The packaging of a thermometer claims that the thermometer is
accurate within 1.5 degrees of the actual temperature in degrees Fahrenheit.
Write and solve an absolute value equation to find the least and greatest
possible temperature if the thermometer reads 87.4° F.

Answer:

3x² + 24x + 36 = 0

Step-by-step explanation:

A quadratic equation has the standard form ax² + bx + c = 0.
a, b and c are constants.

The roots of a quadratic equation represent the two solutions to the quadratic equation

Given that the roots are -2 and -6 we have

x = -2 and x = -6 as the solutions

Add 2 to both sides of x = -2 ==> x + 2 = 0
Add 6 to both sides of x = -6 ==> x + 6= 0

So (x+2)(x+6) = 0 is the factored representation of this equation. We have to multiply by a leading coefficient of 3

So the quadratic equation is
3(x+2)(x+6) = 0

Using the FOIL method
(x + 2)(x + 6) = x² + 6x + 2x + 12 = x² + 8x + 12

The leading coefficient is the coefficient of x² and is given as 3

So the quadratic equation in standard form is
3(x² + 8x + 12) = 0

==>  3x² + 24x + 36 = 0

If you solve this equation on a quadratic equation calculator you will get the solutions x = -2 and x=-6

Answer:

104m

Step-by-step explanation:

23+23+29+29=104m

Step-by-step explanation:

remember : to convert a fraction of one denominator into a fraction of another denominator, we need to multiply both (numerator and denominator) by the same factor, so that the denominator changes to the desired number, and the overall value of the fraction remains unchanged.

4 1/3 - 8

first I convert the mixed number into a full fraction :

4 1/3 = (4×3 + 1)/3 = 13/3

then, to be able to subtract 8, I need to convert 8 into a fraction with the same denominator as 13/3 :

8 = (8×3)/3 = 24/3

so, now I can do the subtraction :

13/3 - 24/3 = -11/3

-11/3 = -3 remainder 2 = -(3×3 + 2)/3 = -3 2/3

5 2/5 - (-2 4/15)

again, we convert all mixed numbers into full fractions :

5 2/5 = (5×5 + 2)/5 = 27/5

2 4/15 = (2×15 + 4)/15 = 34/15

now we need to bring both to the same denominator, and because 5 is a factor or 15, we can bring both to fractions of 1/15, for which we only need to transform the first fraction :

27/5 = 27/5 × 3/3 = 81/15

so, the subtraction is actually

81/15 - (-34/15) = 81/15 + 34/15 = 115/15 = 23/3

23/3 = 7 remainder 2 = (7×3 +2)/3 = 7 2/3

Answer:

283

Step-by-step explanation:

Answer:

28th

Step-by-step explanation:

There will be  a wednesday in the first week

Wed        2nd Wed

1                    8

2                   9          <===== this is the Wednesday in question

                             Monday would be 2 days earlier at 7th

                                then every 7 days there is another Monday

                                      7   14  21  28  <===== this would be the last one

Answer:

Important Ideas:    

Led American troops in War

Led Constitutional Convention
Served as first US President

Minor Details:
Had a $25,000 yearly salary

Had problems with teeth
Had a brother named Lawrence

Answer:

Step-by-step explanation:

Rewrite

y − 4 − 3 >. y − 4 (−3>)

When two angles are vertical angles, then they are congruent, the hypothesis of the conditional is that D. Two angles are vertical angles.

When two lines cross at a point, vertical angles are created. They are always on an equal footing. In other words, four angles are created anytime two lines cross or intersect. It is evident that two opposed angles are equal and are referred to as vertical angles.

It should be noted that if p and q are statements, the conditional of q by p is “if p then q” denoted p → q. We call p the hypothesis of the conditional and q the conclusion.

Therefore, if two angles are vertical angles, then they are congruent, the hypothesis of the conditional is that the two angles are vertical angles.

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Answer: I'm assuming you want our favorite so shaggy

Step-by-step explanation:

x% of 6 plus y% of 6 can be expressed as x + y = 1.83.

A percentage is a quantity or ratio that is expressed as a fraction of 100. The symbol "%" is used to denote percentage. The percentage is denoted by the abbreviations "pct" or "pc". In other words, the percentage is measured in terms of 100 and is defined as the amount of one quantity that is made up of another.

A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.

The sum of x% of 6 and y% of 6 is 11%.

Therefore,

x% of 6 + y% of 6 = 11%

x% × 6 + y% × 6 = 11%

[tex]\frac{x}{100} \times 6 + \frac{y}{100} \times 6 = \frac{11}{100}[/tex]

Taking [tex]\frac{6}{100}[/tex] common.

[tex]\frac{6}{100}(x+y)=\frac{11}{100}[/tex]

6( x + y ) = 11

Dividing each side by 6.

[tex]x + y = \frac{11}{6}[/tex]

x + y = 1.83

Therefore, the equation x + y = 1.83 expresses the statement x% of 6 plus y% of 6.

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Based on the karats on the gold necklace, the weight in grams of the pure gold in the necklace is B. 40.5 grams

When something is said to be 18 karats of gold, it means that there is about 75% pure gold and then 25% of other materials.

If the necklace has 75% gold, the pure gold in grams is:

= 75% x 54

= 40.5 grams

In conclusion, the pure gold weighs 40.5 grams.

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The solution for the inequality is given by: -1  < m < 2 .

In mathematics, an inequality is a link that compares two numbers or other mathematical expressions unfairly. Size comparisons between two numbers are commonly made on the number line. Various types of inequalities can be represented using various notations, such as:

a is smaller than b, as shown by the symbol a<b.

When the expression a > b is employed, it means that an is larger than b.

In no circumstance is a the same as b. These relationships are referred to as strict inequalities since a is strictly less than or strictly greater than b. Equivalence isn't taken into account.

The given inequality is of the form:

−15+ 6 |2m − 1| < 3

Now let us solve the inequality :

or ,  6 |2m − 1| < 3 + 15

or ,  6 |2m − 1| < 18

or,  |2m − 1| < 3

or, -3 < 2m-1 < 3

or, -3+1 < 2m < 3 + 1

or, -2 < 2m < 4

or, -1 < m < 2

Hence  the solution of the inequality is -1  < m < 2 .

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Answer: [tex](-\infty, \infty)[/tex]

Step-by-step explanation:

[tex]f(x)=\frac{2}{9}x+4[/tex] has a domain of all real numbers since it is a polynomial function.

Answer:

Step-by-step explanation:

3rd one

Answer:

It is an acute angle

Step-by-step explanation:

You can tell by looking at it that it is less than 90 degrees, making it an acute angle.

Since the forces are directly opposing each other, we can subtract their magnitude to obtain the net force on the system.

Assume the positive direction is to the left:

[tex]f_{net} = f_{left} - f_{right} \\ f_{net} = 15 - 10 \\ f_{net} = + 5 \: newton[/tex]

5 Newtons to our assumed positive direction, which is to the left, so 5 newtons to the left is the answer.

The solution for given inequality is s ≥ -1/3 or s ≤ -4

In mathematics, an inequality can be taken as a relation which makes a  comparison which is non-equal between two specific numbers or the variables or other mathematical symbols and expressions. It is used mostly when we have to compare two numbers by their size on the number line.

The are various operators which are used while showing the inequality such as the signs of greater than (>) , less than (<), greater than or equals to (≥) , and less than or equals to (≤).

In the given question the inequality is:

-3s+7 ≤ 8 or -2s+4 ≥ 12

solving the equations

=> -3s ≤ 8-7 or -2s ≥ 12-4

=> -3s≤ 1  or -2s ≥ 8

=> -s ≤ 1/3 or -s ≥ 4

=> s ≥ -1/3 or s ≤ -4.

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The complete question is:

Solve the given inequality.

-3s+7 ≤ 8 or -2s+4 ≥ 12

Answer:

Step-by-step explanation:

1/4 of all of it

Answer:

[tex]3 { \times }^{2} - 5 \times - 2[/tex]

For the given right triangle, the tangent of theta is equal to 4/3 so the correct option is D.

Here we have a right triangle, and we want to find the tangent of one shown angle.

Remember that the trigonometric relation for a tangent is:

tan(a) =(opposite cathetus)/(adjacent cathetus).

On the image, we can see that the adjacent cathetus to the given angle has a measure of 6 units, while the opposite cathetus has a measure of 8 units, then we can replace that in the general relation to write:

tan(θ) = 8/6

Now we just can simplify that fraction if we divide both numerator and denominator by 2, we will get:

tan(θ) = 8/6 = 4/3

Then we conclude that the correct option is D.

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The line in standard notation is 2y - 7x = 7 and in slope-intercept form it is:

y = (7/2)*x + 7/2

We want our line to be perpendicular to 2x + 7y = 1

Rewriting that line, we get:

y = (1 - 2x)/7 = 1/7 - (2/7)*x

So the slope is (-2/7), then the slope of a perpendicular line is 7/2.

So our equation is something like:

y = (7/2)*x + b

To find the value of b we replace the values of the point (1, 7), it gives:

7 = (7/2)*1 + b

7 = 7/2 + b

7 - 7/2 = b

7/2 = b

Then the linear equation in slope-intercept is:

y = (7/2)*x + 7/2

And the standard form is:

y - (7/2)*x = 7/2

2y - 7x = 7

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Using proportions, it is found that:

3. Due to the lower cost per pound, the twelve-pack is the better value.

4. Due to the lower cost per cup, the Pacific Coast Coffee is the better value.

5. Lettuce and Asparagus cost the same per pound.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

For item 3, the cost per pound is the proportion of the cost by the weight, hence:

Due to the lower cost per pound, the twelve-pack is the better value.

For item 4, we follow the same procedure, hence:

Due to the lower cost per cup, the Pacific Coast Coffee is the better value.

In item 5, we have that:

Lettuce and Asparagus cost the same per pound.

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If Ian wants to get an expected quiz score of 83, then he needs to spend 3.33 hours in homework that week.

We know that the situation is modeled by the linear equation:

y = 60+ 6.9x

Where y represents the expected quiz score and x the hours spend on homework that week.

If we define y = 83, the value of x will be the number of hours that the students need to do homework such tath the expected quiz score is 83.

Solving the linear equation:

83 = 60 + 6.9*x

(83 - 60)/6.9 = x

23/6.9 = x

3.33 = x

So to get an expected quiz score of 83, they need to spend 3.33 hours in homework that week.

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Answer: The number of hours a student should spend on their homework to expect a score of 83 on the quiz.

Step-by-step explanation: just did it!

Answer:

38 yd

Step-by-step explanation:

Definition:

the perimeter of a polygon is equal to the sum of all sides’ lengths.

Let P be the perimeter.

Then

P = 8 + 9 + 5 + 7 + 9 = 38

The values of the indicated lengths.

We are given a number line with points A, B, C, D and E on it.

We need to find the lengths of:

DE

AB

AC

BD

CE

BE

Now, we are also given that:

AD = 18 units

AE = 27 units

DE = 27 - 18 = 9 units

AB = 18 / 3 = 6 units ( As AB = BC = CD)

AC = 12 units ( as AB + BC)

BD = 12 units

CE = 6 + 9 = 15 units

BE = 15 + 6 = 21 units.

Therefore, we get the values of the indicated lengths.

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Based on the amount deposited by Berno and the annual interest on the account, the amount in the account after fifteen years is $49,012.91.

The interest is said to compound quarterly which means that the periodic interest rate is:

= 3.25% / 4

= 0.8125%

The number of periods is:
= 15 x 4

= 60 quarters

The amount in the account after 15 years is:

= 30,000 x (1 + rate) ^ number of periods

= 30,000 x (1 + 0.8215%)⁶⁰

= $49,012.91

In conclusion, the amount in the account after 15 years would be $49,012.91.

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Answer:

4

Step-by-step explanation:

Slope formula: y2 - y1/ x2 - x1 (this means the second y minus the first 1 divided by the second x minus the first x)

36 - 20 = 16

4 - 0 = 4

16/4 = 4

The slope of the line is 4

Her total cost after purchasing 12x packs of Vanilla Coke is given by the following linear function:

y = 2 + 7x.

A linear function is modeled according to the following rule:

y = mx + b

In which:

For this problem, we have that:

Hence her total cost after purchasing 12x packs of Vanilla Coke is given by the following linear function:

y = 2 + 7x.

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