If y varies directly as x, and y is 6 when x is 72, what is the value of y when x is 8? y = one-ninth y = two-thirds 54 96

The length of BC rounded to 3 significant figures is approximately 3.62 units.

We can use trigonometric function to find the length of BC. First, we can use the fact that ∠CAB = 90° to determine that ∠ACB = 25° (since the angles in a triangle sum to 180°).

Next, we can use the law of sines to relate the lengths of the sides and angles of the triangle:

sin(∠ABC) / AB = sin(∠ACB) / BC

Substituting in the values we know:

sin(65°) / 8.6 = sin(25°) / BC

Solving for BC:

BC = sin(25°) × 8.6 / sin(65°) ≈ 3.62

Rounding to 3 significant figures, we get BC ≈ 3.62 units

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Answer:

x=70

z=20

y=30

Step-by-step explanation:

first find x: the sum of straight angle is 180

x+110=180

x=180-110=70

now find z: the sum of the angles of triangle is 180:

x=70, right angle=90

z+70+90=180

find y:

y+110+40=180

y=180-150=30

z=180-160=20

Answer:

x=70 degrees, y= 30 degrees, z=20 degrees

Step-by-step explanation:

110+x=180 => straight angle def.

180-110+40=y => def. of angles in triangle

x( 70 degrees) +90+z=180, z= 20 => angles in triangle

Answer:

The simplified version is: \(4a+2y+4\)

Step-by-step explanation:

I collected the like-terms which was 3a+ a= 4a

2y is by itself so i left it, and

-5+9 = 4.

Which gave me the answer 4a+2y+4

Have a blessed day!!

1000 cubic millimeters are in a cubic centimeter.

'What is cubic centimeter?'

There are 1000 cubic millimeters in one cubic centimeter (cm³) (mm³). Add 1000 to the cubic cm number to convert it to cubic mm.

For instance, multiplying 10 by 1000 results in 10000 mm3, or how many cubic mm there are in 10 cubic cm.

The volume of small items is measured in cubic centimeters, a tiny unit of measurement. Discover standard units of measurement, the definition of cubic centimeters, how to convert them, and how to measure volume using cubic centimeters. A little cube with sides that are 1 cm long occupies the same amount of space as a cubic centimeter.

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The cost of ordering shirts for a club is 268 units.

Define Function.

A function, according to a technical definition, is a relationship between a set of inputs and a set of possible outputs, where each input is connected to precisely one output.

 This means that a function f will map an object x exactly to one object f(x) in the set of possible outputs if the object x is in the set of inputs (called the codomain).

The statement that f is a function from X to Y using the function notation f: X→Y

The function that represents the cost of the shirts(x) is f(x) = 8x+12

Now, for x = 32

 f(x) = 8x+12

f(32) = 8(32) + 12

        = 256 +12

f(32) = 268 units

.

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Answer:5.03

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

cause u are using 3 gallons which is taking away

Answer:

the answer is only 3

Step-by-step explanation:

you read all of them and you make it an equation and if it is negative or subtraction that would be your answer

Answer: 1 in 2 chance

Step-by-step explanation:

Answer:

6x + 15.

Step-by-step explanation:

3(3x + 5)

= 3 * 2x + 3*5

= 6x + 15.

Hey There!! ~

The answer to this is: Apply the distributive property.

\(3 (2x) + 3 . 5\)

Multiply. 2 by 3 \(6x + 3 . 5\) Multiply  

Multiply 3  by 5.

\(6 x + 15\) Thus, for the answer is: 6x + 15.

Hope It Helped!~

\(ItsNobody\)~

Answer:

Answer is D

Just expand

And remember

\( \sqrt{ - a} = \sqrt{a} i\)

Goodluck tomorrow

The average rate of change of the function is 3.

                     = Δy / Δx =  [f(b) - f(a)] / (b - a)

Given:

x₁ = 0

x₂ = 9

f(x) = 3x

f(x₁) = 0

f(x₂) = 27

Average rate of change, \(A(x) = \frac{f(x_{2})-f(x_{1} ) }{x_{2}-x_{1} }\)

Putting the values, we get

\(A(x) = \frac{27-0}{9-0}\) = \(\frac{27}{9}\) = 3

Therefore, the average rate of change is 3.

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The no. of books read are 21.

What is an array multiplication ?

An arrangement of rows or columns that exactly matches a multiplication equation is known as a multiplication array.

We can calculate the no. of books read by multiplication array.

In the picture, the first row shows the no. of books read by first student,

the 2nd row shows the no. of books read by 2nd student and the 3rd row shows the no. of books read by 3rd student.

If we calculate the total books then, the total books will be 21 (7 + 7 + 7).

Hence, the total no. of books are 21.

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Answer:

I love algebra anyways

The ans is in the picture with the  steps how i got it

(hope this helps can i plz have brainlist :D hehe)

Step-by-step explanation:

Answer:

square root of 17, 4 2/3, 5.2, square root of 32

Step-by-step explanation:

square root of 17 = 4.123105625617661

Square root of 32 = 5.656854249492381

4 2/3 = 4.66.....

The change in the area of the surface of the cube when its side length triples from s units to 3s units is 52s³.

To quantify the change in the area of the surface of a cube when its side length triples from s units to 3s units, we can set up an integral.

Let's denote the side length of the cube as "x". The initial side length is "s" and the final side length is "3s". We want to find the change in surface area, which is the difference between the final surface area and the initial surface area.

The surface area of a cube with side length "x" is given by 6x², as each face of the cube has an area of x² and there are 6 faces.

The change in surface area can be calculated as:

ΔA = ∫(6x²) dx,

where the integral is taken from the initial side length "s" to the final side length "3s".

Now let's evaluate the integral:

∫(6x²) dx = 2x³ + C,

where C is the constant of integration.

To find the change in surface area, we substitute the limits of integration:

ΔA = [2x³]s to 3s

= 2(3s)³ - 2s³

= 2(27)s³ - 2s³

= 52s³

Therefore, the change in the area of the surface of the cube when its side length triples from s units to 3s units is 52s³.

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Answer:

1.8 weeks

Step-by-step explanation:

The number of weeks it takes for consuming the 3 gallons of milk is as follows:

It is given that the total of 10 gallons of milk drink for every 6 week i.e. 5 by 3

Now in order to determine the weeks we have to reciprocal the ratio i.e. 3 by 5

Now for 3 gallons it would be

\(= \frac{3}{5}\times 3\)

= 1.8 weeks

Answer:

735

Step-by-step explanation:

Answer:

C) -180

Step-by-step explanation:

65 + 54 + 43 + 32 + 21 + 10 - 1 - 12 - 23 - 34 - 45 - 56 - 67 - 78 - 89 = -180. Hope this helps!

Given:

Area of rhombus = 96 cm

One diagonal = 12 cm

To find:

The other diagonal.

Solution:

We know that,

\(\text{Area of a rhombus}=\dfrac{1}{2}\times d_1\times d_2\)

where, \(d_1\text{ and }d_2\) are two diagonals of the rhombus.

Putting the given values, we get

\(96=\dfrac{1}{2}\times 12\times d_2\)

\(96=6\times d_2\)

Divide both sides by 6.

\(\dfrac{96}{6}=d_2\)

\(16=d_2\)

Therefore, the length of the other diagonal is 16 cm.

The predicted prestige rating for a person with 15 years of education, based on the least-squares regression equation, is 75.5. Given a residual of -5, the observed prestige rating for this person is 70.5.

The least-squares regression equation, y^ = -10.7 + 5.8x, relates the number of years of education (x) to the predicted prestige rating (y^). To find the predicted prestige rating for a person with 15 years of education, we substitute x = 15 into the equation:

y^ = -10.7 + 5.8(15)

y^ = -10.7 + 87

y^ = 76.3

Thus, the predicted prestige rating for this person is 76.3 (rounded to one decimal place). Now, we need to determine the observed prestige rating using the residual information. The residual represents the difference between the predicted and observed values. In this case, the residual is given as -5. Therefore, we subtract the residual from the predicted prestige rating to obtain the observed prestige rating:

Observed prestige rating = y^ - Residual

Observed prestige rating = 76.3 - (-5)

Observed prestige rating = 76.3 + 5

Observed prestige rating = 81.3

The observed prestige rating for this person, based on the given residual of -5, is 81.3 (rounded to one decimal place).

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The statements that are true to determine whether x=10 is unusually high number of defective items on the next run of 100 products are given by the following option:

I and III.

Unusual values in the normal distribution are found using the range rule of thumb, which states that if a value is more than two standard deviations from the mean, the measure is unusual.

The measures for the binomial distribution are given as follows:

The parameters for this problem are given as follows:

n = 100, p = 0.04.

Then the mean and the standard deviation are given as follows:

Thus the upper bound for usual values is of:

4 + 2 x 1.96 = 7.92.

Which is less than 10, hence 10 is an unusual measure and statement I is correct.

Statement III is also correct, as:

P(X >= 10) < 0.05.

While statement II is false, as we do not look at the exact measure, but an interval of measures.

The problem is given by the image shown at the end of the answer.

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The range for the data set is equal to 48.

In Mathematics and Statistics, a range is the difference between the highest number and the lowest number contained in a data set.

In Mathematics and Statistics, the range of a data set can be calculated by using this mathematical expression;

Range = Highest number - Lowest number

From the given data set, we have:

Highest number = 95.

Lowest number = 47.

By substituting, we have:

Range = 95 - 47

Range = 48.

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\(\overline {LM} \parallel \overline {ON} \ and \ \overline {LO} \parallel \overline {MN}\) because they form congruent alternate interior angles with a common transversal, therefore, LMNO is a parallelogram because the opposite sides are parallel

The reason the above statement are correct is presented as follows:

The given parameters are;

\(\overline {LM}\) is congruent to \(\overline {ON}\) and \(\overline {LO}\) is congruent to \(\overline {MN}\)

Required:

To prove that LMNO (quadrilateral) is a parallelogram

Solution:

The two column proof is presented as follows;

Statement \({}\)           Reason

\(\overline {LM} \cong \overline {ON}\)  \({}\)           Given

\(\overline {LM} = \overline {ON}\)  \({}\)           Definition of congruency

\(\overline {LO}\) ≅ \(\overline {MN}\) \({}\)            Given

\(\overline {LO}\) = \(\overline {MN}\) \({}\)             Definition of congruency

\(\overline{LN}\) ≅

\(\overline{LN}\) =

ΔLNO ≅ ΔLMN \({}\)    Side Side Side (SSS) congruency postulate

∠NLM ≅ ∠LNO \({}\)    Cong. Parts of Cong. Triangles are Cong. CPCTC

∠NLM and ∠LNO are alternate interior angles

\(\mathbf{\overline {LM} \parallel \overline {ON}}\)   \({}\)    Alternate interior angles between parallel lines are congruent

∠MNL ≅ ∠NLO \({}\)    CPCTC

∠MNL and ∠NLO are alternate interior angles

\(\mathbf{\overline {LO} \parallel \overline {MN}}\)  \({}\)     Alternate interior angles formed between parallel lines are congruent

LMNO is a parallelogram because the opposite sides, \(\overline {LM} \parallel \overline {ON}\) and \(\overline {LO} \parallel \overline {MN}\) are parallel

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LMNO is a plane shape which has the properties of a parallelogram. The the explanations below, it has been proven to be a parallelogram.

A parallelogram is a quadrilateral which has some unique properties. These properties can be used to prove if a given shape is a parallelogram or not.

To prove that LMNO as given in the question is a parallelogram:

Thus,

/LM/ ≅ /ON/ (opposite side property)

/LO/ ≅ /MN/ (opposite side property)

        i.e LM || ON and LO || MN

        i.e <MLO + <LMN = \(180^{o}\)

also    

<LON + <MNO = \(180^{o}\)

LN ⊥ MO

     <LMN ≅ <LON  and <MLO ≅ <MNO

Therefore the given quadrilateral LMNO has all the properties described above, then it is a parallelogram.

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The number of platters that can be made is 8.

Given that you need to make a platter which consists of 1 bagel, 2 eggs, and 3 slices of bacon. Since it is needed to calculate the maximum number of platters that can be made with 9 bagels, 17 eggs and a package of bacon containing 36 slices.

Further, If we make 1 platter then we need 1 bagels, 2 eggs and 3 slices of bacon. Therefore, for 8 platters, the material required would be 8 times of 1 platter, that is 8 bagels, 16 eggs and 24 slices of bacon.

Similarly if I have to create 9 platters , the material required would be 9 times of 1 platter, that is 9 bagels, 18 eggs and 27 slices of bacon.

So we can not make 9 platters because we need that one extra egg.

The number of platters is 8.

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The construction that is performed based on the information given will be D. construct a right angle.

It should be noted that construction simply means the accurate drawing of shapes, angles, and the line in geometry.

In this case, the construction that is performed based on the information given will be to construct a right angle.

It should be noted that a right angle has an angle of 90°.

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Answer:

Step-by-step explanation:

6 + 2 = 4,  given

6 + 5 = 11, correct

Answer:

5√26/13

Step-by-step explanation:

5√2/√13 multiply the nominator and denominator by √13 to rationalize the denominator

5√2√13/√13√13 ( √13×√13=13)

5√26/13

there is answer in multiple choice but this is the correct one