10
Select whether the given side lengths of a triangle form a right triangle.
Do Not Form a
Right Triangle
3 cm, 4 cm, 5 cm
8 m, 10 m, 15 m
6 in., 8 in., 10 in.
5 cm, 12 cm, 13 cm
Form a
Right Triangle
0

Answer: height = 1.91 m

Step-by-step explanation: Using the formula

V=πr2h

Solving for h

h=V

πr2=37.5

π·2.52≈1.90986m

The zeroes of 5x^4-26x^3-64x^2+9x-14 are -2, 7 ,  [tex]\frac{1+i\sqrt{19} }{10}[/tex]  and   [tex]\frac{1-i\sqrt{19} }{10}[/tex]  by Using the rational theorem.

f(x) = [tex]5x^{4} - 26x^{3} - 64x^{2} +9x -14[/tex]

Now, put x = -2

f(-2) = [tex]5(-2)^{4} - 26(-2)^{3} - 64(-2)^{2} +9(-2) -14[/tex]

f(-2) = 0

so, -2 is a zero of f(x)

or (x+2) is a factor of  [tex]5x^{4} - 26x^{3} - 64x^{2} +9x -14[/tex]

putting x = 7

f(7) = [tex]5(7)^{4} - 26(7)^{3} - 64(7)^{2} +9(7) -14[/tex]

f(7) = 0

so, (x-7) is a factor of  [tex]5x^{4} - 26x^{3} - 64x^{2} +9x -14[/tex]

Now (x+2)(x-7) would also be a factor so

Divide  [tex]5x^{4} - 26x^{3} - 64x^{2} +9x -14[/tex] by (x+2)(x-7)

or divide  [tex]5x^{4} - 26x^{3} - 64x^{2} +9x -14[/tex] by [tex]x^{2} -5x -14[/tex]

The quotient or other factor will be [tex]5x^{2} - x +1[/tex]

[tex]5x^{2} - x +1[/tex]

By factorizing  [tex]5x^{2} - x +1[/tex]

The other two zeroes are [tex]\frac{1+i\sqrt{19} }{10}[/tex] and  [tex]\frac{1-i\sqrt{19} }{10}[/tex]

To know more about polynomial

https://brainly.com/question/30503176

#SPJ4

The equation of the polynomial is P(x) = 0.16875(x + 8)(x - 10)

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the following readings:

A root of multiplicity 1 at x = -8

A root of multiplicity 1 at x = 10

y-intercept = -13.5

A polynomial is represented as

P(x) = a * (x - zero)^multiplicity

Using the above as a guide, we have the following:

P(x) = a * (x + 8)(x - 10)

The y-intercept is -13.5

So, we have

a * (0 + 8)(0 - 10) = -13.5

This gives

a = 0.16875

Hence, the expression is P(x) = 0.16875(x + 8)(x - 10)

Read more about polynomial at

brainly.com/question/7693326

#SPJ1

Answer:

Step-by-step explanation:

4.8

i got u brainliest please it helps a lot

Object is kind of a vector with the same size as the coefficients in the linear regression model.

In the least squares optimization target, the sum of squared errors (SSE) is typically minimized with respect to the coefficients of the linear regression model. The gradient of the SSE with respect to the coefficients is a vector that provides the direction of steepest ascent, or the direction in which the SSE increases the most rapidly. Setting this gradient vector to zero and solving for the coefficients yields the least squares solution to the linear regression problem.

Therefore, in this context, " " is likely a vector of coefficients that are being optimized to minimize the SSE.

To learn more about regression model here:

https://brainly.com/question/14983410

#SPJ4

The dilated quadrilateral is A' ( -2 , 4 ) , B' ( 4 , 4 ) , C' ( 6 , -2 ) and D' ( 0 , -2 )

Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent

Given data ,

Let the quadrilateral be represented as ABCD

Now , the coordinates of ABCD is given as

A ( -1 , 2 ) , B ( 2 , 2 ) , C ( 3 , -1 ) and D ( 0 , -1 )

Now , when the dilation is of the scale of (x,y) → (2x, 2y) about the origin

Substituting the values in the equation , we get

A' ( x , y ) = A ( 2 ( -1 ) , 2 ( 2 ) )

On simplifying the equation , we get

The coordinates of A' is = A' ( -2 , 4 )

The coordinates of B' is = B' ( 4 , 4 )

The coordinates of C' is = C' ( 6 , -2 )

The coordinates of D' is = D' ( 0 , -2 )

Hence , the dilated figure is solved

To learn more about dilation click :

https://brainly.com/question/13176891

#SPJ9

The length of Mr. Neil's homeroom is (10/11) times the length of Miss Robert's homeroom.

The length of Mr. Neil's homeroom is calculated as follows:

Let's assume that Miss Robert's homeroom has width w and length l, and Mr. Neil's homeroom has width (1¹/₁₀ or 11/10)w and length x.

Both homerooms have the same perimeter, therefore:

2w + 2l = 2(11/10)w + 2x

Simplifying the equation:

2l - 2x = (2/10)w

l - x = (1/10)w

x = l - (1/10)w

To solve for x, we need to express it in terms of l and w.

From the equation above, we can substitute x with l - (1/10)w:

(11/10)w = 2l - x

(11/10)w = 2l - l + (1/10)w

(10/10)w = l + (1/10)w

w = (10/11)l

Substituting w with (10/11)l in the expression for x, we get:

x = l - (1/10)(10/11)l

x = l - (1/11)l

x = (10/11)l

Therefore, the length of Mr. Neil's homeroom is (10/11) times the length of Miss Robert's homeroom.

Learn more about the length of a room at: https://brainly.com/question/28839698

#SPJ1

Answer: 188in^2

Step-by-step explanation:

You can break the figure into 3 smaller shapes

15 x 5

10 x 5

and 9 x 7

The areas of these smaller shapes are 75, 59 and 63

adding these areas together would get you 188 in squared.

The probability of the shuttle launching safely under similar conditions is 0.859, or approximately 86%.

Scientists and statisticians played a crucial role in analyzing the cause of the disaster, which was eventually attributed to the failure of O-ring joints in the shuttle's booster rockets.

To understand the probability of the shuttle launching safely under similar conditions, we need to consider the probability of all six O-ring joints functioning properly. According to experts, the probability of an individual O-ring joint working in cold conditions was 0.977.

Assuming that the O-ring joints succeed or fail independently, we can use the multiplication rule of probability to calculate the probability of all six joints functioning properly.

The multiplication rule states that the probability of two independent events occurring together is the product of their individual probabilities. In this case, the probability of all six joints working properly is:

P(all six joints work) = P(joint 1 works) x P(joint 2 works) x P(joint 3 works) x P(joint 4 works) x P(joint 5 works) x P(joint 6 works)

Plugging in the given probability of an individual O-ring joint working in cold conditions (0.977), we get:

P(all six joints work) = 0.977 x 0.977 x 0.977 x 0.977 x 0.977 x 0.977

P(all six joints work) = 0.977⁶

P(all six joints work) = 0.859

To know more about probability here.

https://brainly.com/question/11234923

#SPJ4

Answer:

Option C

Step-by-step explanation:

First, knowing that two angles on a horizontal line split by a vertical line at any angle is equal to 180 degrees, I try to find which of the combinations of angle x and z equal 180.

A. x = 63, and z = 104 and together they equal 170, so not A

B. x = 76 and z = 63 and together they equal 139 so not B

C. x = 76 and z = 104 and together they equal 180 so it could be C, but we must check D to make sure.

D. x = 63 and z = 76 and together they equal 139 so not D.

From all of this it must be option C

Function 1 and Function 2 have y-intercepts that are equal. The solution has been obtained by using slope-intercept form.

What is slope-intercept form?

The line that represents the graph of the equation y = mx + b has a slope of m and a y-intercept of b. The m and b values are real integers, and the slope-intercept form of the linear equation is used.

We are given two functions.

Now, we will represent the functions in the slope-intercept form to find the y-intercept.

Function 1

⇒4x - 2y = -2

⇒2x - y = -1               (Dividing both sides by 2)

⇒ -y = -1 - 2x

⇒y = 2x + 1

So, the y-intercept is 1.

Function 2

We are given two points as (-1,3) and (0,1)

The slope comes out to be = -2

So, b = 3 - (-2)(-1) = 1

So, the y-intercept is 1.

Hence, function 1 and function 2 have y-intercepts that are equal.

Learn more about slope-intercept form from the given link

https://brainly.com/question/1884491

#SPJ1

The result to the factorization of the polynomial is 3x (x + 10) (x - 10).

Factoring polynomials involves utilizing prime factorization to break the given polynomial down into a product of two or more polynomials. Polynomials can be readily simplified by factoring them.

Writing each term of the longer expression as the product of its elements is the initial step to factorization polynomials.

= 3x³ - 300x

= 3x(x²) - 300x

= 3x(x²) - 3x(100)

= 3x(x² - 100)

= 3x(x² - 10²)

Since both terms are perfect squares, factor using the difference of squares formula, a² − b² = ( a + b ) ( a − b );

where

= 3x (x+10) (x−10)

Learn more about factorizing polynomials here:

https://brainly.com/question/24351176

#SPJ1

So we would expect 8 of the next 20 cupcakes sold to be lemon cupcakes.

What is Algebraic expression?

An algebraic expression is a mathematical phrase that consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The variables can represent unknown values, while the constants represent known values.

Based on the data provided by Celine's Cupcakes, out of the total of 15 cupcakes sold, 6 were lemon cupcakes. This means that the proportion of lemon cupcakes sold is:

6/15 = 0.4

To estimate how many of the next 20 cupcakes sold would be lemon cupcakes, we can assume that the proportion of lemon cupcakes sold will remain the same. Therefore, we can expect that:

0.4 x 20 = 8

Therefore, So we would expect 8 of the next 20 cupcakes sold to be lemon cupcakes.

To learn more about Algebraic expression from given link.

https://brainly.com/question/28884894

#SPJ1

AD is also an internal bisector of ΔABC, this statements prove that AB is congruent to AC.

What is the bisector of the triangle?

The bisector of a triangle is a segment that divides one of its interior angles into two equal parts and continues until it reaches the side opposite that angle. In other words, the bisector of a triangle is a line that divides each interior angle of the triangle into two equal angles.

We have given,

Segment AD is an altitude of ΔABC.

If CD ≅ BD

So, AD is the middle line of the triangle

AD is also an altitude of ΔABC.

So, AD is also an internal bisector of ΔABC

So, AB ≅ AC            ............{Thereom of unity of three lines}

Hence, AD is also an internal bisector of ΔABC, this statements prove that AB is congruent to AC.

To learn more about the bisector of the triangle visit,

https://brainly.com/question/29444532

#SPJ1

Answer:

?

Step-by-step explanation:

The vertex form of the function is  [tex]y = (x+4)^{2} - 19[/tex]

Vertex form of function:

The vertex of the function is located at (h,k) of its vertex form, and will be located at the peak or trough of the parabola on a graph. This is the highest or lowest point of the function, depending on its direction.

The vertex form of the equation is written as,

[tex]y = (x+h)^{2} + k[/tex]

Given function is,

y = x² + 8x + 16 - 3 -16

It is observed that,  

x² +8x + 16 = (x+4)²

So that, we can write as above function,

y = x² + 8x + 16 - 3 -16 = (x+4)² - 3 -16

or

y =  (x+4)² - 19

Learn more about the quadratic function here:

brainly.com/question/25841119

#SPJ1

I would need to work at least 27 hours to make enough money to reach my goal.

What are arithmatic operations?

Arithmetic operations is a branch of mathematics, that involves the study of numbers, the operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication, and Division.

Let's start by finding the amount of money I receive from my allowance and how much more money I need to make to reach my goal:

Allowance per month = $60

Amount of money I need for social life = $260

Additional amount of money I need to make = $260 - $60 = $200

Now, let's divide the additional amount of money I need to make by the amount I make per hour to find how many hours I need to work:

$200 ÷ $7.50 per hour = 26.67 hours

Since we can't work a fraction of an hour, we need to round up to the nearest whole number.

Therefore, I would need to work at least 27 hours to make enough money to reach my goal.

To learn more about the arithmatic operations visit:

https://brainly.com/question/13181427

#SPJ1

If the sum of two angles is 90 degrees, then the angles are called complementary angles.

Complementary angles are a type of angle relationship where two angles add up to exactly 90 degrees. In other words, when you add the measures of two complementary angles together, the sum is always equal to 90 degrees.

For example, if angle A measures 30 degrees, and angle B measures 60 degrees, then angle A and angle B are complementary angles, because 30 degrees + 60 degrees = 90 degrees.

Complementary angles are important in geometry and trigonometry, because they often appear in problems involving right triangles. In a right triangle, one of the angles measures 90 degrees, which means that the other two angles must be complementary.

For example, if one angle in a right triangle measures 30 degrees, then the other angle must measure 60 degrees, since 30 degrees + 60 degrees = 90 degrees.

Understanding complementary angles can be useful in a wide range of mathematical and real-world contexts. For example, in construction or engineering, understanding complementary angles can help ensure that structures are built at the correct angle to provide the necessary support and stability.

To learn more about trigonometry click on,

https://brainly.com/question/12849010

#SPJ4

The fraction that is the ratio of the shaded area of the circle to the area between the two squares is (π−2)/2.

A fraction is a mathematical expression that represents a part or a proportion of a whole.

Let us assume that the radius of the circle is 'r' units. Therefore, the diameter of the circle is 2r units. The diagonal of the inner square is equal to the diameter of the circle, which is 2r units. Hence, the side of the inner square is r√2 units.

Now, let's consider the area of the circle. The formula for the area of a circle is

=>  A=πr².

Therefore, the area of the circle is πr².

The area between the two squares is the difference between the area of the outer square and the area of the inner square. The area of the outer square is

=> (2r)²=4r²,

and the area of the inner square is

=> (r√2)²=2r².

Hence, the area between the two squares is

=> 4r²−2r²=2r².

The shaded area of the circle is the area inside the circle but outside the inner square. We can find this area by subtracting the area of the inner square from the area of the circle. Therefore, the shaded area of the circle is

=> πr²−2r²=(π−2)r².

Now, let's find the ratio of the shaded area of the circle to the area between the two squares. We can express this ratio as a fraction. Thus,

ratio = (π - 2)r² / 2r

We can simplify this fraction by canceling out the common factor r^2 in both the numerator and denominator. Thus,

ratio = (π - 2) / 2

This fraction is closest to the ratio of the shaded area of the circle to the area between the two squares.

To know more about fraction here.

https://brainly.com/question/10354322

#SPJ4

Answer:

slope = [tex]\frac{2}{5}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (5, 2) ← 2 points on the line

m = [tex]\frac{2-0}{5-0}[/tex] = [tex]\frac{2}{5}[/tex]

Answer:

1 pound of strawberries

Step-by-step explanation:

4 x $1.20 = $4.80

$6 - $4.80 = $1.20

one pound is $1.20

Answer:

The function f: A -> B is defined by:

f(x) = { 11, if x = -1 or x = 2,

-1, if x = 0,

-2, if x = 1,

0, if x = 3 or x = 4 }

The range of the function is the set of all possible values of f(x). In this case, the range of f is B = {-2, -1, 0, 11}.

To determine if the function is one-to-one, we need to check if each element in the range has only one pre-image. In other words, we need to check if no two elements in A map to the same element in B. Since each element in B has a unique pre-image in A, the function is one-to-one.

To determine if the function is onto, we need to check if each element in B is the image of some element in A. In this case, every element in B is the image of exactly one element in A, so the function is onto.

Therefore, the function f is one-to-one and onto both.

The shipping charge of an item on the purchase $56 is $2.52.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

The percentage of a number is the value of the number out of 100.

For example, in a class, there are 26 boys and 24 girls. So, the percentage of boys in the class is 26/(26+24) × 100 = 26/50 × 100 = 52%, which means out of 100, 52 are boys.

A company charges  shipping fee = 4.5% of the purchase price for all items,

Cost of an item =$56

So, shipping fee = 4.5% of 56

= 4.5/100 × 56

= 0.045 × 56

= $2.52

Learn more about percentage here :-

https://brainly.com/question/29306119

#SPJ4

Part (a)

ASA = angle side angle

To use ASA, we need two angles and a side between those angles. We already have one pair of angles (DFE and GHI). The other pair of angles must be DEF and GIH to have the side sandwiched between the angles.

===================================================

Part (b)

HL = hypotenuse leg

The sides EF and IH are congruent to one another because of the tickmarks. They are the legs of each right triangle. So that takes care of the "L" of "HL". We need to have the hypotenuses congruent to each other to be able to use HL. This theorem only applies to right triangles.

a) The median would be larger than the mean because the life expectancy of some countries may be much lower than the others, thus affecting the mean.

b) The median should be reported as it is a better measure of central tendency, as it is not affected by outliers.

a) The median is expected to be larger than the mean because the life expectancy of some countries may be much lower than the others, thus affecting the mean. The mean is calculated by adding all the values together and dividing by the number of values, and if there are any values that are much lower or higher than the rest, this will affect the mean significantly. The median, however, is the midpoint of the values, so outliers have less of an influence on it.

b) The median should be reported as it is a better measure of central tendency, as it is not affected by outliers. The median is the midpoint of the values, which means that if there are any values that are much lower or higher than the rest, it will not affect the median as much as it does the mean. This makes the median more accurate in representing the life expectancy of countries, as it is not skewed by outliers. Furthermore, the median is generally more reliable when dealing with skewed distributions, which is often the case with life expectancy data.

Learn more about median here

https://brainly.com/question/28060453

#SPJ4

The equation that represents the image will be w + 1.3 = 2.7. And the value of 'w' will be 1.4.

An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.

The length of both tapes is the same. Then the equation is given as,

w + 1.3 = 2.7

Simplify the equation for w, then we have

w + 1.3 = 2.7

w = 1.4

The equation that represents the image will be w + 1.3 = 2.7. And the value of 'w' will be 1.4.

More about the solution of the equation link is given below.

https://brainly.com/question/29797035

#SPJ1

Answer: ddddddddddddddddddddddddddddddddddddddddddddddbddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddd

Step-by-step explanation:

The ones we don't want are those. We only want 410 of the 560 total, thus the cost is $097.

Contact nations A, B, and C. At the northernmost position for configurations, someone from A is seated. Since the only thing the problem mentions about how delegates can differ is by their country, I decided to represent people in my solution by their respective nations. Now, we can see that there are nCr(8, 2) * nCr(6, 3) = 560 possible arrangements (8 seats choose 2 for the rest of the A country, 6 seats choose 3 for B). It is clear that configurations with three delegates in a row are the ones we don't want. Take note that scenarios for A, B, and C to be together are still valid despite my  placing of A at the start.We now apply the inclusion-exclusion principle. Two cases for an A three in a row. First. A, Master A, A: $20 for B seats at nCr(6, 3). Additionally, there is $20 for each "slant" A set. =$60. *3=180. A and B both: Two cases once more! We identify four ways for B to get three in a row: A, Master A, A, and A. $12 is the same for slant. *3 = $36 (AB, BC, or CA). For all three: This time, we have two of the three aforementioned A circumstances, for a total of six. 180-36+6 Equals 150 in the end. The ones we don't want are those. We only want 410 of the 560 total, thus the cost is $097.

Learn more about cost from

brainly.com/question/481029

#SPJ4

The only statement that must be based on the quadrilateral properties is; Option B: Base angles of quadrilateral Z are congruent

Some of the properties of a quadrilateral are;

1) They have four vertices.

2) They have four sides.

3) The sum of all interior angles is 360°.

4) They have two diagonals.

5) A quadrilateral can be regular or irregular.

Now, from the description of Quadrilaterals T and Z, we can say that;

- The base angles of quadrilateral T are not congruent since at least one pair of parallel side is congruent.

- Base angles of quadrilateral z are congruent since opposite sides are congruent.

- Consecutive angles of quadrilateral Z are not congruent

- Opposite angles of quadrilateral T are not supplementary.

Read more about quadrilateral properties at; https://brainly.com/question/21927684

#SPJ1

Answer:

i think it x = 0 and x = 5

Step-by-step explanation:

[tex]y = {x}^{2} - 4x + 2[/tex]

[tex]y = x + 2[/tex]

[tex]x + 2 = {x}^{2} - 4x + 2[/tex]

[tex]0 = {x}^{2} - 4x + 2 - x - 2[/tex]

[tex]0 = {x}^{2} - 5x[/tex]

[tex]0 = x(x - 5)[/tex]

[tex]x = 0[/tex]

(or)

[tex]x - 5 = 0[/tex]

[tex]x = 5[/tex]