A boat can travel 408 miles on 204 gallons of gasoline how far can it travel on 169 gallons

Answer:

-5x + 1

Step-by-step explanation:

Hello!

We can find the quotient by factoring the numerator, and cancelling common factors.

The quotient is (-5x + 1).

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathbf{\dfrac{15x^2 - 3x}{-3x}}[/tex]

[tex]\huge\textbf{Simplify the current equation:}[/tex]

[tex]\mathbf{= \dfrac{-3x(-5x + 1)}{-3x}}[/tex]

[tex]\huge\textbf{Cancel out \boxed{\bf -3x} \& simplify it:}[/tex]

[tex]\mathbf{= \dfrac{-15x + 3}{3}}[/tex]

[tex]\huge\textbf{Simplify that above:}[/tex]

[tex]\mathbf{= -5x + 1}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{-5x + 1 }}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The rate of change of the the given table is: 3/4soda per dollar.

Rate of change = change in total cost / change in number of sodas.

Using (24, 18) and (28, 21), we would have:

Rate of change = (21 - 18)/(28 - 24)

Rate of change = 3/4

Therefore, the rate of change is 3/4soda per dollar.

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[tex](x - a)(x - b)(x - c) \\ (x {}^{2} - bx - ax + ab)(x - c) \\ x {}^{3} - bx {}^{2} - ax {}^{2} + abx - cx {}^{2} + cbx + cax - abc[/tex]

[tex]x {}^{3} + ( - a - b - c)x {}^{2} + (ab + cb + ca)x - abc [/tex]

[tex] - a - b - c = - 7 \\ ab + ac + bc = 16 \\ - abc = - 12 \: \: \: \: \: abc = 12[/tex]

The final loss percent is 0.25%.

The gap between the cost price and the selling price is what is referred to as a loss. And the loss percent is the loss as a percentage of the actual cost.

Total CP=Rs. 400

Let the CP of the first watch be Rs. x

So, CP of the second watch=Rs.(400-x)

For the first watch,

Gain Percent=5%

SP = [tex](1+\frac{5}{100})*x[/tex]

SP=105x/100

For the second watch,

Loss Percent=5%

SP=[tex](1-\frac{5}{100})(400-x)[/tex]

SP=95(400-x)/100

As the SP of both the watches is the same.

[tex]\frac{105}{100}x=\frac{95}{100}(400-x)[/tex]

105x=38000-95x

105x+95x=38000

200x=38000

x=38000/200

x=190

CP of the first watch=Rs. 190

CP of the second watch=Rs. (400-190)=Rs. 210

SP of first watch=[tex]\frac{105}{100}*190[/tex] =Rs. 199.50

SP of second watch=[tex]\frac{95}{100}*210[/tex]=Rs. 199.50

Total SP=Rs. 399

Final Loss=Total CP-Total SP

                =Rs.(400-399)

                =Rs. 1

Final Loss Percent=100/400

                              =0.25%

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The response variable in this experiment is C. the grade received on each assignment.

The Response Variable is the result of the experiment after manipulating the explanatory variable.

The response variable can also be called the Dependent or Outcome variable.

In research, the researcher develops a question about the response variable.

Thus, the response variable in this experiment is C. the grade received on each assignment.

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Answer:

A. (5, 13)

Step-by-step explanation:

The function f(x) = (x - 4) + 5 is the translation of the function f(x) 4 units right and 5 units up and the rule is:

(x, y) → (x + 4, y + 5)

Apply the rule to the given point to get:

(1, 8) → (1 + 4, 8 + 5) = ( 5, 13)

Correct choice is A

Answer:

[tex]6x^{2} +9x -4x+6\\[/tex]

Step-by-step explanation:

First you take 3x times 2x since its the first of both equations, which will give you 6x squared.

Then take the outer ones of both problems which is 3x times 3 which is 9x.

Then the inner, -2 times 2x which is -4x

Then the last of both individual problems which is -2 times -3 which is positive 6.

Answer:

7)  y⁹

9)  a⁸

Step-by-step explanation:

when we multiply two exponents (of the same base), we can add them

so, a² · a³ = a² ⁺ ³ = a⁵

let's test it out!

(a = 2 in our example)

2² · 2³ = 2⁵

4 · 8  = 32   (2⁵ = 32)

32 = 32

because this is true, we know that we can add exponents of the same base when multiplying them together

now, let's try out the question at hand:

y³ · y⁶

well, we know that 3 + 6 = 9, so y³ · y⁶ can be simplified to y⁹

--

now, we're going to be working with division. We know that division is the inverse of multiplication, so we logically know that instead of adding exponents, we subtract them when dividing

here,

a³ ÷ a² would equal a¹    (3 - 2 = 1)

let's put a = 2 again:

a³ ÷ a² = a³ ⁻ ² = a¹ = a

2³ ÷  2² =   2¹

8  ÷   4   =  2

2   =  2

once again, we have proven this shortcut to be true

now, to the problem at hand!

first, we can multiply a³ · a⁹

a³  ·  a⁹   =  a³ ⁺ ⁹  =  a¹²

so, let's rewrite the problem:

a¹² /  a⁴

because we're dividing with exponents, we can subtract 12 - 4

a¹² / a⁴

a¹² ÷  a⁴

a¹² ⁻ ⁴

a⁸

so, our simplified answer is a⁸

(note: they must be the same base, [the thing that the exponent is attached to] for this to apply)

hope this helps (and makes sense)! have a lovely day :)

The required simplification is   [tex]y^{9}[/tex]  and  [tex]a^{8}[/tex] .

To simplify the following 1 )  [tex]y^3* y^6[/tex]  2 ) [tex]\frac{a^3*a^9}{a^4}[/tex].

The process in mathematics to operate and interpret the function to make the function simple or more understandable is called simplifying and the process is called simplification.

1 )  [tex]y^3* y^6[/tex]
= [tex]y^3* y^6[/tex]
since the base of the exponents is the same so the powers of y get added
[tex]=y^{3+6}[/tex]
[tex]=y^{9}[/tex]

2 ) [tex]\frac{a^3*a^9}{a^4}[/tex]
[tex]=\frac{a^3*a^9}{a^4}[/tex]
since the base of the exponents is the same so the powers of a get added in the numerator.
[tex]=\frac{a^{3+9}}{a^4}[/tex]
[tex]=\frac{a^{12}}{a^4}[/tex]
Now, the power of the numerator will get decreased by the power of the denominator because the base is common i.e. a
[tex]=a^{12-4}[/tex]
[tex]=a^{8}[/tex]

Thus the required simplification is   [tex]y^{9}[/tex]  and  [tex]a^{8}[/tex] .

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Answer:

22.3

Step-by-step explanation:

By the law of Sines, since angle XYZ is 90 degrees,

[tex]\frac{XZ}{\sin 90^{\circ}}=\frac{YZ}{\sin X} \\ \\ XZ=\frac{1}{0.0448} \\ \\ XZ \approx 22.3[/tex]

[tex]\Large\maltese\underline{\textsf{Our problem:}}[/tex]

Find the slope of the line that passes through the pair of points.

[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]

In this problem we have two points given to us, which are...

... and we should find the slope.

[tex]\bf{We\;will\;use\;the\;Slope-Equation:}\\m=\dfrac{y2-y1}{x2-x1}[/tex]

[tex]\bf{\dfrac{0-6}{7-2}=\dfrac{-6}{5} =-\dfrac{6}{5}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Slope:}[/tex]

                                [tex]\bf{=-\dfrac{6}{5}}[/tex]

[tex]\boxed{\bf{aesthetic \not101}}[/tex]

Answer:

29ba - 7 - 5bc

Step-by-step explanation:

8ab-5bc +21ba-7

The terms 8ab, 5bc, and 21ba are made up of units multiplied by each other.  This means that each can be rewritten in a different order.  For example,

8ab is the same as:

8ba, b8a, ab8, ba8, or a8b

We may rewrite the terms to see the ones that can be combined.

8ab-5bc +21ba-7

8ba-5bc +21ba-7

8ba+21ba-7-5bc

29ba - 7 - 5bc

Answer:

1

Step-by-step explanation:

from sohcahtoa

tan = oppisite/ajacent

tan =5/5

tan = 1

Answer:7.07 ft

Step-by-step explanation:

use Pythagoras theorem for this one, in this question you have to find the hypotaneous, just use the formula H squared=b squared + p squared.

h squared =5 squared +5 squared

h squared =50

the squared on h will go on the other side and become the underfoot, so take the underfoot of 50

which givesus h=7.0

Answer:

k = 20

Step-by-step explanation:

1) Isolate the variable

k - 8 = 12

  +8    +8

2) Solve

k = 12+8

k = 20

The total amount of money he had is $160.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given :

I had $13.00.

My Mom gave me $10.00.

My Dad gave me $30.00.

My Aunt, My Uncle, and grandma gave me $100.00.

I had another $7.00.

The initial amount of money he had

= $13 + $7

= $20

His Mom gave him $10.00.

So, the total amount of money now he had is:

= $20 + $10

= $30

His Dad gave him $30.00.

So, the total amount of money now he had

= $30 + $30

= $60

So, the total amount of money now he had

= $60 + $100

= $160

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Using linear functions, it is found that the temperatures would be equal after 8 hours.

A linear function is modeled by:

y = mx + b

In which:

Two functions are equal when they intersect. In this problem, both lines pass through point (8,70), that is, they have the same temperature(of 70 degrees) after 8 hours.

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Answer:

x = 2 and y = -1

Step-by-step explanation:

that is the solution above

Answer:

x = 2

y == -1

Step-by-step explanation:

     x - 10y = 12 ----------------(I)

   10x + 10y = 10 --------------(II)

We can find the value of 'x' by eliminating 'y'. To eliminate 'y', add equations (I) & (II)

           (I)             x - 10y = 12

          (II)         10x + 10y = 10   {Now add the equations}

                         11x          = 22

                                     x = 22 /11

                                  [tex]\sf \boxed{\bf x = 2}[/tex]

Now, Plugin x = 2 in equation (1)

 10*2 + 10y = 10

   20  + 10y = 10

             10y = 10 - 20

             10y = -10

                 y = -10/10

                [tex]\sf \boxed{\bf y = -1}[/tex]

The minimum sample size needed in the research of systolic blood pressure is 68.

Given standard deviation=25 mm Hg, confidence level=90%, Estimation =5 mm Hg.

We have to first find the level of alpha which is known as error.

α=(1-0.9)/2

=0.05

Now we have to find z in the z table as such z has a p value of 1-α,that is z with a p value of 1-0.05

=0.95 ,so Z=1.645.

now finding the margin of error, which is as under:

[tex]M=z st/\sqrt{n}[/tex]

in which st is standard deviation and the n is sample size of population.

By assuming the standard deviation of 25 mm Hg we get values as under:

n is sample size.

[tex]M=z* st/\sqrt{n}[/tex]

[tex]5=1.645*25/\sqrt{n}[/tex]

[tex]5\sqrt{n}=1.645*25\\[/tex]

dividing both sides by 5

[tex]\sqrt{n}=1.645*5[/tex]

squaring both sides we get

n=67.65.

Hence the sample size needed by the researcher is 68.

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The given question is incomplete as it should includes :

standard deviation= 25mm Hg

Confidence level=90%

Estimation 5 mm Hg of u.

Answer:

Khan Academy.

Step-by-step explanation:

You can go on khan academy and search up "equations and expressions" The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.

Step-by-step explanation:

Let the number originally be "x".

Then, According to the question,other number is 3 times [3*] greater as other.

Sum of these two numbers is 24.

ATP, equation'll be :

Solving:

Therefore,one number[x] is 6.

Other number :

Answer:

A.

Step-by-step explanation:

This is a 4th degree polynomial. The function has two roots at x = 0, and two more roots at x = -2 and x = 2. Since the two roots at x = 0 are just one number, the function has three distinct real roots.

Answer: A.

The parabola equation in the factored and standard form are f(x) = (x + 2)(x - 5), and f(x) = (x - 3/2)² - 49/4 respectivly.

It is defined as the graph of a quadratic function that has something bowl-shaped.

We have:
Parabola with zeros at (-2, 0) and (5, 0) and passes through the point (-1, -4)

In factored forms:

f(x) = (x + 2)(x - 5)

Because zeros at (-2, 0) and (5, 0)

In the standard form:

f(x) = x² - 3x - 10 or

f(x) = (x - 3/2)² - 49/4

Thus, the parabola equation in the factored and standard form are f(x) = (x + 2)(x - 5), and f(x) = (x - 3/2)² - 49/4 respectivly.

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Option A is correct answer; i.e. 102 homes were sold in 2017.

A pie chart is a type of graph that records data in a circular manner that is further divided into sectors for representing the data of that particular part out of the whole part.

Here,

Total Homes sold in 2017 = 850 homes.

Homes sold in Southwest region = 12 % of the total.

                                                      = 0.12 X 850

                                                      = 102.

Thus, option A is correct answer; i.e. 102 homes were sold in 2017.

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Answer:

E. Isosceles Triangle


Step-by-step explanation:

It is because it has 2 equal sides and 2 equal angles.

Using Pythagorean theorem and trigonometric ratio, the resultant vector is 30.72km and the angle between is 53.1°

To determine the balloon's resultant vector, we can use the concept of Pythagorean theorem;

x² = 18.5² + 24.6²

x² = 943.72

x = √(943.72)

x = 30.72km

The resulatant vector is 30.72km

Let's calculate the angle of the vector;

To determine the angle of the vector, we can use trigonometric ratios;

tanθ = opposite / adjacent

tanθ = 24.6 / 18.5

tanθ = 1.33

θ = tan⁻¹ 1.33

θ = 53.1°

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The numeric values for the expressions are given as follows:

The numeric value of an expression is found replacing the letters by their numeric values.

The values of the letters are given as follows: A = 5, B = 4.4, C = 4.25.

Hence the values of the expressions are:

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Answer:

Step-by-step explanation:

The ratio of Anne's height: Ben's height is 7:9.

Anne's height is 1.4m.

Find Ben's height.

we can solve with an equation

7 : 9 = 1.4 : x

x = 9 * 1.4 : 7

x = 1.8 m

The true statement about the graph's slope is (c) Its slope is zero.

From the question, we have:

A horizontal line is at y = 2.5.

The horizontal line implies that the cost of lunch do not change

Horizontal lines have a slope of 0

Hence, the true statement about the graph's slope is (c) Its slope is zero.

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Answer:

The answer in decimal form is 33.6.

The answer in fraction form is [tex]33\frac{3}{5}[/tex].

Step-by-step explanation:

To find 40% of 84, multiply 84 and 0.4.

84 × 0.4 = 33.6

The answer in decimal form is 33.6.

The answer in fraction form is [tex]33\frac{3}{5}[/tex].

Hope this helps!