Gas is $2. 09 per gallon at the gas station. If

Nate filled up his car and spent $33. 44, how

many gallons did he put in his car?

Answer:

  see attached

Step-by-step explanation:

Given the pictorial equations, you want to know the single-digit values of each of the images.

There are 6 equations in 5 unknowns, but no numerical values are assigned. Solving the equations will only give ratios of values. From those, we need to determine the numerical values that will keep all numbers in the range 1–9.

Let the icons be represented by letter variables as follows:

Rewriting the equations to standard form, we have ...

  h +b -m -s = 0 . . . . . [eq1]

  h -b +t = 0 . . . . . . . . [eq2]

  b -3s = 0 . . . . . . . . . [eq3]

  h -s -t +m = 0 . . . . .  [eq4]

  h +2s -m = 0 . . . . . . [eq5]

  h +b +s -2t = 0 . . . . . [eq6]

We can add [eq4] to [eq1] and [eq5] to eliminate the m variable.

  (h +b -m -s) +(h -s -t +m) = 0   ⇒   2h +b -2s -t = 0 . . . . [eq7]

  (h +2s -m) +(h -s -t +m) = 0   ⇒   2h +s -t = 0 . . . . . . . . . [eq8]

Adding [eq2] to [eq6], and [eq7] will eliminate the b variable.

  (h +b +s -2t) +(h -b +t) = 0   ⇒   2h +s -t = 0 . . . . same as [eq8]; no help

  (2h +b -2s -t) +(h -b +t) = 0   ⇒   3h -2s = 0 . . . . . [eq9]

Now, we have 3 equations in 4 unknowns:

  b -3s = 0 . . . . . . . [eq3]

  3h -2s = 0 . . . . . . [eq9]

  2h +s -t = 0 . . . . . [eq8]

The smallest positive integer values that will satisfy [eq9] are ...

  h = 2, s = 3

Using these in the remaining equations gives ...

  b -3·3 = 0   ⇒   b = 9

  2·2 +3 -t = 0   ⇒   t = 7

And we can find m using [eq5]:

  m = h +2s = 2 +2·3 = 8

Then the solution is ...

The general formula of a polynomial is:

P(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_2x^2 + a_1x + a_0

A polynomial is a mathematical expression consisting of variables (such as x), coefficients, and exponents. The general formula of a polynomial is P(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_2x^2 + a_1x + a_0. Here, a_n, a_(n-1), ... , a_2, a_1, and a_0 are coefficients, and n is the degree of the polynomial. The highest exponent in the polynomial is the degree of the polynomial. For example, in the polynomial 3x^2 + 5x – 8, x^2 is the highest exponent, so the degree of the polynomial is 2. The coefficient of the highest exponent is known as the leading coefficient. In the example above, 3 is the leading coefficient. Polynomials can be used to represent a variety of functions, from simple linear equations to complex curves.

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Answer:

rate of change = 5

Step-by-step explanation:

the slope m gives the measure of the rate of change of the function

calculate the slope m using the slope formula

m = [tex]\frac{y_{2-y_{1} } }{x_{2-x_{1} } }[/tex]

with (x₁, y₁ ) = (3, 38) and (x₂, y₂ ) = (1, 18) ← 2 ordered pairs from the table

m = [tex]\frac{18-38}{1-3}[/tex] = [tex]\frac{-20}{-2}[/tex] = 5

then rate of change = 5

Reading a math word problem through to the end will help you comprehend what you need to do in order to solve it. After reading it, you may determine which components of the issue that need to be resolved are the most important and which are not.

There are few basic steps to be followed while solving any mathematics problem:

1. Read and understand the problem.

2. Identify what is given and what is needed to solve the problem.

3. Choose an appropriate strategy to solve the problem.

4. Carry out the strategy.

5. Check your answer to make sure it is correct.

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The solution in interval notation b ∈ (-∞ , -7)

-5 times b is no less than 35.

5b  ≥ 35

n order to isolate the variable in this linear inequality, we need to get rid of the coefficient that multiplies it.

-[tex]\frac{5b}{5} = \frac{-35}{5}[/tex]

This can be accomplished if both sides are divided by .

Notice that the inequality sign has changed.

b ≤ -7

We need to reduce this fraction to the lowest terms.

This can be done by dividing out those factors that appear both in the numerator and in the denominator.

In our example, this is the common factor:5

b ∈ (-∞ , -7)

We have already found the solution to the inequality, but since we want to represent the solution in interval notation, we have changed it.

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So, on solving the provided question, we can say that the outlier from the following data set will be 8.

Outliers are data points that deviate from the distribution's typical pattern. a value that is "outside" of the record's typical range (either significantly lower or substantially greater). For instance, both 3 and 85 are "outliers" when the scores are 25, 29, 3, 32, 85, 33, 27, 28, etc. Move away. Look for values that are significantly larger or significantly smaller than all other values to identify outliers. Because it is significantly smaller than all other values, Value 4 is an outlier. An observation that differs unusually from other values in a population sample taken at random is referred to as an outlier.

outlier = 4, 5, 1, 7, 4, 5, 8, 9, 6, 5, 4, 9, 7

outlier = 8

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Answer:

1. 6:2

2.for every 1 yellow paint, she needs 3 red paints

3.an orange

Step-by-step explanation:

1. It would be 6:2 because for every 2 parts yellow she needs 6 parts red

2. Since the ratio is first 6:2, just divide it by 2 since there is 2 yellow and it's asking how much red you need for 1 yellow

The scale factor of dilation explains how the size of the figure has changed. An expansion has a scale factor of x > 1 (greater than 1).

A reduction is a scale factor that is 0 <1 (higher than 0 but less than 1).

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.

A dilatation that results in a reduction (imagine shrinking) or an expansion (think stretching) produces a smaller or bigger picture, respectively.

The picture is reduced if the scale factor is between 0 and 1.

The picture is an enlargement if the scale factor is larger than 1.

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Answer: We can use two variables, x and y, to represent the number of dimes and nickels Adrian has, respectively.

We know that Adrian has twice as many nickels as dimes, so we can write the equation:

y = 2x

We also know that the total value of the coins is $1, and since nickels and dimes have different values, we can write the equation:

0.05y + 0.1x = 1

So the system of equations is:

y = 2x

0.05y + 0.1x = 1

These equations can be solved simultaneously to find the number of nickels and dimes that Adrian has.

Step-by-step explanation:

Answer: X+ywwiww asksn q9ru3

Step-by-step explanation:

88-2

The area of the triangular plot of land from the vertices is 20 square units

From the question, we have the following parameters that can be used in our computation:

A(1,5), B(7,5), and C(8,0)

Represent the vertices properly

So, we have the following representation

A = (1,5)

B = (7,5)

C = (8,0)

The area of the triangle is calculated from the vertices using the following equation

Area = 0.5 * |Ax(By - Cy) + Bx(Ay - Cy) + Cx(Ay - By)|

Substitute the known values in the above equation, so, we have the following representation

Area = 0.5 * |1 * (5 - 0) + 7 * (5 + 0) + 8 * (5 - 5)|

Evaluate the sum of products

Area = 0.5 * |40|

Remove the absolute bracket

Area = 0.5 * 40

Evaluate

Area = 20

Hence, the area of ABC with vertices is 20 square units

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Complete question

The vertices of a trangular plot of land are A(1,5), B(7,5), and C(8,0)

Calculate the area.

The coordinate of the reflection is (-y, -x)

From the question, we have the following parameters that can be used in our computation:

Point = (x, y)

Reflection:  Across the line y=−x

Using the above as a guide, we have the following:

So, we have

Image = (-y, -x)

Hence, the image is (-y, -x)

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Based on the provided information, the APR is 71.4%.

Annual Percentage Rate (APR) is defined as the interest rate which is charged by a lender on an annual basis, expressed in the form of a percentage. The formula for APR is given by

APR = (((Interest Charge+Fees)/(Loan Principal))/(Number of days in loan term)) * 365 * 100

The finance terms in the given case is $29.99 per week for 73week. Hence,

Total amount paid = 29.99*73 = $2,189.27

Loan principal = $1,095

Interest charged = Total amount paid – Loan principal amount = 2,189.27 – 1,095 = $1,094.27

Fees = 0 (as it not mentioned in the question)

Number of days in loan terms = 73*7 = 511 days

Substituting the values in the formula,

APR = ((1094.27/1095)/511) * 365 * 100

APR = 71.4%

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According to unitary method, cat takes 12 steps to cover 9 feet.

Measure your stride length or assume that it is 2.2 feet for women and 2.5 feet for men to determine it. Add the stride length to the number of steps, for example, 2.2 feet multiplied by 1,000 feet equals 2,200 feet. The answer is 2,200 ft / 5,280 0.42 mi when expressed in miles.

Given, it takes a dog three steps to cover the same distance as a cat four steps.

4 steps of a cat = 3 steps of a dog

12 cat steps equal (3/4)*12 to 9 dog steps.

Additionally, a dog's step covers one foot.

The dog moves nine feet in nine steps.

So a cat takes 12 steps to cover 9 feet.

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The true inequalities are:

5/6 > 4/6

3/8< 5/8

2/3 > 1/3

The term "inequality" in mathematics refers to a connection between two expressions or values that is not equal to each other. Inequality originates from an imbalance, thus. The majority of the time, size comparisons between two numbers on the number line are made.

The most notable instances of social inequality include those related to health care, social class, gender inequality, and wealth disparity. Comparatively speaking, some people in the healthcare system receive better and more skilled care. For these services, they are also likely to pay more.

5/6 > 4/6

0.833 > 0.667

so, this inequality is true.

3/8 < 5/8

0.375 < 0.625

so, this inequality is true.

4/5 < 2/5

0.8 < 0.4

so, this inequality is false.

4/7 > 6/7

0.571 > 0.857

so, this inequality is false.

2/3 > 1/3

0.667 > 0.333

so, this inequality is true.

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This given figure carries onto themself at 360, 180, and 60 degrees respectively.

If a rotation between 0° and 360° around the center of a figure in the plane may map the figure onto itself, the figure possesses rotational symmetry. From its starting point, the figure can be rotated and mapped onto itself. The symmetry is of order 4. As a result, the figure displays both rotational and line symmetry.

Given three figures those figures have rotational symmetry from their center point.  The fixed point that the rotation revolves around in a figure or object with rotational symmetry is referred to as the center of rotation.

for figure 1

figure 1 does not have rotational symmetry on any given angles thus, its rotational symmetry would be 1 since it carries onto itself at 360°.

for figure 2

figure 2 has rotational symmetry at 180°. thus, its rotational symmetry would be 2 since it carries onto itself at 180° and 360°.

for figure 3

figure 3 has rotational symmetry at 60, 120, 180, and 240. thus, its rotational symmetry would be 6 since it carries onto itself at 60, 120, 180, 240, and 360°.

therefore, the given figures have 1, 2, and 6 rotational symmetry.

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The solution of this system of linear equations is x=3, y=-5.

To solve this system of linear equations, you can use various methods such as substitution, elimination, or matrices. Here is one way to solve using the substitution method:

4((11+y)/2) + 8y = 24

3((11+y)/2) + 2y = 15

y = -5

x = (11 + (-5))/2

x = 3

4(3) + 8(-5) = 24

3(3) + 2(-5) = 15

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The question is -

Solving a system of linear equations in two variables,

Error interval is 35 ≤ x < 45.

Error intervals working?

Error intervals work by providing a range of values within which the true population value is likely to fall, with a certain level of confidence. The most common level of confidence used is 95%, which means that if the survey or experiment were conducted multiple times, the true population value would fall within the error interval 95% of the time.

We are looking at a rounded value when we employ error intervals. The range of values that were possible before the number was rounded is described by an error interval.

Given: A number x becomes 40 if it is rounded to 1 significant figure

To find: error interval for x

In the given question, an error interval is the range of values that a number x can be equal to before it is rounded to 1 significant figure.

As a number x becomes 40 if it is rounded to 1 significant figure, error interval is 35 ≤ x < 45.

A number x in this interval becomes equal to 40 if it is rounded to 1 significant figure.

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Answer:

2

When you cancel out the m (cause its the common factor) the only thing left is to simplify 10/5 which is 2.

The direction of A with respect to B. N B 73° N A is 287

A direction is the way that something is moving, directing, or moving toward something or someone. The directions could be Up, Down, Left, and Right, or North, South, East, and West.

The ability to specify where one thing is in relation to another is known as position in mathematics. Defining direction entails explaining the direction in which something moves, such as forward, backward, or in a full or half turn.

It is possible to define direction using relative terms like up, down, in, out, left, right, forward, backward, or sideways. A direction can also be denoted by one of the four cardinal directions: north, south, east, or west.

Angles at a point add up to 360 degrees.

⇒ Bearing from A to B is = 360° - 73° = 287°.

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Bonnie will complete four laps before being passed by Annie because she runs an additional quarter lap for every lap she completes. This indicates that Annie and Bonnie are on an equal footing, and Annie must complete an additional lap to pass Bonnie. Annie will have completed five laps after that.

We can use the unitary method to calculate 100% of an amount. For instance, if 10% of the marbles in a pot are 35, then the total number of marbles in the pot will be 35 x 10%, or 350.

The unitary method can be used to calculate how many kilometres a car will travel on one litre of gas if it travels 44 km on two litres of fuel. In other words, the unitary method is the process by which we determine the value of a single unit and then use that information to determine the values of multiple units.

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The equation of line passes through the points (0, 0) and (3a, 5g) will be;

⇒ y = (5g/3a) x

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (0, 0) and (3a, 5g).

Now,

Since, The equation of line passes through the points (0, 0) and (3a, 5g).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (5g - 0) / (3a - 0)

m = 5g / 3a

Thus, The equation of line with slope 5g/3a is,

⇒ y - 0 = 5g/3a (x - 0)

⇒ y = (5g/3a) x

Therefore, The equation of line passes through the points (0, 0) and

(3a, 5g) will be;

⇒ y = (5g/3a) x

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The ball will reach a height of 3 feet at t = 5/4 seconds.

To find the time (t) when the ball reaches a height of 3 feet, we need to use the equation for the height of the ball: h = -16 [tex]t^2[/tex] + 40t + 5

We are given that the height of the ball is 3 feet, so we can set up the equation:

3 = -16[tex]t^2[/tex] + 40t + 5

Then we can solve for t by isolating t on one side of the equation and then solving for t:

3 = -16[tex]t^2[/tex] + 40t + 5

-5 = -16[tex]t^2[/tex] + 40t

16[tex]t^2[/tex] - 40t - 5 = 0

We can factor the left side of the equation:

(4t - 5)(4t + 1) = 0

So we have two possible solutions:

t = 5/4 or t = -1/4

However, the time cannot be negative, so the only valid solution is t = 5/4.

So the ball will reach a height of 3 feet at t = 5/4 seconds.

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So the polygon has 22 sides.

A polygon's sides are made up of straight line segments that are joined end to end. As a result, the line segments of a polygon are referred to as sides or edges. The place where two line segments meet is known as the vertex or corners, and an angle is generated as a result. A triangle with three sides is an example of a polygon.

The sum of the interior angles of a polygon can be calculated using the formula:

(n-2) * 180 = sum of the interior angles

Where n is the number of sides of the polygon.

We know that the sum of the interior angles is 20*180, so we can substitute this into the formula:

(n-2) * 180 = 20 * 180

Solving for n, we get:

n = (20 * 180) / 180 + 2

n = 20 + 2

n = 22

So the polygon has 22 sides.

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Answer:

x = 8

Step-by-step explanation:

572 - 500 = 72

72 / 8 = 9.

But in order to spend less than 572, he has to buy 8 cases. If he buys 9 cases he will be exactly 572.

Answer:

9 or fewer cases

Step-by-step explanation:

Solving a two step equation:

First, determine how much he has left to spend

572 - 500 = 72

He has 72 dollars left to spend on soda

Each case is 8 dollars.

Divide how much he has to spend by the cost of each case

72/8 = 9

He can buy up to 9 cases and stay under budget.

Straight line has the equation is, y = 5x - 4.

An endless number of points that are connected on both sides of the point make up a straight line.

The slope of a straight line, "m," is determined by:

m = y2 - y1 / x2 - x1

A linear equation has the expression y = mx + b in slope-intercept form. X and Y are the variables in the equation. The numbers m and b stand for the line's slope (m) and the value of y at x = 0.

The graph's acquired points are (0,-4) and (1,1)

The slope is ,

m = 1-(-4) / 1-0

  = 5/1

  = 5

The line's equation will be as follows since it crosses the y-axis at its intersection point, where C = -4.

⇒ y = mx + c

⇒ y = 5x + (-4)

⇒ y = 5x - 4

As a result, y = 5x - 4 is the equation for the straight line depicted below.

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Answer:

False

Step-by-step explanation:

y < -2x -2 Substitute in -1 for x and 0 for y and see if the statement is true.

0 < -2(-1) - 2

0 < 2-2

0 < 0  

This is a false statement.                                                                                                                                                                                                                                                                  

Answer: A / No.

Step-by-step explanation:

     We will substitute the point given, (-1, 0) and see if the inequality is true after simplifying.

     Given:

y < -2x - 2

     Substitue:

0 < -2(-1) - 2

     Multiply:

0 < 2 - 2

     Subtract:

0 < 0 ✗

     0 is not less than 0, so this point is not a solution.

EXPLANATION

2025 is a perfect square number hence we can determine its square root. 45 is the square root of 2025 as 45 multiplied by 45 gives the number 2025. Interestingly, – 45 × – 45 is also 2025. Hence It is represented as √2025 = 土45.

Answer:

  y = -5x +4

Step-by-step explanation:

You want the point-slope equation of the line with y-intercept +4 and through the point (1, -1).

The graph shows you the line decreases 5 units from +4 to -1 as x increases 1 unit from 0 to 1. This tells you the slope is ...

  m = rise/run = -5/1 = -5

The y-intercept is the value of y where the line crosses the y-axis:

  b = 4

These values go into the point-slope equation:

  y = mx +b . . . . . . line with slope m and y-intercept b

  y = -5x +4 . . . . . . line with slope -5 and y-intercept 4