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Select the correct answers from each drop-down menu.
Complete the steps in the proof that show quadrilateral KITE with vertices K(0, -2). I(1, 2). T(7,5), and E(4,-1) is a kite.
Using the distance formula, KI = √√(2 – (-2)² + (1 - 0)² = √17. KE =
-
IT =
and TE=
Therefore, KITE is a kite because
→

Polynomial is divisible by x+2, therefore the first root is -2.  The second and third roots of the function, we can estimate them utilizing the quadratic equation formula.

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.

Let the given polynomial function be

F(x)=2x³ - 9x² - 6x + 40, the first potential roots are -2, 4 and 5/2.

Solving for the first root, we divide the given function by x+2 where the result is 2x² - 13x + 40.

Since the given polynomial exists divisible by x+2, therefore the first root exists -2.

For the second and third roots of the function, we can estimate them utilizing the quadratic equation formula.

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Answer:

-3x^2-3

Step-by-step explanation:

1: 3x^2

2: -3x^2

3:

The dimensions of the corral of maximum area 80 x 160 feet

What is Area?

Area is a quantity that describes the extent of an area on a plane or curved surface. The area of ​​a planar region or planar region refers to the area of ​​a shape or planar layer, while surface area refers to the area of ​​an open surface or boundary of a three-dimensional object

Set each side perpendicular to the wall x

Parallel to the wall would be 320-2x

the area would be:

A(x) = x (320-2x)

A(x) = 320x-2x ^ 2

It is quadratic with a = -2 and b = 320

The largest area will happen when x = -b / 2a

= -320 / (- 2 * 2)

= 80 feet

so the width will be 80 feet and the length will be:

length = 320-2 * 80

           = 160 feet

Hence, The dimensions of the corral of maximum is 80 x 160 feet

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Step-by-step explanation:

Answer:

F and D are whole numbers

Answer:

A and E

Step-by-step explanation:

I see no other correct answer option.

3(2 + 6D) = 3×2 + 3×6D = 6 + 18D

= (3×2)+(3×6D)

with or without brackets this is the same thing as per the priorities of mathematical operations (first multiplications and divisions, and only then secondly additions and subtractions).

The total feet you and your friend can paint in 22 minutes are 143 feet.

A unit rate is the rate for only one of anything. This is expressed as a ratio with a denominator of 1.

Given:

You can paint 14 feet in 4 minutes and your friend can paint 18 feet in 6 minutes.

The unit rate for you = 14/4 = 7/2 feet/min

The unit rate for your friend  = 18/6 = 3 feet/min

The total feet you and your friend paint in 22 minutes is,

Multiply the 22 feet with the respective unit rates of you and your friend and add them up,

22×7/2 + 22×3 = 77 + 66 = 143 feet

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Answer:

5$

Step-by-step explanation:

480$+120$=600$ 600÷120=5

Mr. and Mrs. Crone needs to deposit $2164.31 to have $20000 in 10 years.

Finalize the compound growth formula using the amounts. Then equate for the unknown digit.

A = P[tex](\frac{1+r}{n} )^{nt}[/tex]

where A is the account balance, P is the investment amount that needs to be figured out, r is the annual interest rate which is 1.25%, t is the year which is 10 years, and n is the number of annual interest rates which is 52,

Filling in the given values, we have

20000 = P[tex](\frac{1 +.0125}{52} )^{520}[/tex]

20000 = P(0.092403)

P = 20000 ÷ 0.092403

P ≈ 2164.31

Therefore, $2164.31 is required to have $20000 in 10 years.

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Answer:

Step-by-step explanation:

Total reduction over the given period is the product of the two numbers above:

95 % is the percentage of person that have diabetes that also tested positive for the disease.

To do this we would have to loot at the top of the table and the information that is at the left hand side of the table.

At the top we have the column that is tagged, test powitive and the test negative columns.

On the side we have the have diabetes and do not have diabetes row. We are interested in the people that have diabetes and also have tested positive to the disease.

On the table, this is tagged as 36.1%

Then the total = 38%

hence we would have

36.1%/38% x 100

= 0.361 / 0.38 x 100

= 0.95 x 100

= 95%

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Answer:

no

Step-by-step explanation:

12+16+12+16=56

48 is smaller than 56

Using a system of equations, it is found that she bought:

To find how many bags of each candy she bought, we have to solve a system of equations, in which the variables are given as follows:

She bought three more bags of Reese's than lollipops, hence the first equation is:

y = x + 3.

She bought two fewer bags of Starbursts than lollipops, hence the second equation is:

z = x - 2.

Bags of lollipops cost $3.75 each, bags of Reese's cost $5.50 each and bags of Starbursts cost $4.25 each. She spent a total of $48.50, hence the third equation is:

3.75x + 5.5y + 4.25z = 48.50.

We have the variables y and z as a function of x, hence we can replace them into the third equation and solve for x as follows:

3.75x + 5.5(x + 3) + 4.25(x - 2) = 48.50

13.50x + 8.50 = 48.5.

13.50x = 40.50.

x = 40.50/13.50.

x = 3. (number of lollipops bags).

Hence the number of Reese's bags is:

y = x + 3 = 3 + 3 = 6.

The number of Starbursts bags is:

z = x - 2 = 3 - 2 = 1.

The problems asks for the number of bags of each candy that was purchased.

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Maggie made a mistake while combining similar terms of x using vertical angles; the result is -3x rather than 3x, hence the right answer is x = 9.

When two lines intersect, vertical angles are two angles that are opposed by the same vertex and are congruent, meaning they have the same measure.

The vertical angles for this issue are as follows:

4x + 2.

7x - 25.

Since they agree, the following equation may be used to determine the variable x:

4x + 2 = 7x - 25.

The following results from shifting all terms with x to the left side of the equality and all terms that are constant to the right side, with the opposite signal:

4x - 7x = -25 - 2

Combining similar phrases yields the following results:

-3x = -27.

Maggie made a mistake here since 4x - 7x = -3x, thus the proper answer is as follows:

3x = 27

x = 27/3

x = 9.

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It is required to combine the radicals which can be done as follows:

Option D is correct.

The monomial if the expression is the square of that monomial is; ⁵/₄a⁶b³

A monomial is defined as a polynomial, which has only one term or defined as an algebraic expression with a single term.

We are given the expression;

1⁹/₁₆ a¹²b⁶

Now, we can convert the mixed fraction to improper fraction to get;

²⁵/₁₆a¹²b⁶

The question is asking for the monomial, and the given is squared. What we will do is to extract that square from expression, and ensure that it's done applying a squared root, because that's the opposite operation of a squared power:

√(²⁵/₁₆a¹²b⁶) = ⁵/₄a⁶b³

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The x and y-intercept of the linear equation 10x - 7y = -8 in an ordered pair form are ( -4/5, 0 ) and ( 0,  8/7 ) respectively.

The intercept of a line on a graph is simply the point at which it intersects either the x-axis or y-axis.

Given the data in the question;

To find the x-intercept, substitute in 0 for y and solve for x.

10x - 7y = -8

10x - 7(0) = -8

10x - 0 = -8

10x = -8

Divide both sides by 10

10x/10 = -8/10

x = -8/10

x = -4/5

Therefore, the x-intercept is ( -4/5, 0 ).

To find the y-intercept, substitute in 0 for x and solve for y.

10x - 7y = -8

10(0) - 7y = -8

0 - 7y = -8

-7y = -8

Divide both sides by the coefficient of y

-7y / -7 = -8 / -7

y =  -8 / -7

y = 8/7

Therefore, the y-intercept is ( 0,  8/7 ).

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The equivalent expression of the expression 1.1 × 10 - 32.2 × 10⁴ will be

⇒ - 3,31,989

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is;

⇒ 1.1 × 10 - 32.2 × 10⁴

Now,

Solve the expression as;

The expression is;

⇒ 1.1 × 10 - 32.2 × 10⁴

⇒ 11 - 3,22,000

⇒ - 3,31,989

So, 1.1 × 10 - 32.2 × 10⁴ =  - 3,31,989

Thus, The equivalent expression of the expression 1.1 × 10 - 32.2 × 10⁴ will be

⇒ - 3,31,989

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The slope of the line passing through (-2,2) and (2,-8) is -5/2

The ratio of the "vertical difference" to the "vertical change" between (any) two unique points on a line is used to compute slope.

a)The slope of the line passing through (0,-1) and (5,6) is 7/5 .

The slope of the line passing through (4,-7) and (2,-2) is -5/2 .

b) line 1 and line 2 are perpendicular.

line 3 and line 2 are perpendicular.

line 1 and line 3 are parallel .

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Answer:y=-9x+3

Step-by-step explanation:

In a y=mx+b equation (slope intercept form) like this one m is the slope and b is the y intercept.

Answer:

2.  See below.

4.  Domain = {57, 68, 93, 99}

Step-by-step explanation:

Given relation:

[tex]\{ (1,5),(2,3),(3,2),(4,1),(5,0)\}[/tex]

The given relation is a set of ordered pairs (x, y), where the first element is x and the second element is y.

To express the given relation as a table, enter the x-value of each ordered pair in the left column, and the corresponding y-value of each ordered pair in the right column:

[tex]\begin{array}{|c|c|}\cline{1-2} x & y\\\cline{1-2}1&5\\\cline{1-2}2&3\\\cline{1-2}3&2\\\cline{1-2}4&1\\\cline{1-2}5&0\\\cline{1-2}\end{array}[/tex]

An ordered pair is used to represent the position of a point on the coordinate plane.  Therefore, to represent the given relation as a graph, plot each ordered pair on the given coordinate plane.  

(See attachment 1).

To represent the given relation as a mapping diagram:

(See attachment 2)

The domain is the set of all x-coordinates.

Therefore, the domain of the given mapping diagram is {57, 68, 93, 99}.

a claim that is accepted as true without evidence, also referred to as an axiom. Lemmas and theorems are deduced from postulates, which serve as their fundamental building block.

For instance, Euclid's postulates, a set of five postulates, provide the foundation of all of Euclidean geometry.

Why are theorems and postulates crucial in geometry?

The foundation of any mathematical system, including geometry, algebra, and trigonometry, are postulates and theorems. Mathematicians have created entire systems of mathematics by utilizing postulates to argue theorems that can then be proved by other theorems.

A statement that has been proven true or that can be proven is known as a theorem in mathematics. A logical argument that uses the deductive system's inference rules to establish a theorem is called a proof.

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Answer:

6

Step-by-step explanation:

1 and 1/2 is equal to 1 and 2/4, or 6/4. This means that it would take 6 teaspoons to add 1 1/2 teaspoons of baking soda. hope this helps!

Answer:

Solution Below.

Step-by-step explanation:

This question tests on the concept of angle properties.

From the question above, we can form up an equation:

x + 2x + (x + 30) = 180 (Sum of angles in a triangle)

Now, we can solve for x to find the angles of each side.

[tex]x + 2 x + x + 30 = 180 \\ 4x + 30 \\ 4x = 150 \\ x = 37.5[/tex]

Now we can find the angles for each side:

x = 37.5

2x = 2 × 37.5 = 75

x + 30 = 37.5 + 30 = 67.5

Answer:

37.5, 75, and 67.5

Step-by-step explanation:

The angles of a triangle add up to 180 so everything inside is equal to 180.

180=x+2x+x+30, simplify

180=4x+30, subtract 30 on both sides

150=4x, divide 4 on each  side

37.5=x

solve now knowing x

x= 37.5

x+30= 67.5

2x= 75

Answer:

= 12.5% decrease

Step-by-step explanation:

Decrease = Original Number - New Number

Then: divide the decrease by the original number and multiply the answer by 100.

% Decrease = Decrease ÷ Original Number × 100

Therefore, the answer is 12.5% decrease

There is an infinite number of values that are in both the domain and range.

Here, we are given a function f(x) = m, where m is a real number greater than 0.

For a function, domain is all the input values that the function can take and range is all the output value that the function can take.

Here, all the x values are the domain and the set of all the values that m can take is the range of the function.

Here m can take all values except 0. Whereas there is no constraint on the x values.

Since the range can never have the value 0, options 1 and 2 are eliminated.

Clearly, there can be many values that are both in the domain and range of the given function.

Thus, there is an infinite number of values that are in both the domain and range.

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Answer:

| -0.125 | >  | 0.0125 |

Step-by-step explanation:

Due to the absolute value signs, the negative sign is null and void. Therefore, 0.125 > 0.0125.

Answer:

0.1375

Step-by-step explanation:

Answer: yes it is interesting because u also know more about finance and you would have a much easier life after this

Step-by-step explanation: