The average score Josie had in 6 subjects is 72 and her average score after 2 additional subjects were added is 74.25. If she scored 80 in the 7th subject, what was her score in the 8th subject correct to the nearest whole number?

The given side lengths of 12, 17, and 24 give a unique triangle from which the measure of angle ∠B, taken as the angle opposite the side of length 17, and found using cosine rule, is approximately 41.56°

The law of cosines states that the the square of the length of a side of a triangle is given by the sum of the square of the other two sides, less the product of two and the other two sides, and the cosine of the angle between them

Mathematically, a²= b² + c² - 2·b·c·cos(A)

The given lengths of the sides are; 12, 17 and 24

The measure of the angles are given by the law of cosines as follows;

a² = b² + c² - 2·b·c·cos(A)

Which gives;

2·b·c·cos(A) = b² + c² - a²

Which gives;

\(cos(A) = \dfrac{b^2 + c^2 - a^2}{2\cdot b \cdot c}\)

Let a = 12, b = 17, and c = 24, we have;

\(cos(A) = \dfrac{17^2 + 24^2 - 12^2}{2\times 17 \times 24} =\dfrac{721}{816}\)

\(A = arcos\left(\dfrac{721}{816}\right)\approx 27.9^{\circ}\)

Similarly, we have;

\(cos(B) = \dfrac{a^2 + c^2 - b^2}{2\cdot a \cdot c}\)

\(cos(B) = \dfrac{12^2 + 24^2 - 17^2}{2\times 12 \times 24} = \dfrac{431}{576}\)

\(B= arcos\left( \dfrac{431}{576}\right)\approx 41.56^{\circ}\)

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Answer:

Step-by-step explanation:

This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.

Answer:

5.3 x 10^-23 g

Answer:

4:7

Step-by-step explanation:

The word ACCOMPLISHMENT has 4 vowels (A, O, I, and E), which is where I got the four. It also has 7 consonants (C, C, M, P, L, S, H, M, N, T). Hence where the 7 was found.

\( \huge \pink{ \underline \mathfrak{ \green{Answer}}} \: \\ \\ \: \: \rightarrow \fbox{ a). \blue{ \: 54 \: }}\)

Step-by-step explanation:

\( \bf{Given} \: \colon 4w² + w-6, when \: \: w = -4 \\ \\ \tt \underline \red{Solution} \colon \\ \\ \rightarrow \: 4w {}^{2} + w \: - 6 \\ \\ \: put \: \: value \: \: of \: \: w \: \: in \: \: given \: \: equation \\ \\ \rightarrow \: 4( - 4) {}^{2} + \: (- 4 )\: - 6 \\ \\ \rightarrow \: 4(16) \: - 4 \: - 6 \\ \\ \rightarrow \: 64 \: - 10 \\ \\ \bf \rightarrow54\)

Answer:

A = 22.62°

B = 67.38°

c = 26

Step-by-step explanation:

\(a^2+b^2=c^2\\10^2+24^2=c^2\\100+576=c^2\\676=c^2\\26=c\)

\(\sin A=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{10}{26}\\\\A=\sin^{-1}(\frac{10}{26})\\\\A\approx22.62^\circ\)<-- You can also use other trig ratios

\(B=180^\circ-(90^\circ+22.62^\circ)=180^\circ-112.62^\circ=67.38^\circ\)

There's no specific order in how to solve for A and B, so there may be more than one way to approach these solutions.

Pythagorean theorem is represented by triangle B.

In this question we find four cases of triangle, of which we must determine what triangle can be explained by Pythagorean theorem. This theorem offers a relationship between the three sides of the triangle:

r² = x² + y²

Where:

Please notice that hypotenuse is the longest side of the triangle. Graphically speaking, there is a right triangle, that is, a triangle with one right angle. Then, triangle B express the relationship according to Pythagorean theorem.

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Answer:

11 mm, 21 mm, and 16 mm.

Step-by-step explanation:

since 11+21>16, 11+ 16>21>11, You can form a triangle with 11,21,16

9514 1404 393

Answer:

  17.  n -16 = 29

  18.  the solution to the third equation is not n=13

Step-by-step explanation:

17. As with many "doesn't belong" questions, you can make up a rule that will select just about any answer you want to choose. For example, the equation ...

  12 +n = 25

is the only equation that has n as the second term, not the first term. It could be said not to belong on that basis.

Similarly, the fourth equation is the only one with single-digit constants, so it could be said not to belong based on that.

__

However, if we look at the solutions to these equations, we see another way to decide "doesn't belong."

So, we can choose the third equation as "doesn't belong" on the basis of its solution being different from the others.

__

18. The reasoning is shown above. The third equation is the only one with a solution that is not n = 13.

Answer:

whichever one also says -x

Step-by-step explanation:

parallel lines have the same slope

Answer:

a)

b) 1/3

c) 1/2

d) 1/2

e) 0

Step-by-step explanation:

a) There are 2 different types of dessert and 3 different ice cream flavors.      

   Therefore, there are 6 possible ice cream orders:

b) There are 2 different desserts with apricot ice cream.

⇒ P(apricot ice cream) = 2/6 = 1/3

c) There are 3 combinations of sundae.

⇒ P(sundae) = 3/6 = 1/2

d) P(chocolate) = 2/6 = 1/3

   P(blackberry waffle cone) = 1/6

⇒ P(choc) OR P(BWC) = 1/3 + 1/6 = 1/2

e) P(orange sherbet) = 0

as orange sherbet was not an option!

Answer:

The reference angle is π/6.

Cosine is -(√3)/2.

Step-by-step explanation:

To find the reference angle, find the acute angle in quadrant I and use it as a reference for the given expression.

For the cosine, the cosine is the sine of the complementary angle. The complementary angle is the given angle beside it minus a right angle, which is exactly 90 degrees. If the angle is 25 degrees, its complementary angle will be double its amount, 50 degrees. Then, for angle angle measured "theta", the cosine is equal to the sine's right-angle subtracted by theta.

Answer: 7

Step-by-step explanation:

We know that the base sides of the triangular prism are 6cm, 5cm, and

\(x\) cm. We also know that the length of the prism is 20.

To calculate the lateral surface area of the triangular prism, we need to use the following equation:

\((a + b + c)\) x \(length\)

So we can input our values, to get this:

\((6 + 5 + x) 20 = 360\)

Then we solve the equation by the following steps:

\(= > 6+5+x = \frac{360}{20} = 18\\= > 11 + x = 18\\= > x = 7\)

Hope this helps, if you have any further inquiries about this, please reply back. :)

Answer:

$2.70

Step-by-step explanation:

Answer:

Step-by-step explanation:

it would be "c" because the question asks for the number that makes the inequality true

4x≤ x+3

the graph in c is saying that every number that is 1 or less than 1 makes the inequality true. so lets take -7 as an example

4 x -7=-28

-28+3=-25

-25 is greater than -28 so the inequality is true. the reason why graph d doesnt work is because if we plug in 2 into the equation, then 4x =8 and x+3=5

5 is not greater than 8 so it doesnt work

The points on the number line have been correctly matched to the corresponding rational numbers.

A rational number is any number that can be expressed as the ratio of two integers, a/b, where b is not equal to zero. Rational numbers include natural numbers, whole numbers, and integers, as well as fractions, decimals, and percent.

A: -0.5
B: -19
C: 1/2
D: 1
E: 0

Rational numbers are numbers that can be expressed as fractions, with both a numerator and a denominator, and are numbers that can be written as a ratio of two integers. In this example, the rational numbers on the number line have been matched to the corresponding points A through E. Point A is -0.5, which is a rational number that can be expressed as -1/2. Point B is -19, which is a rational number that can be expressed as -19/1. Point C is 1/2, which is a rational number that can be expressed as 1/2. Point D is 1, which is a rational number that can be expressed as 1/1. Lastly, Point E is 0, which is a rational number that can be expressed as 0/1. Therefore, the points on the number line have been correctly matched to the corresponding rational numbers.

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The rational numbers that correspond to the locations on the number line have been accurately matched.

Any number that can be written as the difference between two integers, a/b, where b is not equal to zero, is a rational number. Natural numbers, whole numbers, integers, fractions, decimals, and percentages are all examples of rational numbers.

A: -0.5

B: -19

C: 1/2

D: 1

E: 0

Rational numbers are those that can be described as a ratio of two integers and that can be expressed as fractions having both a numerator and a denominator. In this illustration, the relevant points A through E have been matched to the rational numbers on the number line. Point A is the rational number -0.5, which can be written as -1/2. Point B is the rational integer -19, which can be written as -19/1. A rational number that can be represented as 1/2 is point C, which is half. The value at point D is 1, a rational integer that may be written as 1/1. Last but not least, Point E is 0, a rational number that may be written as 0/1. As a result, the rational numbers that correspond to the locations on the number line have been accurately matched.

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Answer:

D. y = –6x – 4

Step-by-step explanation:

Find the slope of the original line and use the point-slope formula  y − y 1 = m ( x − x 1 )  to find the line parallel to  y = − 6 x + 2 .

y = − 6 x − 4                 PARALLEL

...............................................................................................................................................

Find the negative reciprocal of the slope of the original line and use the point-slope formula  y − y 1 = m ( x − x 1 )  to find the line perpendicular to  y = − 6 x + 2 .

y = 1 /6 x + 13/ 6            PERPENDICULAR

Answer:

D

Step-by-step explanation:

Answer:

prob wrong but

first one is-3/4

second is 3/5 since you convert the decimal

Answer:

WHAT DOES TGAT EVEN MEAN

Step-by-step explanation:

Answer:

Step-by-step explanation:

In a isosceles triangle. one angle is 9° greater than each of the other two equal angles. find the measure of all three angles

suppose the 'other two angles' measure =x degrees. then the first-mentioned angle has to measure = x+9

Sum of the angle in a triangle = 180°

Therefore the measure of all the three angle will be

57 , 57 , 57+9 = 66

Hence the final answer are 57 , 57 and 66

Answer:

you're answer is negative 15

Step-by-step explanation:

To find the percent increase, divide the increase by the original price.

P1 = price yesterday

P2 = price today

To find percent increase

\( \frac{(p2 - p1)}{p1} \)

Or to answer the question,

P1 = 9.74

P2 = 9.87

\( \frac{(9.87 - 9.74)}{9.74} = 0.013347\)

Or 1.33%

Answer:

a. N(t) = 1.25 (1/2)^t/7

b. 0.1160933038mg.

Step-by-step explanation:

The formula for half life =

N(t) = No(1/2)^t/t½

Where N(t) = Amount of Substance left

No = Initial amount not Substance

t = time after t years

t½ = Half life of the substance

From the question:

No = 1.25mg

t½ = 7 years

a. Find a model for the amount of albuterol left in the body t hours after an initial dose of 1.25 mg.

N(t) = No(1/2)^t/t½

No = 1.25mg

t½ = 7 years

N(t) = 1.25 (1/2)^t/7

b. How much albuterol is left in the body after 24 hours?

Using the model in the above question

N(t) = 1.25 (1/2)^t/7

N(t) = 1.25(1/2)^24/7

N(t) = 1.25(0.5)^3.4285714286

N(t) = 0.1160933038mg

Therefore, the quantity of albuterol left in the body after 24 hours is 0.1160933038mg.

Answer:

y = -3x² - 3x + 6

Step-by-step explanation:

main formula: r×(x² - (a + b)x + ab) = y

r×(x² - (-2 + 1)x -2×1) =y

r×(x² +x -2) = y

by using the point (0,6) →

r×(0² + 0 -2) = 6

r×-2 = 6

r= -3

so

y= -3x² -3x +6

Answer:

An annual fee is a yearly charge by banks and financial institutions to customers for use of their credit cards.

Answer:

Most of the mens shoes in the data sets cost more than the womens shoes

Step-by-step explanation:

i did this and got it correct

Answer:

The answer is 13.

Step-by-step explanation:

Angle ABC and PQR are equivalent, although angle PQR is just scaled down by a factor of 9. Line CA is 54, line PR is 6, 54/6=9. So, line PQ has to be equal to 9 because 81/9=9.  So you input all values into the expression until you get the product of 9.

Work: 2(13)-17=9, so 13 is your answer.

Answer:

The slope-intercept equation of the line that goes through the points (1, 5) and (2, 8) is​ \(\mathbf{y=\frac{3}{2}x+\frac{7}{2} }\)

Step-by-step explanation:

We need to find the slope-intercept equation of the line that goes through the points (1, 5) and (2, 8)

The general equation for slope intercept form is ​ \(y=mx+b\) where m is slope and b is y-intercept

Finding slope

Slope can be found using formula \(Slope=\frac{y_2-y_1}{x_2-x_1}\)

We have \(x _1=1, y_1=5, x_2=2, y_2=8\)

Putting values and finding slope

\(Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{8-5}{2-1}\\Slope=\frac{3}{2}\)

So, we get slope \(m=\frac{3}{2}\)

Finding y-intercept

y-intercept can be found using slope \(m=\frac{3}{2}\) and point (1,5)

\(y=mx+b\\5=\frac{3}{2}(1)+b\\b=5- \frac{3}{2}\\b=\frac{10-3}{2}\\b=\frac{7}{2}\\\)

So, we get y-intercept \(b=\frac{7}{2}\)

Equation of line

So, equation of line having slope \(m=\frac{3}{2}\) and y-intercept \(b=\frac{7}{2}\) is:

\(y=mx+b\\y=\frac{3}{2}x+\frac{7}{2}\)

The slope-intercept equation of the line that goes through the points (1, 5) and (2, 8) is​ \(\mathbf{y=\frac{3}{2}x+\frac{7}{2} }\)

Answer:

0.43 gallons

Step-by-step explanation:

172 inches is is 14.33 feet

assuming the wall is a parallelogram to find the area you times the two sides 6x14.33

that would equal 86

once you have that you must find out how much 86 is out of 200

do this by dividing one number with the other and then multiply the result by 100.

that being 0.43