solve the system of equations​

The statement that is best supported by the graph is; Jillian's car holds more gasoline, but Nikki's car gets better gas mileage.

The total amount of gasoline each car tank can hold is shown on the left of each graph on the y-axis.

Jillian's car holds 22 gallons.

Nikki's car holds 20 gallons.

Jillian's car holds more gasoline.

Now we need to see which car gets better gas mileage. Getting better gas mileage means you can go farther with each gallon of gas.

With Jillian's car, after using 22 gallons of gas, you have gone 350 miles, and the gas tank is empty.

350 miles with 22 gallons is 350/22 = 15.9 miles per gallon.

With Nikki's car, you start with only 20 gallons. By the time you drive 350 miles, you still have some gas left. Not only did you start with less gas, 20 gal vs. 22 gal, but after driving the same distance, 350 miles, there is still some gas left in the tank, 6 gallons.

That means Nikki's car used 20 - 6 = 14 gallons to drive 350 miles. 350/14 = 25 miles per gallon.

The more miles per gallon you get, the better the mileage. Thus;

25 miles per gallon is better mileage than 15.9 miles per gallon.

Nikki's car has a smaller gas tank, but it gets better mileage.

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Answer: The answer would be  12 39/72

Step-by-step explanation:

903 divided by 72, you'd get 12.5417. You could also express 903/72 as a mixed fraction: 12 39/72.

So basically 130+90=220 and 6+8=14. And 220+14=234.

Since the isotope has only a very little amount in nature, it does not largely affect the  atomic mass of lithium.

The term isotope has to do with the atoms of the same element that do have the same atomic number but different mass numbers. The implication of this is that isotopes have the same number of protons but do not have the same number of neutrons.

Note that the average atomic mass of an atom is the weighted average of the atomic masses of all the isotopes of the compound. The isotopes that contribute greatly towards the atomic mass are those that have a larger percentage abundance.

Given that the new lithium isotope, 8Li identified  is a trace isotope, meaning that it exists in a very tiny quantity, it does not any noticeable effect on the  atomic mass of lithium.

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∠6 and ∠12 are supplementary angles. That means, they add up to 180°

Substitute ∠6 by 53° to find ∠12.

Subtract 53 from both sides to find ∠12.

Answer: ∠12 = 127°.

Answer:

13.3 liters of petrol left

Step-by-step explanation:

80 ÷ 6 = 13.3

Answer:

(5, 4)

Step-by-step explanation:

What is Orthocenter?

A point where the altitudes of the triangle meet is known as the point of concurrency or simply the orthocenter of the triangle

The solutions of the quadratic equation  x² = 16x - 65 are:

x = 1/2 +  1/32i

x = 1/2 - 1/32i

We know that a quadratic equation is an equation that is of the sort ax^2 + bx + c = 0. Hence, the equation would be solved and it could have a complex root. By this I mean that the root of the equation could be a complex number as we have in the case of the equation here.

x² = 16x - 65 = 0

x² - 16x + 65 = 0

When we solve by the formula method;

x = -b ±√b^2 - 4ac/2a

x = -(-16) ±√(-16)^2 - 4 (1) (65)/2(16)

x = 16 ±√256 - 260/32

x = 16/32 ±√-4/32

x = 1/2 ± 1/32i

Thus

a =  1/2

b = 1/32

We then obtain;

x = 1/2 +  1/32i

x = 1/2 - 1/32i

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25.42 marked down by 33 % is 17.0314.

This is a question of percentages.

Percentage

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

Percentages have no dimension. Hence it is called a dimensionless number.

33 % of 25.42 is given by:-

(33/100)*(25.42) = (33*25.42)/100 = 838.86/100 = 8.3886

25.42 marked down by 33 % = 25.42 - 8.3886 = 17.0314.

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The value of AC when BD= 12 and AC = x+ 23 is 28

A line segment can be defined as the part of a straight line that is being bounded by two different end points, and also contains all the points on the line between its endpoints.

From the information given, we have that line AD is a line with segments, line AB, line BC, line CD with B and C as the midpoints.

Given the points as;

We have that;

AC + BC = AD

But line BD = 14 + x, we have;

Line AC = x + 23 - 14 + x

Line AC = 2x + 9

substitute the values into the equation

2x + 9 +12 = 26 + x

collect like terms

2x - x = 26 - 21

Add or subtract like terms

x = 5

But, we have that;

Line AC = x + 23

Line AC = 5 + 23

Add the values

Line AC = 28

Hence, the value is 28

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The converse statement is "If a person is 13 years old or older, then the person is a teenager. The converse is valid" . Option D

The converse of a conditional statement is defined as a statement that is formed when the hypothesis and conclusion of a sentence are both reversed or interchanged.

If the conditional statement is expressed as a → b

The converse statement is referred to as b → a

It is important to note that the original statement must be a conditional statement for a converse statement to derived from it.

Given the conditional statement:

"If a person is a teenager, then the person is 13 years old or older."

The converse statement would be written as;

If a person is 13 years old or older, then the person is a teenager.

We can see that the converse statement is valid because anyone that is 13 or older is a teenager

Hence, the converse statement is valid. Option D

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Step-by-step explanation:

1) 5.45 ÷ 65

2) 109/20 x 1/65=

3) 109/1300 or 0.08384615

The solution of given inequalities are x > -3 and x ≤ 5.

When resolving an inequality, you can do one of the following: add the same amount to each side; deduct the same amount from each side; multiply or divide each side by the same positive amount. You must flip the inequality sign if you multiply or divide each side by a negative number.

Given inequalities are 2x - 5 > -11 and -10x - 6 ≥ 44.

To solve the first inequality,

2x - 5 > -11

Adding 5 on both sides,

2x - 5 + 5 > -11 + 5

2x > -6

Divide both sides by 2,

x > -3

To solve the second inequality,

-10x - 6 ≥ 44

Adding 6 on both sides,

-10x - 6 + 6 ≥ 44 + 6

-10x ≥ 50

Divide both sides by -10, and change the inequality sign

x ≤ 5

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Answer:

see explanation

Step-by-step explanation:

the volume (V) of the container is

V = 10 × 4 × 5 = 200 m³

change the dimensions of the box to m , to be same as container

l = 50 cm = 0.5 m , b = 40 cm = 0.4 m , h = 20 cm = 0.2 m

then

volume of box = 0.5 × 0.4 × 0.2 = 0.04 m³

Number of boxes that can be stored in container is

200 ÷ 0.04 = 5000

thus no more than 5000 boxes can be placed in the container

The decomposition of 240 - 135 = 105 will be 15(16 - 9) = 15(7) = 105

It should be noted that decomposition simply means breaking down of the numbers that are given or illustrated.

It should be noted that the numbers 240 - 135 = 105 all have a common factor of 15. This will be broken down as:

240 - 135 = 105

15(16 - 9)

= 15(7)

= 105

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There are different 2,808,000 passwords possible which are the correct answer would be option (B)

A permutation is defined as a mathematical process that determines the number of different arrangements in a set of objects when the order of the sequential arrangements.

Sue picks a new password for her email that consists of 3 letters, 2 digits, and a special character (! or #) which is given in the question.

As per the given condition,

For the first letter, we have 26 options.

For the second letter, we have 25 options, because one letter is already used.

For the third letter, we have 24 options, because 2 letters are already used.

For the first digit, we have 10 options.

For the second digit, we have 9 options, because one is already used.

For the first special character (! or #), we have 2 options.

Then the total number of combinations is:

Combinations = 26×25×24×10×9×2 = 2,808,000

So if we can not repeat digits or letters, we can make 2,808,000 different passwords.

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Answer:

24

Step-by-step explanation:

it just is, I don't know how I get this. I just did.

[tex]\frac{2n+48}{3}[/tex]

The frequency of the 10 inch violin string will be 630 cycles per second or Hertz if the violin string 14 inches long vibrates at a frequency of 450 cycles per second.

As per the question statement, A violin string 14 inches long vibrates at a frequency of 450 cycles per second and we are supposed to find out the  frequency of a 10-inch violin string.

We should be knowing that the length of a violin string varies inversely as the frequency of its vibrations.

f = m/l, where "f" is the frequency and "l" is the length and "m" is the constant number

450 = m / 14

m = 6300

Therefore New frequency = 6300 / 10 = 630 cycles per second

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The expression 8 ( 3x - 7 ) when expanded gives 24xx - 56.

The cornerstone of mathematics is the theory of operations; we use it to compute and remember fundamental truths. The subsequent three characteristics are applied to addition and multiplication: Commutative Property, Associative Property, and Distributive Property.

The distributive property of binary operations in mathematics generalizes the distributive law, which states that in elementary algebra, equality is always true.

Consider the expression 8( 3x - 7 ),

Let's say y is equal to 8( 3x - 7 ).

By using the distributive property:

y = 8 × 3x - 8 × 7

y = 24x - 56

Therefore,

8( 3x - 7 ) = 24x - 56

Therefore, when the expression 8( 3x - 7 ) is expanded we obtain the expression 24x - 56.

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Answer:

216 miles

Step-by-step explanation:

so the base fee is 18.99, subtract the total (219.87) by 18.99.

219.87-18.99=200.88

200.88 divided by 0.93 (charge for each mile driven)

200.88/0.93=216

thats a lot of miles.

Equation is y= 56x that models the relationship between x ,the number of hours Mark reads, and y, the number of pages of the book he reads.

The term rate of change (ROC) describes the rate at which something changes over time. Thus, it is not the amount of individual changes themselves but rather the acceleration or deceleration of changes (i.e., the rate). Rate of change is a tool used in finance to comprehend price returns and spot trend momentum.

Given Data

The hours are indicated by = x

The calculation for the number of pages is =y

Read 42 pages every [tex]\frac{3}{4}[/tex] hour

You can model the equation as follows:

y = mx +b

Rate of change = [tex]\frac{change in y}{change in x}[/tex]

Rate of change = 42 ÷[tex]\frac{3}{4}[/tex]

Rate of change = 42 ×[tex]\frac{4}{3}[/tex]

Rate of change = 56

Equation y= 56x

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This how we change 23 out of 25 to a percentage

The numerator of a question is the number that appears above the bar; in this case, the numerator is 23.

The denominator is the number beneath the bar, and in this question, it is 25.

To calculate the value of a fraction, divide the numerator by the denominator.

Therefore, we must divide 23 by 25.

23/25 = 0.92

To determine the percentage, multiply the outcome by 100.

The percentage value will be obtained by multiplying 0.92 by 100.

0.92 x 100 = 92%

As a result, 92% is the answer to the question.

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Answer:

[tex]-9k-7[/tex]

Step-by-step explanation:

Replace n with -9k.

A man's taxable income is $3060 if tax is paid at 12%, then the man's net income is $3477.27

The taxable income = $3060

The tax percentage = 12%

Income tax is the a type of tax impose on income generated by businesses and individuals by the government

Consider the net income as x

Then,

12% of the income = x×(12/100)

Therefore the equation will be

x -  x×(12/100) = 3060

x(1-(12/100) = 3060

x(1-0.12) = 3060

0.88x = 3060

x = 3060/0.88

x = $3477.27

Hence, a man's taxable income is $3060 if tax is paid at 12%, then the man's net income is $3477.27

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The simplified expression for -27z^3-9z^4+18z^6, using the greatest common factor, is given as follows:

9z³(-3 - z + 2z³).

To find a symbolic expression by the greatest common factor, we have to:

Then we multiply these GCFs.

For this problem, the numeric coefficients are given as follows:

27, 9 and 18, hence the GCF is of 9.

The exponents are given as follows:

z³, z^4 and z^6, hence the GCF is of z³, which is the expression with the lowest exponent.

Then the GCF of the expression is given as follows:

9z³.

To simplify the expression, each term of the expression is divided by 9z³, hence the factored expression is:

9z³(-3 - z + 2z³).

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Proved [tex]Cos^{4}x - Sin^{4}x + 1[/tex] = 2Cos²x

We will use the Pythagorean Theorem:

Sin²x + Cos²x = 1

from which we can get:

Sin²x = 1 - Cos²x

Also, note that the difference in the similarity of squares can be written:

A² - B² = (A - B)

We can use this with A = Sin²x and B = Cos²x as follows:

[tex]Sin^{4}x - Cos^{4}x[/tex]

= (Sin²x)² - (Cos²x)²

= (Sin²x - Cos²x) (Sin²x + Cos²x)

= Sin²x - Cos²x

= (1 - Cos²x) - Cos²x

= 1 - 2Cos²x

Now move the 1 and negative symbols to the left.

[tex]Cos^{4}x - Sin^{4}x + 1[/tex] = 2Cos²x

The trigonometric ratios are related to each other by equations called trigonometric identities.

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The equation for the line that is parallel to the given line y=3/4x + 7 and that passes through the given point G (8,3) is y= (3/4)x -3.

As given in the question,

Equation of the given line :

y=3/4x + 7

Slope of the given line = (3/4)

Equation of line with slope (3/4) & passing through point (8, 3) is given by:    

y - 3 = [tex]\frac{3}{4}[/tex] (x - 8)      

⇒ 4 (y - 3) = 3 (x - 8)

⇒ 4y - 12 = 3 x - 24

⇒ 4 y = 3 x - 24 + 12

⇒ 4 y = 3 x - 12

⇒ y = (3/4)x - 3

Therefore, the equation for the line that is parallel to the given line

y=3/4x + 7 and that passes through the given point G (8,3) is y= (3/4)x -3.

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Using linear function concepts, it is found that:

The slope-intercept representation of a linear function is:

y = mx + b.

In which:

For this problem, we will use a calculator from the points on the table to build a linear function of best-fit. The points are given as follows:

(5, 17.9), (10, 18.7), (15, 19.7), (20, 20.5), (25, 21.3).

Then the function is:

y = 0.172x + 17.04.

Then:

The table is missing, and is given by the image at the end of the answer.

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The value of x is 18 and the value of ∠A (interior angle) is 73°.

According to the given figure,

We have:

∠A = 6x-35°

∠B = 3x+53°

The two parallel lines have been cut by another line.

(Note that when a line divides two parallel lines then the sum of the interior angles on the same side is 180° and the alternate interior angles are equal to each other.)

So, we will have the following expression:

∠A + ∠B = 180°

(6x-35+3x+53)° = 180°

9x+18 = 180

9x = 180-18

9x = 162

x = 162/9

x = 18

Now, putting the value of x in ∠A,

∠A = 6x-35°

∠A = (6*18-35)°

∠A = (108-35)°

∠A = 73°

Hence, the value of x is 18 and the measurement of ∠A is 73°.

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julia wants to purchase a pair of headphones that are on sale for $42.79. the sales tax rate in her county is 6%. then Julia have to pay $2.57 as sales tax on purchase of headphones.

Given,

The cost of headphones which Julia wants to purchase on sale = $ 42.79

The sales tax in Julia's country = 6%

We have to calculate the amount of sales tax Julia will pay on the purchase:

That is,

Sales Tax Value = Percentage of sales tax × Price of headphones

Sales Tax Value = (6 / 100) × 42.79

Sales Tax Value = 0.06 × 42.79

Sales Tax Value = 2.5674

Sales Tax Value ≈ 2.57

Therefore, Julia have to pay $2.57 as sales tax on purchase of headphones.

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