How do I solve this problem 16x^2 + 1 =8x Using this quadractic x=-b+ square root b-4ac /2a

show work so I can better see

The expected temperature of the soda after an additional 13 minutes is estimated to be 72°F. This estimation is based on the assumption of a linear temperature increase, calculated from the temperature change observed during the first 5 minutes outside.

The student's question involves the expected temperature of soda after a certain time outside in a hotter environment. Since this scenario does not involve a phase change like melting ice, but rather heating up from the surrounding air, we can infer that Newton's Law of Cooling may be applicable. The Law states that the rate of heat transfer between an object and its surroundings is proportional to the difference in temperature between them. However, without a specific rate of heat transfer given, we cannot apply a formula directly. Therefore, we might assume an approximate linear relationship based on the information provided.

Here's a possible approach:

This logic assumes a simple linear rate, which might not be precisely accurate but should provide an estimated answer.

Answer:

  5/178 gal/mi

  35.6 mi/gal . . . . . take your pick

Step-by-step explanation:

As you have written the question, it is

  (1.25 gal)/(44.5 mi) = (5/178) gal/mi ≈ 0.0280899 gal/mi

___

Usually, mileage is expressed in miles per gallon in the US. The unit rate in those units is ...

  178/5 mi/gal = 35.6 mi/gal

_____

Comment on mileage unit rates

A "unit rate" is any rate that has 1 unit in the denominator. That is, the rate 5 gal/(178 mi) is not a unit rate, but (5/178) gal/mi is a units rate. They both use the same fraction, but the latter has 1 unit in the denominator and the fraction in the numerator: (5/178 gal)/mi.

Outside the US, mileage (energy use for transportation) is often expressed in terms of (amount of fuel)/(given distance). For example, the above mileage might be expressed as 1.745 gal/(100 km), or 6.607 L/(100 km). The "unit" in this scenario is 100 km.

In the US, the typical mileage specification is (distance)/(gallons). So, your question in terms of gallons per mile could mean that is the unit rate you're looking for (.028 gal/mi). Or it could mean we need to convert it to the typical US mileage specification. We cannot tell.

Answer:

35 and remainder is 4

Step-by-step explanation:

Simple interest is the interest calculated on the principal at a given rate for a time period.

The formula for simple interest:

SI = PRT / 100

P = principal

R = rate

T = time in years

The monthly payment is $168.35.

The interest amount to pay is $360.45.

It is the interest calculated on the principal at a given rate for a time period.

The formula for simple interest:

SI = PRT / 100

P = principal

R = rate

T = time in years

We have,

Principal = $2670

Time = 18 months = 18/12 = 1.5 years

Rate = 9%

Simple interest:

SI = P x R x T / 100

SI = (2670 x 9 x 1.5) / 100

SI = $360.45

Now,

Total amount to pay:

= Principal + SI

= 2670 + 360.45

= 3030.45

The monthly payment:

= 3030.45 / 18

= $168.35

Thus,

The monthly payment is $168.35.

The interest amount to pay is $360.45.

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Final answer:

The monthly payment is $168.35, and the interest amount to pay is $360.45.

Explanation:

Simple interest is calculated on the principal amount at a given rate over a specific time period. The formula for simple interest is SI = PRT / 100, where P represents the principal, R denotes the rate, and T signifies the time in years. In this scenario, the principal is $2670, the time is 18 months (or 1.5 years), and the rate is 9%. Substituting these values into the formula, we find that the simple interest amounts to $360.45. Adding this interest to the principal, the total amount to pay becomes $3030.45. Finally, by dividing this total by the time in years (18 months or 1.5 years), we determine that the monthly payment is $168.35. Therefore, the monthly payment is $168.35, and the interest amount to pay is $360.45.

The ratio will remain constant. Then the number of cups of sugar used in 1 and 1/2 batches of these cookies will be 1.125.

A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A percentage is a mathematical expression in which two things are equal.

A recipe for 1 batch of cookies uses 3/4 cup of sugar.

Then the number of cups of sugar used in 1 and 1/2 batches of these cookies will be

We know that the ratio will remain constant. Then we have

1 and 1/2 can be written as 3/2.

Let x be the number of cups of sugar.

Then the ratio will be

[tex]\rm \dfrac{x}{3/2} = \dfrac{3/4}{1}\\\\x = \dfrac{3 \times 3}{2 \times 4}[/tex]

Then we have

x = 9/8

x = 1.125 cups of sugar

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Answer:

[tex]\frac{8}{24} =\frac{1}{3}[/tex]

Step-by-step explanation:

In order to solve this, you just have to add up the fractions and calculate how much is that:

[tex]\frac{24}{24}- (24(\frac{1}{2} )+\frac{4}{24} )\\[/tex]

Now you just have to add up and then withdraw from the total:

[tex]\frac{24}{24}- (24(\frac{1}{2} )+\frac{4}{24} )\\\frac{24}{24}- \frac{12+4}{24} \\\frac{24}{24}- \frac{16}{24} =\frac{8}{24}[/tex]

SO now we know that he has 8/24 problems to do, if we reduce that we have that he still has to do 1/3 of the problems.

To find the rate of the faster car, set the speed of the slower car as 'x' km/h and the speed of the faster car as 'x + 16' km/h. Since they meet in 2 hours, and the total distance is 300 km, the equation is 2x + 2(x + 16) = 300. The faster car's speed is found to be 83 km/h.

The question involves solving for the rate of the faster car when two cars travel towards each other from a distance of 300 kilometers apart and meet after 2 hours. We'll designate the speed of the slower car as 'x' km/h, which implies the speed of the faster car is 'x + 16' km/h. Since they meet in 2 hours, the total distance covered by both cars together is 300 kilometers.

Using the formula for distance (distance = rate × time), we can set up an equation:

2x + 2(x + 16) = 300

Simplifying this equation:

2x + 2x + 32 = 300

4x = 268

x = 67

The speed of the slower car is 67 km/h, and therefore, the rate of the faster car must be 67 + 16, which is 83 km/h.

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The solution is :

A represents the decimal 3.23

B represents the decimal 3.34

C represents the decimal 3.17

A decimal is a number that consists of a whole and a fractional part. Decimal numbers lie between integers and represent numerical value for quantities that are whole plus some part of a whole.

here, we have,

Calculating the decimal values:

We can see that there are 10 divisions between 3.2 and 3.3.

The difference between the two points for 10 divisions is 3.3 -3.2 = 0.1 unit.

Therefore, one division will be equal to 0.1/10 = 0.01 unit

So, point A is 3 divisions after 3.2, thus

A = 3.2 + 0.01×3

A = 3.23

Similarly,

B = 3.3 + 0.01×4

B = 3.34

And,

C = 3.2 - 0.01×3

C = 3.17

Hence, The solution is :

A represents the decimal 3.23

B represents the decimal 3.34

C represents the decimal 3.17

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Answer: The width of the room = 5 meters

The length of the room = 9 meters

Step-by-step explanation:

Let the w denotes the width of the room , then length of the room will be :-

[tex]\text{length}=4+w[/tex]

The formula of perimeter of rectangle :-

[tex]\text{Perimeter}=2(l+w)\\\\\Rightarrow\ 28=2(4+w+w)\\\\\Rightarrow\ 28=2(4+2w)\\\\\Rightarrow\ 28 =8+4w\\\\\Rightarrow\ 4w=20\\\\\Rightarrow\ w=5[/tex]

Hence, The width of the room = 5 meters

The length of the room = 5+4 = 9 meters

The width of the room is 5 meters, and the length is 9 meters.

To find the dimensions of the rectangular room, let's assign variables. Let x be the width of the room. Since the length is 4 meters longer than the width, we can represent the length as x + 4.

Given that the perimeter is 28 meters, we can write an equation: 2(x + 4) + 2x = 28.

Simplifying the equation, we get 4x + 8 = 28. Subtracting 8 from both sides gives 4x = 20. Dividing both sides by 4, we find x = 5. The width of the room is 5 meters, and the length is 5 + 4 = 9 meters.

Final answer:

The degree of the polynomial 5x+7 is 1; it has two terms, 5x and 7, and therefore, it is classified as a binomial.

Explanation:

To find the degree of the polynomial 5x+7 and determine whether it is a monomial, binomial, or trinomial, we first examine the terms of the polynomial. This polynomial has two terms, which are separated by a plus sign. The first term is 5x and the second term is 7. The degree of a polynomial is the highest power of the variable x that appears in the polynomial. In the term 5x, x is to the first power (since x is equivalent to x^1), and in the term 7, x is to the zero power (since any number to the zero power is 1, and the term does not contain x). Therefore, the degree of the polynomial is 1, which is the degree of the term 5x.

Since 5x+7 consists of two terms, it is known as a binomial. A monomial would have only one term, a binomial has two terms, and a trinomial has three terms. Therefore, the polynomial 5x+7 is a binomial of degree 1.

To find the equation of a line parallel to -x+5y=25 and passing through (-5, -5), we determine that the slope of the given line is 1/5. Using the point-slope form with the given point and the slope, we derive the slope-intercept form of the equation as y = 1/5x - 4.

To write the slope-intercept form of the equation of the line parallel to -x+5y=25 and passing through the point (-5, -5), we first need to find the slope of the given line. To do this, we rearrange the equation into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.

Starting with the given equation:

-x + 5y = 25

Add x to both sides to isolate the y-terms:

5y = x + 25

Now divide everything by 5 to solve for y:

y = (1/5)x + 5

From this, we can see that the slope (m) of the line is 1/5. Since parallel lines have the same slope, the slope of our new line will also be 1/5.

Now we will use the point-slope form of the equation to find the line that passes through (-5, -5) with a slope of 1/5. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line.

Substituting the given point and the slope into the point-slope form, we get:

y - (-5) = 1/5(x - (-5))

Simplify the equation:

y + 5 = 1/5(x + 5)

Now distribute the slope:

y + 5 = 1/5x + 1

Finally, subtract 5 from both sides to find the y-intercept (b):

y = 1/5x - 4

This is the slope-intercept form of the equation of our line: y = 1/5x - 4.

To sketch sin, cos, and tan waves, determine the amplitude and period, plot points on a graph, and connect them smoothly.

The positive integer for which its square added to two times the integer equals 195 is 13. This is found by solving the quadratic equation x² + 2x - 195 = 0, which factors to (x + 15)(x - 13) = 0.

To find the positive integer where the square of the integer added to two times the integer equals 195, we need to represent this algebraically. Let's denote the integer as x. The equation based on the given condition is:

x² + 2x = 195

To solve for x, we rearrange the equation into a standard quadratic form:

x² + 2x - 195 = 0

We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. The factoring method seems suitable here, as we can look for two numbers that multiply to -195 and add to 2. In this case, the integers are 13 and -15.

So our factored equation is:

(x + 15)(x - 13) = 0,

giving us the solutions x = -15 and x = 13. Since we are looking for a positive integer, the answer is x = 13.

The probability that the second number rolled is greater than or equal to the first number when rolling a fair eight-sided die twice is 1/16.

To find the probability that the second number rolled is greater than or equal to the first number when rolling a fair eight-sided die twice, we need to determine the favorable outcomes and the total number of possible outcomes.

There are 8 possible outcomes for the first roll and 8 possible outcomes for the second roll. However, since the die is fair and has different numbers on each side, the second roll can only be greater than or equal to the first roll for 4 of the outcomes.

Therefore, the probability is 4 favorable outcomes out of 64 total outcomes, which simplifies to a probability of B

Two angles whose sum is 180° are called supplementary angles. The value of x is 10, while the value of z is 96.

Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

The measure of ∠Z will be equal to 96° because ∠AOB and ∠COD are vertically opposite angles.

The sum of the measure of ∠AOB and ∠BOC will be equal to 180°, since both lie on the same line, therefore,

∠AOB + ∠BOC = 180°

96° + (14x - 56)° = 180°

14x - 56 = 180 - 96

14x = 140

x = 10°

Hence, the value of x is 10, while the value of z is 96.

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Final answer:

The correct answer is option b. percentage, probability, and proportion, because these terms relate to ratios or fractions of a whole and can often be used interchangeably in various statistical contexts. So the correct option is b.

Explanation:

The question is asking which of the following groups contain terms that can be used interchangeably. The correct answer is b. percentage, probability, proportion. These terms can often be used interchangeably because a percentage is a way of expressing a proportion as a number out of 100, and probability is the measure of the likelihood that an event will occur, often expressed as a decimal or a proportion. None of the other options provided (a, c, and d) contain directly interchangeable terms.

Steps:

Answer:

about 10 bins

Step-by-step explanation:

First, we need to find out how many doorknobs are square:

166 - 98 = 68

Then, we need to divide the number of square doorknobs, 68, by the number of square doorknobs in each bin, 7: 68 ÷ 7

68 is closer to 70. So,

68 ÷ 7 is about 70 ÷ 7.

So, 68 ÷ 7 is about 10.

Answer:

p(v)= 4500/v

Step-by-step explanation:

took it

To find the fourth term of a geometric sequence with a first term of 15 and a second term of 6, we first calculate the common ratio (r = 2/5), and then successively multiply by the common ratio to find subsequent terms. The fourth term is determined to be 24/25.

The question involves finding the fourth term of a geometric sequence where the first term (a₁) is 15, and the second term (a₂) is 6. In any geometric sequence, each term is found by multiplying the previous term by a common ratio (r). Thus, we can find r by dividing the second term by the first term: r = a₂ / a₁ = 6 / 15 = 2 / 5.

Now that we have the common ratio, we can find the third term by multiplying the second term by the ratio: a₃ = a₂ × r = 6 × 2 / 5 = 12 / 5. Finally, we find the fourth term by multiplying the third term by the ratio: a₄ = a₃ × r = (12 / 5) × (2 / 5) = 24 / 25.

Therefore, the fourth term of the geometric sequence is 24/25.