A triangle with vertices A(0,0), B(6,0), and C(0,9) is rotated 360 about the y-axis. What is the volume of the figure?

The solution of the given algebraic expression is: ⁷/₁₂ + ⁴/₆q

We are given the algebraic expression as:

¹¹/₁₂ - ¹/₆q + ⁵/₆q - ¹/₃

Combining Like terms gives us:

(¹¹/₁₂ - ¹/₃) + (⁵/₆q - ¹/₆q)

Solving both brackets individually gives us:

((11 - 4)/12) + ⁴/₆q

= ⁷/₁₂ + ⁴/₆q

Thus, we conclude that is the solution of the given algebraic expression problem

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Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

The value of common ration r is 4.

Given that,

a₁ = 9

a₅ = 2304

We know that,

A geometric sequence  is a sequence in which each term (except from the first term) is multiplied by a fixed amount to obtain the following term.

The following term in the geometric sequence must be obtained by multiplying it by a set term (referred to as the common ratio), and the previous term in the sequence can be obtained by dividing it by the same common ratio.

Since we know that nth term of GP is,

\(a_{n}\) = a₁ \(r^{n-1}\)

Therefore,

a₅ = a₁ \(r^{4}\)  = 2304

⇒  9 x \(r^{4}\)  = 2304

⇒        \(r^{4}\)  = 256

⇒           r = 4

Hence, r = 4

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Answer: 4:5

Step-by-step explanation:

4/9×?=120

9×30=270

120÷4/9=?

Boys Girls All students

4               5          9

40    50          90

80       100             180

120        150             270

The proportional relationship y = 200x, showing the number of calories y burned as a function of the time swimming of x hours, is given as follows:

A proportional relationship is a special case of a linear function, as even though it has a constant rate of change, the intercept is of zero.

The general format of a proportional relationship is given as follows:

y = kx.

In which the constant of proportionality k represents the constant rate of change.

Supposing that for each hour swimming, the person spends 200 calories, the constant is given as follows:

k = 200.

Hence the proportional relationship that gives the number of calories y burned as a function of the time swimming of x hours is given as follows:

y = 200x.

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Answer:

y=4x+14

Step-by-step explanation:

Step-by-step explanation:

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

Answer:

200

Step-by-step explanation:

\(a^{2}\) + \(b^{2}\) = \(c^{2}\)

\(120^{2}\) + \(160^{2}\) = \(c^{2}\)

14400 + 25600 = \(c^{2}\)

40000 = \(c^{2}\)

\(\sqrt{40000}\) = \(\sqrt{c^{2} }\)

200 = c

Jesus love you.

Step-by-step explanation:

To calculate the correlation coefficient (r) given SSxx, SSxy, and other information, we need to use the following formula:

r = √(SSxy / SSxx)

Given SSxx = 950 and SSxy = 205.2, we can substitute these values into the formula:

r = √(205.2 / 950)

Calculating the value:

r = √(0.216)

r ≈ 0.465

The correlation coefficient (r) is approximately 0.465.

Interpretation: The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, the value of r = 0.465 indicates a positive linear relationship between the variables, but it's not a strong relationship. The closer the value of r is to 1 or -1, the stronger the relationship. Since r = 0.465 is relatively close to zero, it suggests a weak positive linear association between the variables being an analyzed.

hope it help you

The Pearson's correlation coefficient (r) based on given data is approximately 0.44, implying a moderate positive correlation.

The formula for calculating Pearson's correlation coefficient (r) in this case is given as: r = SSxy / sqrt(SSxx * SSyy). However, we don't have the value for SSyy directly, but we can calculate it. We know that SSyy = Σy² -(Σy)² / n. Given that Σy² is 2028 and Σy is 120 and number of samples n is 12, we can calculate SSyy as: SSyy = 2028 - (120)² / 12 = 52. Now, substitute SSxx = 950, SSxy = 205.2 and SSyy = 52 in the formula to find r: r = 205.2 / sqrt(950 * 52), giving us an r-value of approximately 0.44. This value of r suggests a moderate positive correlation between the variables in the dataset.

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Answer:

16%

Step-by-step explanation:

To know the area of a figure, you would like to know its shape and estimations. The steps to take on how to draw a figure with the use of a ruler and a pencil is given below.

Begin by selecting the kind of figure you need to draw. Make use of a ruler to draw the sides of the figure. Make sure that the lines are straight and have the right length.

E.g. If the figure may be a rectangle or a parallelogram, you wish to create beyond any doubt that inverse sides are parallel to each other. If the figure is triangle, you would like to draw three lines that shows at three distinctive points. At last, name the sides and vertices of the figure.

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The angle m1 will be equal to 50°. The correct answer is option A.

The complete question is as below:-

Mr Jefferson is building a seesaw for the playground using the diagram shown. (see picture) In the diagram, the seesaw board is parallel to ground level and the triangle is an isosceles triangle.

What is m1?

A. 50º

B. 65º

C. 115º

D. 130º

Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.

We can find the angle using the opposite angles theorem.  When two are lines are crossed, there are four angles formed between them, and the opposite angles will be always equal.

Now, since the seesaw board is parallel to the ground, we can deduct (applying the opposite angles theorem) that both angles formed at the base of the triangle are equal to 65°.

Also, we must remember that the sum of the three interior angles of a triangle will be always equal to 180°, so:

m1 = 180 - ( 65 + 65 0

m1 = 50°

Therefore the angle m1 will be equal to 50°. The correct answer is option A.

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Answer:

A'B'=2AB

Step-by-step explanation:

Line A'B' is also dilated by the same scale factor of 2 and is therefore equal to 2*AB or 2AB

Answer:

To one decimal place,

y = 16.3 m

Step-by-step explanation:

Using SOHCAHTOA,

In this case we need to use CAH,

WE know the angle = 25 and the hypotenuse H = 18,

so,

y = adjacent

\(cos(angle) = y/H\\y = (18)(cos(25))\\y = 16.3135\\y = 16.3\)

Answer: 16.3 in.

Step-by-step explanation:

use SOH CAH TOA

cos x = adj/hyp

cos 25  = y/18

18 cos 25  = y

y= 16.3

Answer:

Step-by-step explanation:

step 1:

determining the values for standard form for the equation of a line,

y = mx + c

Step 2:

calculation of m, where m is the gradient or slope which determines how steep the line is.

step 3:

calculation of c, where c is the height at which the line crosses the y - axis also known as y - intercept

Answer:

1500mm

Step-by-step explanation:

Multiply the length by 1000

therefore, 1.5×1000

Answer:  -2

Step-by-step explanation:

We know that the slope of a secant line over a interval [a,b] is given by :-

\(m=\dfrac{f(b)-f(a)}{b-a}\)

Given f(x) =\(-2x^2 + 4\)

Then, the slope of the secant line over the interval [-1, 2] is given by :-

\(m=\dfrac{f(2)-f(-1)}{2-(-1)}\\\\=\dfrac{(-2(2)^2+4)-(-2(-1)^2+4)}{2+1}\\\\=\dfrac{(-2(4)+4)-(-2(1)+4)}{3}\\\\=\dfrac{(-8+4)-(-2+4)}{3}\\\\=\dfrac{-4-2}{3}\\\\=\dfrac{-6}{3}\\\\=-1\)

Hence, the slope of the secant line over the interval [-1, 2] is -2.

Answer: $1346.40

Step-by-step explanation:

Volume of the pool is:

\((6)(8)(8)+\frac{1}{2}(6)(8)(6)=528\)

This has a cost of \((528)(2.55)=\boxed{\$1346.40}\)

The volume of the pool will be 528 cubic feet. Then the cost to fill the pool will be $1,346.4.

Let the prism with A is the base area and a height of H. Then the volume of the prism is given as

V = A × H

Then the volume of the pool will be

V = [(6 × 8) + (1/2 × 6 × 6)] × 8

V = (48 + 18) × 8

V = 66 × 18

V = 528 cubic feet

Then the cost to fill the pool will be

C = $2.55 × 528

C = $1,346.4

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Two triangles are congruent if they meet one of the following criteria. : All three pairs of corresponding sides are equal. : Two pairs of corresponding sides and the corresponding angles between them are equal. : Two pairs of corresponding angles and the corresponding sides between them are equal.

Freida can use her 1/2 fraction of cup measuring cup twο times tο get 1/2 cup because twο 1/2 cups equal 1 cup.

Fractiοns are a way tο represent a part οf a whοle οr a divisiοn οf a quantity. They are written as a numeratοr (the tοp number) οver a denοminatοr (the bοttοm number) and separated by a line.

Freida is using a 1/2 cup measuring cup. When she fills it up οnce, she has 1/2 cup. Then, when she fills it up again and adds it tο the first 1/2 cup, she has a tοtal οf 1 cup.

This can be visualized by imagining a rectangular shape that represents 1 cup οf liquid. If we divide this shape intο twο equal parts, each part represents 1/2 cup. When Freida fills up her 1/2 cup measuring cup and adds it tο the first 1/2 cup, she is essentially filling up οne οf these parts. When she repeats this prοcess, she fills up the bpart, and the twο parts tοgether make up the entire 1 cup shape.

Hence, Freida can use her 1/2 cup measuring cup twο times tο get 1/2 cup because twο 1/2 cups equal 1 cup.

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Answer:

3

Step-by-step explanation:

1/2 x 10 is 5

8 - 3 is 5

1/2 x 10 = 8 - 3

Answer:

3

Step-by-step explanation:

1/2 * 10 = 5

8-5=3

To find the height of the ball the 5th time it goes up the cylinder we just need to plug n=5 in the expression given:

Therefore, the height the ball reaches the 5th time it goes up is 1/2 inches (or 0.5 inches in decimal form)

Answer:

786 rounded to the nearest ten is 770.

Step-by-step explanation:

To round to the nearest 10, look at the units digit. if the units digit is 5 or more, round up. If the units digit is 4 or less, round down.

Need photo of the segment.

Answer:

30 dollars. I think

Step-by-step explanation:

3x5=15

15+15=30

Note: Deposit means to put in!
The correct answer is 30 dollars.

How did I get my answer? Well I did:
$3 per day times 5 days which is $15. I then added that $15 to the $15 it already contained which was $30

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Please remember to revise this and make it in your own words if you want! I hope this helps you. -Doodle

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you cannot be able to factorized the expression

Answer: 63

Step-by-step explanation:

From the question, we are informed that Steve sold 252 fruit basket for a school fundraiser while Evie aold 25 fruit baskets for each 100 baskets that Steve sold. This means that Evie sold 25/100 = 1/4 of what Steve sold.

Therefore, the number of fruit baskets sold by Evie will be:

= 1/4 × 252

= 63

Answer:

install socratic and by suerte i think es A

Step-by-step explanation:

Answer:

y = - \(\frac{1}{3}\) x + 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x + 3 ← is in slope- intercept form

with slope m = 3

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{3}\) , then

y = - \(\frac{1}{3}\) x + c ← is the partial equation

to find c substitute (- 6, 9 ) into the partial equation

9 = - \(\frac{1}{3}\) (-6) + c = 2 + c ( subtract 2 from both sides )

7 = c

y = - \(\frac{1}{3}\) x + 7 ← equation of perpendicular line