Which questions are True or False?

1.) Supplementary angles always add up to 90°.

2.) Complementary angles always add up to 180°.

3.) Vertical angles always have the same measure.

4.) ∠x is complementary to the 34°angle.

5.) ∠z is vertical to the 112°angle.

6.) ∠y is a linear pair with the 146°angle.

The binomial factors of x³- 4x²+x+6​ are (x+2), (x+3), and (x-1).

Using the splitting and grouping the terms:

x³ + 4x² + x - 6

= x³ + 2x² + 2x² + x - 6  [Splitting 4x² = 2x² + 2x²]

= (x³ + 2x²) + (2x² + x - 6)

= x² (x + 2) + (2x² + 4x - 3x - 6)

= x² (x + 2) + [ 2x (x + 2) - 3 (x + 2)]

= x² (x + 2) + (x + 2) (2x - 3)

= (x + 2) ( x² + 2x - 3)

= (x + 2) ( x² + 3x - x - 3)

= (x + 2) [x (x + 3) - 1 (x + 3)]

= (x + 2) (x + 3) (x - 1)

Hence, the binomial factors are (x + 2), (x + 3) and (x - 1)

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Answer:

1) 29 equals n over 3

2) x + 4 = 6

3) p − 53 = 118

4) L over 4 equals 24

Step-by-step explanation:

1) twenty-nine is one-third of the number n is

29 = 1/3 • n

29 = 1/3 • n/1

29 = n/3

So, the answer is 29 equals n over 3

2) The song was 6 minutes long and she has already sung 4 minutes

Let's find the equation to be used to see how much longer she will have to sing?

? + 4 = 6

x + 4 = 6

3) The equation to be used to find the pencils left according to the question is p − 53 = 118 since he has 118 pencils left out of collecting 53 pencils so the remaining pencil would be 118 - 53

Where, p is representing the pencil remaining

So, the answer is p − 53 = 118

4) I think you made a typo in this question

Correction

Julia has a square poster of a puppy on her bedroom wall. The length is one-fourth the width of the picture. If the width is 24 inches, write and solve an equation to determine the length

Answer

so the answer to this question is L over 4 equals 24

L/4 = 24

L = 24*4

L = 96

so, the length is equal to 96 inches and the equation is L over 4 equals 24

Answer:

27.883

Step-by-step explanation:

75.847

-47.964

27.883

The volume generated by rotating the region bounded by the curves \($x = \sqrt{y}$\), \($x = 0$\), and \($y = 4$\) about the x-axis using the method of cylindrical shells is \($4\pi$\) cubic units.

The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.

To find the volume generated by rotating the region bounded by the curves \($x = \sqrt{y}$\), \($x = 0$\), and \($y = 4$\) about the x-axis using the method of cylindrical shells, we need to follow these steps:

Sketch the region and the axis of rotation. The region bounded by the curves \($x = \sqrt{y}$\), \($x = 0$\), and \($y = 4$\) is a quarter-circle with radius 2 centered at the origin. The axis of rotation is the x-axis.

Choose a vertical strip with width $\Delta x$ that runs parallel to the y-axis and intersects the region. The height of this strip is given by the equation $y = 4 - x^2$.

Imagine rotating this strip around the x-axis to form a cylindrical shell with thickness \($\Delta x$\), height \($4 - x^2$\), and radius \($x$\).

The volume of this cylindrical shell is given by the formula \($V = 2\pi x(4-x^2)\Delta x$\).

To find the total volume of the solid, we need to add up the volumes of all the cylindrical shells. This can be done by taking the limit as the width of the strips $\Delta x$ approaches zero and summing up the volumes of the resulting shells. This gives us the integral:

\($V = \int_{0}^{2} 2\pi x(4-x^2) dx$\)

We can simplify this integral by expanding the expression inside the parentheses, which gives us:

\($V = \int_{0}^{2} 8\pi x - 2\pi x^3 dx$\)

We can then integrate each term separately to get:

\($V = [4\pi x^2 - \frac{1}{2}\pi x^4]_{0}^{2}$\)

\($V = (4\pi \cdot 2^2 - \frac{1}{2}\pi \cdot 2^4) - (4\pi \cdot 0^2 - \frac{1}{2}\pi \cdot 0^4)$\)

\($V = 8\pi - 4\pi = 4\pi$\)

Therefore, the volume generated by rotating the region bounded by the curves \($x = \sqrt{y}$\), \($x = 0$\), and \($y = 4$\) about the x-axis using the method of cylindrical shells is \($4\pi$\) cubic units.

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Answer:

.2 would be the correct answer I believe.

Step-by-step explanation:

Probability of A or B Independent

Formula for the probability of A and B (independent events): p(A and B) = p(A) * p(B). If the probability of one event doesn't affect the other, you have an independent event. All you do is multiply the probability of one by the probability of another.

If i'm wrong please don't say anything I haven't learned this stuff yet. :)

The values of x in the inequalities are x< -2 and x < 4

Given the inequalities;

To determine the value of x for each, we have;

-3x + 2 < 8

collect like terms

-3x < 8 - 2

-3x < 6

Make 'x' the subject

x < 6/ -3

x< -2

1/2x - 5 < -3

Find the Lowest common multiple

x - 10 / 2 < -3

cross multiply

x - 10 < -3 × 2

x - 10 < -6

collect like terms

x < - 6 + 10
x < 4

Thus, the values of x in the inequalities are x< -2 and x < 4

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Answer:

150 degrees

Step-by-step explanation:

Hi,

Since one of the angles is 30 degrees and this is a line, we know that 30 + u must equal 180 degrees.

30 + u = 180

Subtract 30 from 180 to find the value of u.

u is 150 degrees.

I hope this helps :)

Answer: 150 degrees

Step-by-step explanation:

A line is 180 degrees in total, since that acute angle is 30 degrees you just subtract 30 from 180, which gives you the other side ( which has to equal 180) of 150 degrees. If it were 40 degrees ( instead of 30) it would be 140 degrees on the other side.... etc

Answer:

B

Step-by-step explanation:

Hopes This Helps :)

Answer:

b

Step-by-step explanation:

just did the test

Answer:

------------------------

Find the slope of AB:

Use point-slope form and point A(2, 4) to determine the line:

Multiply both sides by 9 to clear fraction:

Open parenthesis and convert the equation into ax + by + c = 0:

Answer: The number of hours a student should spend on their homework to expect a score of 76 on the quiz.

Answer:

the first one equals 3 the second  one is 6 and the third one is 9

Step-by-step explanation:

Answer:

:D

Step-by-step explanation:

thx i needed this answer

prettStep-by-step explanation:

Answer:

24

Step-by-step explanation:

Answer:

\(y=-\frac{6}{5}x-11\)

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals of each other. The slope of the given line is 5/6, so the slope of the line we want to find is -6/5.

So, the equation is \(y=-\frac{6}{5}x-11\).

Answer:

Step-by-step explanation:

1 pint = 16 fl oz.

(20 oz) / (16 oz/pt) = 1.25 pints

The required solution from the graph that variable X and Y have a strong negative association.

Correlation is a statistical measure that expresses the extent to which two variables are linearly related. Correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data.

Given:

The given graph attached below .The graph is between variable x and variable y.

According to given question we have

The graph slopes downwards as variable X increases, hence we have a negative relationship between X and Y.

The graph shows strong negative because we see a correlation of downwards sloping.

The trend produced by the graph is straight forward with points close to one another, hence forming a well - defined pattern. These depicts a Strong association between the variable.

Therefore, the required solution from the graph that variable X and Y have a strong negative association.

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1)The ratio of Kelly’s blue bracelets to green bracelets is 5:4.

2)The snow days to days ratio is 20:1

3)There are 42 girls in the competition. The ratio of girls to boys who participated in the quiz bowl was 7 : 5. Solving the two ratios, Therefore, There are 30 boys in the competition.

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1)The ratio of Kelly’s blue bracelets to green bracelets is 5:4.

2)The snow days to days ratio is 20:1

3)There are 42 girls in the competition. The ratio of girls to boys who participated in the quiz bowl was 7 : 5. Solving the two ratios, Therefore, There are 30 boys in the competition.

Define ratio?

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Young adults might value credit in case of an emergency for several reasons. Firstly, credit provides financial flexibility, allowing them to access funds quickly when unexpected expenses arise.

This can be essential for covering costs related to medical emergencies, car repairs, or other unforeseen events that may strain their limited savings. Secondly, young adults often have less established financial safety nets than older individuals. They may not have significant savings, insurance policies, or support from family members to fall back on during emergencies. Credit, in this case, acts as a temporary financial cushion, enabling them to manage immediate needs without resorting to high-interest loans or further jeopardizing their financial stability.

Thirdly, responsible use of credit can help young adults build a positive credit history. Demonstrating responsible borrowing and repayment habits will make it easier for them to access more favorable credit terms in the future, such as lower interest rates or higher credit limits. This can prove valuable when making significant purchases, like buying a home or financing higher education.

Lastly, having access to credit can also provide young adults with a sense of financial independence and empowerment. Knowing they have the means to handle emergencies without relying on others can boost their confidence in managing personal finances and help them make more informed financial decisions as they navigate adulthood.

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The answer is option b \(\sqrt[4]{80^x}\)

Exponent is a mathematical operation, written as an. Here the expression an involves two numbers, the base 'a and the exponent or power 'n'. Exponents are used to simplify algebraic expressions.

Given here: The exponent as \(80^{x/4}\) =\(\sqrt[4]{80^x}\)

Hence, The answer is option b \(\sqrt[4]{80^x}\)

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Answer:

Therefore, a ribeye steak dinner costs $18.772 each, and a grilled salmon dinner costs $10.676 each.

The given expression is factored as \(4v^{7} x^{3} (7y^{6} -3v^{2} x^{6} )\)

Given expression: \(28v^{7}x^{3}y^{6}-12v^{9} x^{9}\)

In order to factorize the given expression, take out the common terms and then simplify further.

\(28v^{7}x^{3}y^{6}-12v^{9} x^{9}=4v^{7} x^{3} (7y^{6} -3v^{2} x^{6} )\)

In mathematics, a factor is a divisor of a given integer that divides it exactly, leaving no leftover.

A number can have either positive or negative factors.

A number has a finite number of factors.

A number's factor will never be more than or equal to the provided number.

Every number contains at least two factors, 1 and the actual number, with the exception of 0 and 1.

Finding a number's factors involves using the division and multiplication operations.

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Answer:

I think that the answer that 1.13815789. I hope that this helps:)

Step-by-step explanation:

Answer:

  1

Step-by-step explanation:

Any non-zero value raised to the zero power is 1.

  x^0 = 1

Answer:

5.79 & 6.89 units

Step-by-step explanation:

Cos(40) =a/h

Cos(40) x 9=a

a=6.89

9^2 - 6.89^2 = a^2

33.5279 =a^2

Square root to get a to be 5.79

the lengths of the other two sides are 5.79 units and 6.89 unit.

Option A) is the correct answer.

Given the data in the question;

To get length of side a, we use the expression;

sinA = Opposite / Hypotenuse

sin40° = a / 9

a = sin40° × 9

a = 0.64278761 × 9

a = 5.79 units

sinB = b / hypotenuse

b = sin( 50° ) × 9

b = 0.766044443 × 9

b = 6.89 unit

Therefore, the lengths of the other two sides are 5.79 units and 6.89 unit.

Option A) is the correct answer.

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(i) Since P(t) gives the population of the culture after t seconds, the population after 1 second is

P(1) = 3•1² + 3e¹ + 10 = 13 + 3e ≈ 21.155

In Mathematica, it's convenient to define a function:

P[t_] := 3t^2 + 3E^t + 10

(E is case-sensitive and must be capitalized. Alternatively, you could use Exp[t]. You can also specify that the argument t must be non-negative by entering a condition via P[t_ ;/ t >= 0], but that's not necessary.)

Then just evaluate P[1], or N[P[1]] or N <at symbol> P[1] or P[1] // N to get a numerical result.

(ii) The average rate of change of P(t) over an interval [a, b} is

(P(b) - P(a))/(b - a)

Then the ARoC between t = 2 and t = 6 is

(P(6) - P(2))/(6 - 2) ≈ 321.030

In M,

(P[6] - P[2])/(6 - 2)

and you can also include N just as before.

(iii) You want the instantaneous rate of change of P when t = 60 (since 1 minute = 60 seconds). Differentiate P :

P'(t) = 6t + 3e^t

Evaluate the derivative at t = 60 :

P'(60) = 6•60 + 3e⁶⁰ = 360 + 3e⁶⁰

The approximate value is quite large, so I'll just leave its exact value.

In M, the quickest way would be P'[60], or you can differentiate and replace (via ReplaceAll or /.) t with 60 as in D[P[t], t] /. t -> 60.

Answer:

A = P (1 + i)^n     where the principal P equals amount A after n periods

P = 1000     and i = .025 / yr

A1 = A (1.025) = 1025

A2 = A1 (1.025) = A (1.025)^2     etc

A5 = A (1.025)^5 = 1000 * (1.025)^5 = 1131 after 5 years

Answer:

\(a(1) = 144\)

\(a(n) = 144{( - \frac{1}{6} )}^{n - 1} \)

\(a(n) = - \frac{1}{6} a(n - 1)\)

In given fractions 8/9 is 1/36 large than 31/36

Finding the larger and smallest fraction in between two or more fractions is known as comparing fractions.

We need to change fractions with unlike denominators into fractions with similar denominators in order to compare them. For this, we will find the denominators' Least Common Multiple (LCM).    

If the denominators are the same then it is easy to compare the fractions.

Here we have

31/36 and 8/9

To find the largest fraction convert both denominators into the same  

Here LCM(36, 9) = 36  

Now multiply both numerator and denominators of fractions with a number to change the denominators  

=> \(\frac{31}{36} \times \frac{1}{1} = \frac{31}{36}\)  

=> \(\frac{8}{9} \times \frac{4}{4} = \frac{32}{36}\)  

From the above calculations given fractions are 31/36 and 32/36

Difference = \(\frac{32}{36} - \frac{31}{36} = \frac{1}{36}\)  

Therefore,

In given fractions 8/9 is 1/36 large than 31/36

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The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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