Write Y=3x^2+6x+7 in vertex form

Answer:

x=-0.625

Step-by-step explanation:

24x+15=0

     -15   -15

24x=-15

x=-0.625

The length of the shorter leg of the triangle ABC is approximately 24.49 units. Let's denote the right triangle ABC, where C is the right angle.

Let D be the midpoint of AB, and E be the foot of the altitude from C to AB. Then we have:

CD = 1/2 AB (definition of median)

CE = 12 (given altitude to the hypotenuse)

Let x be the length of the shorter leg of the triangle ABC. Then we have:

AE = x (definition of altitude)

EB = AB - x (definition of complementary leg)

By the Pythagorean theorem, we have:

AC^2 = AB^2 + BC^2

(2CD)^2 = AB^2 + x^2

AB^2 = 4CD^2 - x^2

By the similarity of triangles AEC and ABC, we have:

CE/AC = AE/AB

12 / (AB + BC) = x / AB

AB = x / (12/x + 1)

Substituting AB into the previous equation, we get:

4CD^2 - x^2 = x^2 / (12/x + 1)^2

Simplifying and solving for x, we get:

x^4 - 576x^2 - 14400 = 0

This is a quadratic equation in x^2, so we can solve for it using the quadratic formula:

x^2 = [576 ± sqrt(576^2 + 4*14400)] / 2

x^2 = [576 ± 624] / 2

Since x is a length, we take the positive square root:

x^2 = 600

x ≈ 24.49

Therefore, the length of the shorter leg of the triangle ABC is approximately 24.49 units.

Learn more about triangle here:

https://brainly.com/question/2773823

#SPJ11

Answer:

1017 square ft.

Step-by-step explanation:

pi x r x r x h

3.14 x 6 x 6 x9 =1017.36

rounding to the nearest whole number, the answer is 1017 square feet

Answer:

angle relationship is co-interior

x = 3.94

Step-by-step explanation:

(34x - 1 ) + 45 = 180 [co-interior angles add up to 180 degrees]

34x - 1 = 135

34x = 134

x= 134/34 =3.94

We can infer that people with shorter arm lengths are more likely to own the fewest number of books.

If there is a correlation of 0.99 between one's arm length and the number of books they own, it implies a strong positive relationship between these two variables. In this context, it means that as arm length increases, the number of books owned also tends to increase.

Given this correlation, we can make an inference about people who own the fewest number of books. Since there is a strong positive correlation, individuals with shorter arm lengths are more likely to have fewer books compared to those with longer arm lengths. However, it's important to note that correlation does not imply causation, and there may be other factors at play influencing the number of books owned by individuals.

Therefore, based on the given information, we can infer that people with shorter arm lengths are more likely to own the fewest number of books.

Learn more about   length from

https://brainly.com/question/2217700

#SPJ11

Answer:

hey!

a.To convert a fraction into a percentage, you can divide the numerator by the denominator and then multiply the result by 100. In this case, to convert 21 out of 71 into a percentage:

(21/71) * 100 = 0.2957 * 100 ≈ 29.57%

Therefore, 21 out of 71 is approximately 29.57% when expressed as a percentage. this could be rounded to 29.6% to 1dp

b.

do the same here but with different numbers. so:

(46/154)*100= 29.9% to 1dp or 29.87% to 2dp

hope you found that helpful :))

Using the equation of the plane and the provided point (1,2,3) with the unit values perpendicular to the plane .The answer is \(\frac{x-1}{3.14} + \frac{y-2}{3.14} + \frac{z-3}{3.14} = 1\)

A plane is a doubly ruled surface in two dimensions that is spanned by two linearly independent vectors. A hyperplane is a generalization of the plane to higher dimensions. The dihedral angle is the angle formed by two intersecting planes.

A normal in geometry is a piece of geometry that is perpendicular to another piece of geometry, such as a line, ray, or vector. For instance, the (infinite) line perpendicular to the tangent line to the curve at the point is the normal line to a plane curve at the point.

x1=1

y1=2

z1=3

\(\frac{x-x1}{\sqrt{x1^{2}+y1^{2}+z1^{2}}} + \frac{y-2}{\sqrt{x1^{2}+y1^{2}+z1^{2}}} + \frac{z-3}{\sqrt{x1^{2}+y1^{2}+z1^{2}}} = 1\)

\(\frac{x-1}{3.14} + \frac{y-2}{3.14} + \frac{z-3}{3.14} = 1\)

To learn more about planes visit:

https://brainly.com/question/1962726

#SPJ4

Answer:

0 remainder 13

Step-by-step explanation:

Step 1:

Start by setting it up with the divisor 16 on the left side and the dividend 13 on the right side like this:

 1 6 ⟌ 1 3  

Step 2:

The divisor (16) goes into the first digit of the dividend (1), 0 time(s). Therefore, put 0 on top:

       0    

 1 6 ⟌ 1 3  

Step 3:

Multiply the divisor by the result in the previous step (16 x 0 = 0) and write that answer below the dividend.

       0    

 1 6 ⟌ 1 3  

       0    

Step 4:

Subtract the result in the previous step from the first digit of the dividend (1 - 0 = 1) and write the answer below.

       0    

 1 6 ⟌ 1 3  

     - 0    

       1    

Step 5:

Move down the 2nd digit of the dividend (3) like this:

       0    

 1 6 ⟌ 1 3  

     - 0    

       1 3  

Step 6:

The divisor (16) goes into the bottom number (13), 0 time(s). Therefore, put 0 on top:

Step 7:

Multiply the divisor by the result in the previous step (16 x 0 = 0) and write that answer at the bottom:

       0 0  

 1 6 ⟌ 1 3  

     - 0    

       1 3  

        0  

Step 8:

Subtract the result in the previous step from the number written above it. (13 - 0 = 13) and write the answer at the bottom.

You are done, because there are no more digits to move down from the dividend.

The answer is the top number and the remainder is the bottom number

16 divided by 13 is equal to 1 remainder 3, which can be written as 1 and 3/13.

Division is one of the fundamental arithmetic operations in mathematics. It involves splitting a quantity or number into equal parts or groups. In division, a dividend is divided by a divisor to obtain a quotient.

To perform long division for 16 divided by 13, follow these steps:

      1                                                                                                          

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

13 | 16

     -13

      --

       3

= 1 R 3

= 1 3/13

So, 16 divided by 13 equals 1 with a remainder of 3

Therefore, 16 divided by 13 is equal to 1 remainder 3.

Learn more about Division here:

https://brainly.com/question/2273245

#SPJ6

Answer:

Step-by-step explanation:

11 is the same as 9

10 is the same as number 9

12 i dont know

By the definition of the mode, we can say the mode of this data is 33.

What is the mode?

The mode in statistics refers to a number in a set of numbers that appears the most often. For example, if a set of numbers contained the following digits, 1, 1, 3, 5, 6, 6, 7, 7, 7, 8, the mode would be 7, as it appears the most out of all the numbers in the set.

We have given,

Data set 18 16 11 45 33 16 33 14 18 33.

To find what is the mode for this data set.

Solution: We have given

Data set 18 16 11 45 33 16 33 14 18 33.

Mode: The mode of a set of data values is the value that appears most often.

So,

We can see the most repeated number is 33. ( 3 times)

Hence, by the definition of the mode, we can say the mode of this data is 33.

To learn more about the mode visit,

https://brainly.com/question/11231592

#SPJ1

The angle of elevation is approximately 36.87 degrees.

The tangent function can be used to determine the angle of elevation. We'll abbreviate the distance "d" between the object and the spot where the shadow meets the ground.

Then, we have:

tan(θ) = shadow length / d

tan(θ) = 3 / 4

Solving for θ, we have:

θ = \(tan^-1(\frac{3}{4})\)

The tangent function can be used to calculate the elevation angle. We'll refer to this distance as "d" from the item to the point where the shadow lands on the ground.

θ (degrees) = θ (radians) * 180 / π

Approximating, we have:

θ (degrees) =  \(tan^-1(\frac{3}{4})\) * 180 / π

θ (degrees) ≈ 36.87 degrees

So, the angle of elevation is approximately 36.87 degrees.

For more such questions on angle of elevation

https://brainly.com/question/16716174

#SPJ4

Answer:

y=2x+3

Step-by-step explanation:

Lets verify

\(\\ \sf\longmapsto -1=2(-2)+3=-4+3=-1\)

\(\\ \sf\longmapsto 1=2(-1)+3=-2+4=1\)

Hence verified

Answer:

C): y = 2x + 3

Step-by-step explanation:

• when x is -2:

\({ \tt{y = 2(- 2) + 3}} \\ { \tt{y = - 1}}\)

• when x is -1:

\({ \tt{y = 2( - 1) + 3}} \\ { \tt{y = 1}}\)

• since y holds for -2 and -1, it'll hold for other positive integers.

Answer: C

n > 1 where n is an integer

Answer:

C) \(n\geq 1\)

Step-by-step explanation:

Answer:

The quotient of two polynomials is always a polynomial.

Step-by-step explanation:

There is no guarantee that a quotient of polynomials can be expressed as a polynomial, even though it sometimes can.

Answer: The answer is the quotient of two polynomials is always a polynomial.

Step-by-step explanation:

Answer:

x = -12.57

Step-by-step explanation:

2x + 45 - 56 = 9x + 54 + 23

2x - 11 = 9x + 77

-11 = 7x + 77

-88 = 7x

x = -12.57

Answer:

c / square root of 5

Step-by-step explanation:

Answer:

square root of 5

Step-by-step explanation:

Answer:

9.

Step-by-step explanation:

f(-1) = -(-1) + 2 = 1+2 = 3.

f(-1)f(-1) = 3^2 = 9..

Answer:

0.5 inches

Step-by-step explanation:

Volume of a cube = L × L × L = L³

0.125 = L³

L = ³√0.125

L = 0.5 inches

The condition that is not met is that the sample size must be large enough to assume that the sample proportions are normally distributed.

Number is a mathematical object used to count, measure, and label. It is one of the fundamental building blocks of mathematics and is essential for any kind of calculation or measurement. Number is an abstract concept that is used in many different ways, from counting objects to expressing complex mathematical systems. Numbers can be used to represent anything from a single item to the entire universe. Numbers are also used to represent abstract ideas such as time, money, and probability.

With a sample size of only 25, it is not possible to assume that the sample proportions follow a normal distribution. As such, calculating a confidence interval for the population proportion of bags with too much salt is not possible.

To know more about number click-
https://brainly.com/question/24644930
#SPJ1


Complete questions as follows-
sapling a quality control inspector takes a random sample of 25 bags of potato chips from the thousands of bags filled in an hour. of the bags inspected, 3 had too much salt. which of the conditions for calculating a confidence interval for the population proportion of bags with too much salt is not met?

Answer:

Step-by-step explanation:

0.4375

Answer:

6.25%of 112 is 7

Step-by-step explanation:

hope it helps you

Answer:

x = 7

Step-by-step explanation:

Answer:

x=7

Step-by-step explanation:

3x+15=36

    -15  -15

      3x=21

        x=7

Answer:

Starting average customer rating was 5.

Step-by-step explanation:

Equation representing the average customer rating at Austin's bakery over time is,

y = 0.25x + 5

Here, 'x' represents the time or duration.

Starting average customer rating means value of y at x = 0.

Therefore, y = 0.25(0) + 5

y = 5

Starting average customer rating was 5.

Answer:Starting average customer rating was 5.

Step-by-step explanation:

The type of study design used in the scenario you provided is a retrospective cohort study. (option b).

In this study, the researcher selected a group of 14-year-old girls and looked back in time to compare their previous dietary habits and exposures between those who had already started having monthly periods and those who had not.

It is important to note that this study design has some limitations. For instance, the researcher is relying on self-reported data from the girls, which may not always be accurate.

This study design involves selecting a group of individuals and looking back in time to compare their exposures or characteristics between those who developed the outcome of interest and those who did not. By identifying potential risk factors, the researcher can gain insights into the onset of early menses in 14-year-old girls.

Hence the correct option is (b).

To know more about study design here

https://brainly.com/question/31147631

#SPJ4

Complete Question:

Which type of study design is used in the following scenario: A researcher interested in the onset of early menses compared 1,000 14-year-old girls, half of whom had already begun to have monthly periods and half of whom had not. The girls were interviewed regarding previous exposures. including their prior dietary habits.

a) Prospective cohort study

b) Retrospective cohort study

c) Case-control study

d) Clinical trial

e) None of the answers listed

Answer: The unit circle is an essential tool in trigonometry because it helps in understanding and visualizing the relationships between angles and the values of the sine, cosine, and tangent functions.

The unit circle is a circle with a radius of one unit and centered at the origin of a coordinate plane. It is divided into 360 degrees or 2π radians. By placing this circle on the coordinate plane, we can easily determine the sine and cosine values of angles in standard position.

For any given angle θ, the sine value is the y-coordinate of the point where the terminal side of the angle intersects the unit circle, and the cosine value is the x-coordinate of that same point. The tangent function, which is the ratio of sine to cosine, can also be determined using the unit circle.

The unit circle also helps in understanding the periodicity of the sine and cosine functions. Since the circumference of the unit circle is 2π, the sine and cosine functions repeat themselves after every 2π radians or 360 degrees. This periodicity allows for the use of trigonometric identities and formulas to simplify and solve complex trigonometric equations.

In summary, the unit circle is an essential tool in trigonometry as it provides a visual representation of angles and their corresponding sine, cosine, and tangent values, and allows for the use of trigonometric identities and formulas to solve complex problems.

Terraced building. administrative or ceremonial purposes. . Its design allows for maximum use of the space, utilizing all levels of the building for various activities.

A terraced building is a large rectangular building made up of several levels, where the higher levels recede from the lower levels. Stairs lead from the bottom to the top level, and it was primarily used for administrative or ceremonial purposes.

A terraced building is a large rectangular structure that has multiple levels, with the higher levels receding back from the lower levels. A set of stairs provides access from the bottom to the top level, allowing for easy navigation throughout the building. This type of structure was primarily used for administrative or ceremonial purposes, such as for holding meetings, conferences, or other important events. Its design allows for maximum use of the space, utilizing all levels of the building for various activities.

Learn more about maximum here

https://brainly.com/question/29156925

#SPJ4

Answer:

1

2

3

4

6

12

43

86

129

172

258

516

Step-by-step explanation:

516 is divisible by?

Answer: 3

Step-by-step explanation:

(-3/4)/(-2/8)=(-3/4)(-8/2)=(-3/4)(-4)=3

Answer:

Each friend is running a half mile.

They are running 1/2 mile.

The operations of addition, subtraction, multiplication, division, exponentiation, and modulus are carried out by the arithmetic operators.

They cover the study of numbers, including the order of operations, which are useful in algebra, data handling, and geometry, among other areas of mathematics.

Given Hotah and his 3 friends are each running 1/4 of a 2-mile relay race

total distance covered by them out of 2 miles is

2 x 1/4 = 1/2 miles

Therefore each person runs at 1/2 a mile.

Learn more about arithmetic operations;

https://brainly.com/question/25834626

#SPJ2

height of pentagonal prism is h unit.

The prism is one that has two pentagonal bases from which one acts as bottom and the other acts as top. The pentagonal prism has five rectangular sides. This prism has 10 vertices and 15 edges. It is also said five-sided polygon prism.

given, area of pentagonal prism = 34 square unit

volume of pentagonal prism = 180.2 cubic unit

we know the formula for the area of the pentagonal prism.

Total surface area = 5ab + 5hb

Volume of pentagonal prism = 5/2 a b h

where, a =apothem length

b = base length

h = height of the prism

according to the given statement, 34 = 5 a b + 5 h b

          180.2 = 5/2 a b h

from the above two equation, we get, the height of prism = h unit.

To know more about pentagonal prism visit:

https://brainly.com/question/27476

#SPJ1