took a motorboat 1 hour longer to travel 84 miles against the current than travel the same distance with the current.
The speed of the current is 1 mph.

What is the speed of the motorboat in still water?

Answer:

17 cm

Step-by-step explanation:

A box has a length of 5 cm, a width of 10 cm, and a height of 2 cm. the volume of the box is: 17 cm

Answer:

C) Matched pairs

Step-by-step explanation:

Matched samples (also called matched pairs, paired samples or dependent samples) is a type of sampling that involves pairing participants that share every characteristic except for the one under study. The paired participants could be same individuals studied at different time such as:

Answer: 12 INCHES

Step-by-step explanation:

Answer:

128

Step-by-step explanation:

multiply length, width, and hight.

[Not including the "triangle roof"] 128 in²

    V = L * W * H

    V = 8 in * 4 in * 4 in

    V = 128 in²

[Including the "triangle roof"] 176in²

    V = \(\frac{ L * W * H}{2}\)

    V = \(\frac{8\text{ in }*\,4\text{ in }*\,3\text{ in }}{2}\)

    V = \(\frac{96\;in^2}{2}\)

    V = 48 in²

        -

    48 in² + 128 in² = 176in²

The fence in dead center is about 399 feet from the third base.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

For the triangle in this problem, we have that:

Hence the distance is obtained as follows:

d² + 90² = 409²

\(d = \sqrt{409^2 - 90^2}\)

d = 399 ft.

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By proving that ΔEAB and ΔFDC have congruent corresponding angles and proportional corresponding sides, we can conclude that ΔEAB ≅ ΔFDC.

Given:

- Triangle ΔAEB and ΔDFC

- Line ABCD is straight (implies AC and BD are collinear)

- AE is parallel to DF

- EB is parallel to FC

- AC = DB

To prove: ΔEAB ≅ ΔFDC

Recall that:

AE || DF

EB || FC

AC = DB

AE || DF, EB || FC (Parallel lines with transversal line AB)

Corresponding angles are congruent:

  ∠AEB = ∠DFC (Corresponding angles)

  ∠EAB = ∠FDC (Corresponding angles)

Corresponding sides are proportional:

  AE/DF = EB/FC (Corresponding sides)

  AC/DB = BC/DC (Corresponding sides)

  AC = DB

  BC = DC (Equal ratios)

ΔEAB ≅ ΔFDC (By angle-side-angle (ASA) congruence)

∠EAB = ∠FDC

∠AEB = ∠DFC

AC = DB, BC = DC

Therefore, by proving that ΔEAB and ΔFDC have congruent corresponding angles and proportional corresponding sides, we can conclude that ΔEAB ≅ ΔFDC.

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Answer:

there are 700 species in every acre

Step-by-step explanation:

divide the amount of species by the amount of acres.

Answer:

7,000,000

Step-by-step explanation:

If there is 70,000 in each acre, just multiply 70,000 times 100 acres.

Answer:

Answer:

x = -2

Step-by-step explanation:

Answer:

x = -2

Step-by-step explanation:

y = -3x + 2.5

if y = 8.5 then:

8.5 = -3x + 2.5

-3x = 6

x = -2

Answer:

Answer: There is 1 1/2 times more juice than ginger ale; there is 2/3 as much ginger ale as there is punch.

Step-by-step explanation:

Answer:

Answer A:

Step-by-step explanation:

2 parts ginger ale to 3 parts raspberry juice.

Answer:

$45 in all

Step-by-step explanation:

30 + 15 = 45 that is me

Answer:

Y=375x

Step-by-step explanation:

thats the answer

Answer:

-11

Step-by-step explanation:

4c - 3   Substitute -2 for c

4(-2) - 3

-8 - 3

-11

Answer:

-11

Step-by-step explanation:

We are given the value of c, so we just need to plug it in. We can do this by replacing "c" with "-2" in our given expression.

4c - 3 ⇒ 4(-2) - 3

Now, we can simplify this.

-8 - 3 = -11

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Hence the sum of rational expressions is \(\frac{9x^2-5x+2}{7x^2-14x}\) option  D is correct.

You must be familiar with rational numbers, which are written as p/q. On the other hand, rational expressions are the ratio of two polynomials.

Polynomial expressions must be set equal to zero in order to find the root or zero. But, once the expression has been condensed to its simplest form, we must only set the numerator equal to zero in order to obtain the zeros of rational functions or expressions.

The lowest terms are those in which neither the numerator nor the denominator has any common factors. It is not in the lowest form, like in the case of a fraction, like 2/8. Taking 2 into consideration as a common element will further minimize it. The lowest form is therefore 1/4.

The rational expression is

\(\frac{2x-1}{7x}+\frac{x}{x-2}\)

to add expression first take LCM

and cross multiply

\(=\frac{(2x-1)(x-2)+7x^2}{7x(x-2)}\\\\=\frac{2x^2-4x-x+2+7x^2}{7x^2-14x}\\\\=\frac{9x^2-5x+2}{7x^2-14x}\)

Hence the sum of a rational expression is \(\frac{9x^2-5x+2}{7x^2-14x}\) option  D is correct.

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Answer:

2(x+3)(2x-1)

Step-by-step explanation:

Answer:

Oops no image

Step-by-step explanation:

Answer:

Hi mate.....can't see the image....pls recheck

Step-by-step explanation:

The parametrization shown below,

            \(x(t),y(t),z(t)=10cost,5,10sint\)

Given equation of sphere,

                 \(x^{2} +y^{2} +z^{2} =125\)

Substitute y = 5 in above relation.

         \(x^{2} +z^{2}=125-25=100\\ \\x^{2} +z^{2}=10^{2}\)

For parametrization,

Substitute \(x=rcos(t),z=rsin(t)\) and \(r=10\)

So that,  \(x(t),y(t),z(t)=10cost,5,10sint\)

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The translation of the verbal expression "4 less than twice a number" in to an algebraic expression is 2n - 4.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

Given:

Danielle is working on practice problems and must translate the verbal expression "4 less than twice a number" in to an algebraic expression.

Let the number is n.

The phrase can be expressed as,

2n - 4.

Therefore, the expression is 2n - 4.

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ANSWER:

The value of n is 8

STEP-BY-STEP EXPLANATION:

Due to the picture we can make the following equation each ball represents 1, therefore:

Solving for n:

Answer:

It looks like everything is correct :)

Step-by-step explanation:

Answer:

2.90

Step-by-step explanation:

-37 + 46 - 6.1 = 2.90

Answer:

3.5 gallons

Step-by-step explanation:

Answer:

3 to 8

Step-by-step explanation:

There are 24 total shapes, 9 of which are circles. So we have the ratio 9 to 24, or 3 to 8.

Answer:

65

Step-by-step explanation:

The lines are parallell so m1 = m5, and m3=m8. 180-115 is 65

Answer: 4000

Step-by-step explanation:

Answer:

-6 + 2 = -4

Step-by-step explanation:

-6 + 2 = -4

Answer:

\(f(2) = 12\)

\(f(5) =320\)

\(f(-2) =\frac{5}{2}\)

\(g(3) = \frac{1}{135}\)

Step-by-step explanation:

Solving (1):

\(f(x) = \frac{1}{3}*6^x\) at \(x=2\)

Substitute 2 for x in f(x)

\(f(2) = \frac{1}{3}*6^2\)

\(f(2) = \frac{1}{3}*36\)

\(f(2) = \frac{1*36}{3}\)

\(f(2) = \frac{36}{3}\)

\(f(2) = 12\)

Solving (2):

\(f(n) =10*2^n\) at \(n =5\)

Substitute 5 for n in f(n)

\(f(5) =10*2^5\)

\(f(5) =10*32\)

\(f(5) =320\)

Solving (3):

\(f(n) =10*2^n\) at \(n =-2\)

Substitute -2 for n in f(n)

\(f(-2) =10*2^{-2\)

\(f(-2) =10*\frac{1}{2^2}\)

\(f(-2) =10*\frac{1}{4}\)

\(f(-2) =\frac{10*1}{4}\)

\(f(-2) =\frac{10}{4}\)

\(f(-2) =\frac{5}{2}\)

Solving (4):

\(g(x) = \frac{1}{5}*(\frac{1}{3})^x\) at \(x = 3\)

Substitute 3 for x in g(x)

\(g(3) = \frac{1}{5}*(\frac{1}{3})^3\)

\(g(3) = \frac{1}{5}*(\frac{1^3}{3^3})\)

\(g(3) = \frac{1}{5}*\frac{1}{27}\)

\(g(3) = \frac{1}{135}\)

Solving (5):

Graph of \(f(x) = 4 * 2^x\)

First, we determine the points to plot the graph.

When \(x = 0;\ f(0) = 4 * 2^0 = 4*1 = 4\)

When \(x = 2;\ f(2) = 4 * 2^2 = 4*2 = 16\)

When \(x = 4;\ f(4) = 4 * 2^4 = 4*16 = 64\)

So, we have: (0,4), (2,16) and (4,16)

See attachment 1 for graph

Solving (6):

Graph of \(f(x) = 4 * (\frac{1}{2})^x\)

First, we determine the points to plot the graph.

When \(x = 0;\ f(0) = 4 * (\frac{1}{2})^0 = 4*1 = 4\)

When \(x = 2;\ f(2) = 4 * (\frac{1}{2})^2 = 4*\frac{1}{4} = 1\)

When \(x = 4;\ f(4) = 4 * (\frac{1}{2})^4 = 4*\frac{1}{16} = \frac{1}{4}\)

So, we have: (0,4), (2,1) and (4,1/4)

See attachment 2 for graph

The solution is 9x - 36u + 27.

What is the linear equation?

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. An example of a linear equation is y=mx + b.

We have given

-9(-×+4u-3)

When you multiply a negative number by another negative number, the result is positive.

So, to solve this problem, we can use the distributive property and simplify:

-9(-x + 4u - 3) = -9(-x) + -9(4u) + -9(-3)

= 9x - 36u + 27

Hence, the solution is 9x - 36u + 27.

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Answer:

x=9 which makes angle q 28 degrees

Step-by-step explanation:

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