Lucy is driving to her aunt's house. The table shows the amount of gasoline in Lucy's car after the given number of hours driving. Determine the
initial amount of gasoline in the car when she started the trip. Assume that the relationship between the two quantities is linear.
a. 14
b. 12
c. 2
d. 0

Step-by-step explanation:

As always, the "unit rate" can be written two ways. You have not specified which one you want.

.. (30 lb)/(1/3 ac) = 90 lb/ac

.. (1/3 ac)/(30 lb) = (1/90) ac/lb

Answer:

90 pounds per arce

Step-by-step explanation: cause he said

the slope is 0.1 or one tenth as a fraction.

slope equation:

change in Y divided by change in X

**underlined numbers are x values and bold numbers are y values**

(3,-5) and (-7, -6)

our two Y values looking at the coordinates are -5 and -6, since coordinates are (x,y)

our two X values are 3 and -7

now plug these into the equation:

-5 - (-6)

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

3 - (-7)

**PAY ATTENTION TO THE SIGNS**

now the numerator is -5+6 which is 1

and the denominator is 3+7 which is 10

that makes 1/10 as a fraction -your slope

simplify it and you have:

slope = 0.1 or 1/10

i hope this helps!!

The expression representing the total number of people involved in the competition is 2n + 5.

Algebraic expressions are defined as the statements in mathematics which consist of constants, coefficients of the variables and variables connecting with basic operations like addition, multiplication, subtraction, etc.

Algebraic equations are something with an algebraic expression equal to something. But in algebraic expressions, there will be no equal to sign.

There are basically three classes of algebraic expressions, namely, monomial, binomial and polynomial expressions.

Number of couple dancing in a competition = n

Number of people involving in a couple dance is 2.

Total number of people dancing as couple = 2n

Number of organizers in the competition = 5

Total number of people involved = 2n + 5

Hence 2n + 5 number of people are involved in the competition program.

To learn more about Algebraic Expressions, click on the link given below :

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#SPJ5

Answer:

the answer is c

Step-by-step explanation:

because it mets up

Answer:

A= 18

Step-by-step explanation:

To find the height, find the blocks inside the shape that is completely attached (they have to be in a straight vertical line).  In this case, you can see that three vertical blocks in the middle of the shape is completely attached.  That means your height is 3.

To find the width, look at the how many horizontal boxes make up the top.  6 block inside the shape corispond with 6 blocks on top of the shape, so the width is six.

Multiply 6 by 3 to get 18.

Answer:

x = 9

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

50° is an exterior angle of the triangle, thus

38 + 4x - 24 = 50 , that is

14 + 4x = 50 ( subtract 14 from both sides )

4x = 36 ( divide both sides by 4 )

x = 9

Answer:

[tex]\huge\boxed{\sf x = 9}[/tex]

Step-by-step explanation:

The measure of the exterior angle is equal to the sum of non-adjacent interior angles.

So,

50 = 38 + 4x - 24

50 = 4x + 14

Subtract 14 to both sides

50 - 14 = 4x

36 = 4x

Divide 4 to both sides

36 / 4 = x

x = 9

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

x^2 - y^2) - (x^2 -3x +2)

Step-by-step explanation:

Answer:

-y to the second power + 3x-2

Step-by-step explanation:

Please mark brainlliest if you want.

Answer:

The answer is B :

Step-by-step explanation:

x²y = k, where k is a real constant.

When x = 3.5, y = 8.

=> (3.5)²(8) = k, k = 98.

When y = 8/9,

we have x²(8/9) = (98).

=> x² = 110.25

=> x = 10.5 or x = -10.5.

Since we want the negative value,

the answer is x = -10.5.

The required negative value of variable x when y = 8/9 is -10.5. To understand the calculations, check below.

Important information:

Using the given inverse proportional statement, we get

[tex]y\propto \dfrac{1}{x^2}[/tex]

[tex]y=\dfrac{k}{x^2}[/tex]     ...(i)

Substitute [tex]x=3.5,y=8[/tex].

[tex]8=\dfrac{k}{3.5^2}[/tex]

[tex]8=\dfrac{k}{12.25}[/tex]

[tex]8\times 12.25=k[/tex]

[tex]98=k[/tex]

Substitute [tex]k=98[/tex] in (i).

[tex]y=\dfrac{98}{x^2}[/tex]

Substitute [tex]y=\dfrac{8}{9}[/tex].

[tex]\dfrac{8}{9}=\dfrac{98}{x^2}[/tex]

[tex]x^2=98\times \dfrac{9}{8}[/tex]

[tex]x^2=110.25[/tex]

[tex]x=\pm \sqrt{110.25}[/tex]

[tex]x=\pm 10.5[/tex]

We need only negative value.

[tex]x=-10.5[/tex]

Therefore, the required value of variable x is -10.5.

Find out more about 'Proportion' here:

https://brainly.com/question/15179946

Answer:

-5pi/4

Step-by-step explanation:

Answer:

$1785

Step-by-step explanation:

you have to multiply the monthly rent by 2 since she has to pay the first and last months rent and then add the $355 security deposit

Answer:

$1985

Step-by-step explanation:

715 x 2 = 1430

1430 +355 = $1985

Answer: 6 cm

Step-by-step explanation:

Total surface area of cubical box = [tex]6a^2[/tex] , a= edge length of cube   (i)

As per given ,

Total surface area of one box  = [tex]\dfrac{\text{Cost of polishing}}{\text{Rate} \times\text{Number of boxes}}[/tex]

[tex]=\dfrac{151200}{20\times35}\\\\=\dfrac{151200}{700}\\\\= 216\ sq. cm[/tex]   (ii)

Now from (i) and (ii) ,

[tex]6a^2 = 216\\\\\Rightarrow\ a^2= 36\\\\\Rightarrow\ a= 6 \text{ [By taking square root on both sides]}[/tex]

Hence, the edge of each cubical box​ = 6 cm.

Answer:

An equation of a line that passes through the point (4,3) and is perpendicular to the graph of the equation will be:

Step-by-step explanation:

We know that the slope-intercept form of the line equation is

[tex]y=mx+b[/tex]

where

Given the line

y = -13x+4

comparing with the slope-intercept form of the line equation

The slope of the line = m = -13

We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:

slope = m = -13

Thus, the slope of the the new perpendicular line = – 1/m = -1/-13 = 1/13

Using the point-slope form of the line equation

[tex]y-y_1=m\left(x-x_1\right)[/tex]

where

substituting the values of the slope m = 1/13 and the point (4, 3)

[tex]y-y_1=m\left(x-x_1\right)[/tex]

[tex]y-3=\frac{1}{13}\left(x-4\right)[/tex]

Add 3 to both sides

[tex]y-3+3=\frac{1}{13}\left(x-4\right)+3[/tex]

[tex]y=\frac{1}{13}x-\frac{4}{13}+3[/tex]

[tex]y=\frac{1}{13}x+\frac{35}{13}[/tex]

Therefore, an equation of a line that passes through the point (4,3) and is perpendicular to the graph of the equation will be:

Answer:

11.3

Step-by-step explanation:

First solve how many grams of each mineral you need.

To do this use this equation

[tex]\frac{3}{5} =\frac{x}{y} ; x+y=400[/tex]

Solve the system of equations to get

x=150, y=250

Since there are 1000 grams in 1 kg then the amount of kg of each material you need will be

[tex]x=\frac{150}{1000}; y=\frac{250}{1000}[/tex]

So you need to 0.15 of a kg of mineral a and 0.25 kg of mineral b.

Multiply 0.15 by 42 to get the amount of money needed to buy mineral a.

0.15*42=6.3

Multiply 0.25 by 20 get the amount of money needed to buy mineral b.

0.25*20= 5

Add them to get the final amount

6.3+5=11.3

Answer:

14

Step-by-step explanation:

As we can see BD is the median of the Triangle ABC

So it breaks into two equal parts

AD = 7

And CD = 7

So

AC = AD + CD

= 7 + 7

= 14

Hope it will help :)

Answer:

A

Step-by-step explanation:

Answer:

x=65

Step-by-step explanation:

90 degree angle

90-25= 65

It is a straight line with angle measures of 90°, x° and 25° opposite to the angle marked 180°.

Hence, their sum is 180°.

➛[tex]90 \degree + x + 25 \degree = 180 \degree[/tex]

➛[tex]115 \degree + x = 180 \degree[/tex]

Then,

➛[tex] x = 180 \degree - 115 \degree[/tex]

➛[tex]x = 65 \degree[/tex]

The measure of the angle will be 65° (Ans)

~[tex] \large{ \blue{ \sf{FadedElla}}}[/tex]

Answer:

C5, [5]+, (55)

i think this is it but i might be wrong

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

The solution to the system of equations be:

(x, y) = (15, -25)

Therefore, the fourth system of equations i.e. 2x+y=5 and 2x – y=55 has the ordered pair (15, – 25) as its solution.

Step-by-step explanation:

Let us solve and check the 4th system of equations

2x+y=5

2x – y=55

solving the system of equations

[tex]\begin{bmatrix}2x+y=5\\ 2x-y=55\end{bmatrix}[/tex]

subtracting

[tex]2x-y=55[/tex]

[tex]-[/tex]

[tex]\underline{2x+y=5}[/tex]

[tex]-2y=50[/tex]

so the system of equations becomes

[tex]\begin{bmatrix}2x+y=5\\ -2y=50\end{bmatrix}[/tex]

solve -2y = 50

[tex]-2y=50[/tex]

Divide both sides by -2

[tex]\frac{-2y}{-2}=\frac{50}{-2}[/tex]

[tex]y=-25[/tex]

[tex]\mathrm{For\:}2x+y=5\mathrm{\:plug\:in\:}y=-25[/tex]

[tex]2x-25=5[/tex]

Add 25 to both sides

[tex]2x-25+25=5+25[/tex]

Simplify

[tex]2x=30[/tex]

Divide both sides by 2

[tex]\frac{2x}{2}=\frac{30}{2}[/tex]

simplify

[tex]x=15[/tex]

Thus, the solution to the system of equations be:

(x, y) = (15, -25)

Therefore, the fourth system of equations i.e. 2x+y=5 and 2x – y=55 has the ordered pair (15, – 25) as its solution.

Answer:

yes

Step-by-step explanation:

They both have a 25 degree angle, and the second one is just the first one but put on the page at a different angle

Answer: A) The initial number of bacteria is 350.

Step-by-step explanation:

Exponential growth equation: [tex]f(x)=A(1+r)^x[/tex] , where A=Initial value, r= growth rate.          (i)

Given: A bacteria sample can be modeled by the function [tex]f(x) = 350(1.20)[/tex]which gives the number of bacteria in the sample at the end of x days.

Here, [tex]f(x)=350(1+0.20)[/tex]

Compare this equation to  (i) , we get A = 350 and r= 0.20 = 20% (growth rate)

So, the  best interpretation of one of the values in this function are:

A) The initial number of bacteria is 350.

Answer:

A

Step-by-step explanation:

I did the prep

Answer:

1.) -4 and 12

y-intercept: -4

x-intercept: 12

2.) -11 and 11

y-intercept: -11

x-intercept: 11

Step-by-step explanation:

x - 3y = 12

0 - 3y = 12

-3y/-3 = 12/-3

y = -4 (y-intercept)

x - 3y = 12

x -3(0) = 12

x = 12 (x-intercept)

2x - 2y = 22

2(0) - 2y = 22

-2y = 22

-2y/-2 = 22/-2

y = -11 (y-intercept)

2x - 2y = 22

2x - 2(0) = 22

2x = 22

2x/2 = 22/2

x = 11 (x-intercept)

Step-by-step explanation:

I can't really remember this but it should be

5n +2

Something like this, I am not sure but when you fix in the values you'll get the answer. Do you understand what I'm saying?

Answer:

do u have to find the pattern?

Step-by-step explanation:

Answer:

can you explain a little bit more

Step-by-step explanation:

Answer:

6.12x10¹⁴

Step-by-step explanation:

...........................

Answer:

A

Step-by-step explanation:

3.4x10^-14 x 1.8x10^28

3.4x1.8 x 10^-14+28

6.12 x 10^14

Answer:

associative

Step-by-step explanation:

u switched parentheses