Diego’s family car holds 14 gallons of fuel. Each day the car uses 0. 6 gallons of fuel. A warning light comes on when the remaining fuel is 1. 5 gallons or less.


Diego says the expression 14-0. 6t helps him understand this situation. In this situation, what does this expression represent, and what does the variable t stand for?

The equation (7 × 10) + (7 × 10%) + (7 × 10²) = 700 070.07 can be rewritten as:

7x + 0.7y + z = 700 070.07

To find a set of values for x, y, and z that satisfies this equation, we can use trial and error. One possible set of values is:

x = 100

y = 10

z = 7000

If we plug these values into the equation, we get:

(7 × 100) + (7 × 0.1) + (7 × 7000) = 700 070.07

Which simplifies to:

700 + 0.7 + 49000 = 700 070.07

This equation is true, so the values x = 100, y = 10, and z = 7000 are a solution to the original equation.

Answer:

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Answer:

5.36^2+5.36^3=182.720256

Step-by-step explanation:

Answer: perpendicular bisector

Step-by-step explanation: Hope you see it helpful!

Answer: x= 38/11

Step-by-step explanation: x-12x-14=24

-11x-14=24

Add 14 to both sides

simplfy

-11x=38

Divide both sides by the same factor

x=11-38/11

Answer:

3

Step-by-step explanation:

Answer: 5x-3=3x+9=4y+20

2x+6+20=180

answer is 74

Step-by-step explanation:

The distance between the points (3,5) and a line with the equation 5x-3y+10=0 is 10/√34 units.

Given that,

We have to find the distance between the points (3,5) and a line with the equation 5x-3y+10=0.

We know that,

We have a formula that is

Let (x₁, y₁) be the point and ax + by + c = 0 be the line.

Then the distance between a point and a line will be

d=|ax₁+by₁+c|/√(a²+b²)

Here,

(x₁,y₁)=(3,5)

a=5, b=-3 and c=10

So, substituting

d=|5(3)+(-3)(5)+10|/√(5²+(-3)²)

d=|15-15+10|/√25+9

d=|10|/√34

d=10/√34

Therefore, the distance between the points (3,5) and a line with the equation 5x-3y+10=0 is 10/√34 units.

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Answer: If two lines are parallel, it means that they have the same slope. Therefore, to find the value of x in this problem, you need to find the slope of line m and line n, and then set them equal to each other.

The slope of a line can be found using the formula:

slope = (y2 - y1)/(x2 - x1)

In this case, you are given the equation of line m in the form "x + 1", and the equation of line n in the form "7x - 5". To find the slope of each line, you can rewrite these equations in the form y = mx + b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis).

For line m, we have:

y = x + 1

The slope of this line is m = 1.

For line n, we have:

y = 7x - 5

The slope of this line is m = 7.

Since line m and line n are parallel, their slopes must be equal. Therefore, we can set these slopes equal to each other and solve for x:

1 = 7

This equation has no solution, which means that there is no value of x that will make these two lines parallel. Therefore, the answer is that there is no solution.

Step-by-step explanation:

it is simple : it always has to be the corresponding side of the other triangle. all sides must have the same scaling factor.

d/p = e/q = f/r

d/e = p/q

e/f = q/r

f/d = r/p

The equations that go with the statements are; e/f = q/r and f/d = r/p

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inversely proportional, can be built to find the desired measures in the problem.

We want the different ways sides of similar triangles can be shown as proportional.

Corresponding sides

From shorter to longer, the corresponding sides in similar triangles are ...

Smaller ... Larger

 b . . . . . . . e

 a . . . . . . . d

 c . . . . . . . f

d/p = e/q = f/r

d/e = p/q

e/f = q/r

f/d = r/p

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The correct justification for the given steps are;

Step 1; Addition property of equality.

Step 2; Subtraction property of equality.

Step 3; Division property of equality.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

For the given condition,

⇒ 200 + 20w = - 100 + 25w

Where, 'w' is number of weeks.

Now,

Since, For the given condition,

⇒ 200 + 20w = - 100 + 25w

Where, 'w' is number of weeks.

Solve for w as;

⇒ 200 + 20w = - 100 + 25w

Apply Addition property of equality,

⇒ 200 + 20w + 100 = - 100 + 25w + 100

⇒ 300 + 20w = 25w

Apply Subtraction property of equality,

⇒ 300 + 20w - 20w = 25w - 20w

⇒ 300 = 5w

Apply Division property of equality,

⇒ 300/5 = 5w/5

⇒ 60 = w

⇒ w = 60

Thus, The correct justification for the given steps are;

Step 1; Addition property of equality.

Step 2; Subtraction property of equality.

Step 3; Division property of equality.

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I believe that x²y²/((y+x)(y+x)) is identical to (1/x-1/y)/(1/x+1/y) based on the expression above.

An expression, also known as a mathematical expression, is a finite combination of symbols that are well-formed in accordance with context-dependent rules. Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.

Here,

Expression:

=(1/x-1/y)/(1/x+1/y)

Option:

=((y+x)/(y-x))

=((y-x)(y+x))/x²y²

=x²y²/((y+x)(y+x))

=(y-x)/(y+x)

From the above expression, I think x²y²/((y+x)(y+x)) is equivalent to (1/x-1/y)/(1/x+1/y).

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Answer: aka (D) edg 2023

Step-by-step explanation:

trust ^.^  hoped this helped

Answer: 2%

Step-by-step explanation:

First, take $60 divided by $600, then times 100% = 10% rate for five years

Then take 10 divided by 5 = 2% per year

Answer:

x value= 3

Step-by-step explanation:

Hope this helps!!

Dividing 1.25 by 1: 1.25 / 1 = 1.25

Dividing 1.25 by 5: 1.25 / 5 = 0.25

Dividing 1.25 by 8: 1.25 / 8 = 0.15625

Dividing 1.25 by 10: 1.25 / 10 = 0.125

The annual percentage yield (APY) for the investment $8000 at 5.75% compounded daily is; 5.918%

The Annual percentage yield(APY) is defined as the amount of interest you'll earn in one year from a savings account.

Annual percentage yield (APY) is calculated by the usage of the formula;

APY= (1 + r/n )ⁿ – 1

Where;'

r is the said annual interest rate

n is the variety of compounding intervals every year.

Thus, we are given;

r = 5.75% = 0.0575

n = 365 days

Thus;

APY= (1 + (0.0575/365 )³⁶⁵ – 1

APY = 5.918%

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The value of h(-5) in the given function, h(x) = -3|x - 1| + 4, is h(-5) = -14

From the question, we are to evaluate the given function for the given value

The given function is

h(x) = -3|x - 1| + 4

We are to determine the value of h(-5).

To determine the value of h(-5), we will substitute -5 for x in the given function.

That is,

h(x) = -3|x - 1| + 4

h(-5) = -3|(-5) - 1| + 4

h(-5) = -3|-5 - 1| + 4

h(-5) = -3|-6| + 4

h(-5) = -3(6) + 4

h(-5) = -18 + 4

h(-5) = -14

Hence, the value of h(-5) is -14

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The measure of arc PD is 56.

What is a measure of arc?

The central angle that creates the intercepted arc's central angle, or the arc measure, is expressed in degrees. Arc length can be estimated as a percentage of the circle's circumference by multiplying the circle's diameter by the arc length, divided by 360.

Here, we have

Given: DR = 4x +4

PR = 50°

The sum of the measure of arc PR + DR = 180°

50° +  4x +4 = 180°

x = 4

Now we can find the measure of the arc of PD. we put the value of x in 12x+ 8 and we get

12(4) + 8 = 56

Hence, the measure of arc PD is 56.

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Answer:

[tex]\huge{\boxed{2 \text{ units}}}[/tex]

Step-by-step explanation:

N.B. I attached an image of the number line as presented by the problem.

The absolute value of a number is its distance from zero.  A simple way to say that is that the absolute value of a number is the number made positive and is denoted by "||"

i.e.

|-4| = 4

|4| = 4

|-219| = 219

The distance between two points on a number line is the absolute value of their difference.  Thus, simply do:

|5 - 3|

|2|

2

OR

|3 - 5|

|-2|

2

Thus, the length of the segment is simply 2.

Hope it helps :) and let me know if you want me to elaborate.

Answer:

4.6

Step-by-step explanation:

298 divided by 65=4.58....

Answer:

largest number= 9754

smallest number = 4579

Step-by-step explanation:

largest number - 9754

9 is the larger number in 5,7,4,9

7 is the second largest

so you basically count it backwards

smallest number=4579

4 is the smalleat number in 5,7,4,9

so you basically count forward

This mean for the data for those events is that data will only be used for measurement purposes.

Given :

You have ads  personalization enabled for your property, but want to exclude specific events.

You may use digital advertising to help reach people online and drive conversions on your application and website when you enable personalization in analytics .

Example :

By activating you gain the ability to use your analytics audiences to personalize your digital , which can improve the performance of your campaigns.

You can adjust  personalization for a specific event type or user property in your analytics  property.

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To invest in order to cover the cost of the TV is 964.62.

In the simplest terms possible, interest is the cost of borrowing money. It's the portion of a credit card or loan balance you have to pay back to your lender. However, interest can also be paid to you; prominent ways to do so include certificates of deposit and savings accounts.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.

TV price was $900.

3.5% interest rate

Investment period of 2 1/2 years: p (1 +r/100)n 900((1 + 3.5)/100)2 1/2 964.62

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Answer: the answer is 2

Step-by-step explanation: he explains how and why he individuals are being studied

Answer:

16b2-56b+49

Step-by-step explanation:

hope this helps

Augustus used a total of 12 gallons + 1.8 gallons = 12+1.8=13.8 gallons of chocolate syrup in the three mixtures.

What is a percentage?

Percentages are essentially fractions where the denominator is 100. To show that a number is a percent, we use the percent symbol (%) besides the number. For example, if you got 75 questions right out of 100 on a test (75/100), you would have scored 75%.

Since Augustus used 10% chocolate syrup and 90% milk for the first mixture and 30% chocolate syrup and 70% milk for the second mixture, the total percentage of chocolate syrup he used in the first two mixtures is 10% + 30% = 40%.

Since Augustus made a total of 30 gallons of chocolate milk, he used 30 gallons * 40% =3040.01=12 gallons of chocolate syrup in the first two mixtures.

For the final mixture, Augustus used 15% chocolate syrup and 85% milk. The total percentage of chocolate syrup he used for the final mixture is 15%.

Since Augustus used a total of 12 gallons of chocolate syrup in the first two mixtures, he used an additional 12 gallons * 15% = 1215.01=11.8 gallons of chocolate syrup for the final mixture.

Hence, Augustus used a total of 12 gallons + 1.8 gallons = 12+1.8=13.8 gallons of chocolate syrup in the three mixtures.

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The value of x in the figure is 5√3.

What is the trigonometry?

Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are among the trigonometric functions (also known as the circle functions) that make up trigonometry.

What does cos 30 mean?

The trigonometric function "Cosine" is denoted by the notation "Cos." The definition of cosine is the ratio of a right-angle triangle's hypotenuse to base length (the longest and slant side). Cos (x), where x is the angle formed by the two sides, equals base/hypotenuse, or b/h.

What is the formula of Cos 30?

Cos 30° = √3/2

3/2 is the value of Cos 30°, which is a trigonometric ratio or trigonometric function of a specific angle. The exact value of cos 30 degrees is expressed as 0.8660 roughly.

Cos 30°= b/h

√3/2 = x/10

X= √3/2 × 10

X= 5√3

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Answer:

(x+6)^2 + (y-8)^2 = 10^2

or

(x+6)^2 + (y-8)^2 = 100

Step-by-step explanation:

Equation of a circle in standard form: (x-h)^2 + (y-k)^2 = r^2

(h,k) represent the center of the circle

h = -6

k = 8

r = the length of the radius

10^2 = 100

Given the rate at which the zookeeper is giving the animals hay and grain, on which day will she have the same amount of grain and hay remaining is 6 days.

Every three days, one pound of hay and one pound of feed are used.

10 pounds of grain and 8 pounds of hay are present.

There are 6 pounds of hay and 6 pounds of grain left on the sixth day.

A rate in mathematics is the comparison of two related values expressed in different units.

The numerator of the ratio indicates the rate of change in the other (dependent) variable if the denominator of the ratio is written as a single unit of one of these quantities, and if it is assumed that this quantity may be modified systematically (i.e., is an independent variable).

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According to the given information 62% of its original price was a dress sold.

A % is a quantity or ratio that, in mathematics, representing a portion of one hundred. A non - dimensional connection between two numbers can be represented in a variety of ways, such as through ratios, fractions, as well as decimals. The sign "%" is frequently put after the number to indicate percentages.

Each dress price = $76

If Original price = $200

Formula = (price difference/ original price)100

Prince deference = 200-76 = $124

In percentage :

[tex]\left(\frac{124}{200}\right) \times 100[/tex]

= 12400/200

= 62%

Thus the final answer is 62% .

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