What constant must be added to both sides of the equation x^2-6x=-5 in order to complete the square?

The proof that shows that ΔLMN ≅ ΔQPN by either SSS or SAS is explained below.

If we can show that two triangles have two pairs of congruent sides and a pair of corresponding congruent included angles, then we can state they are congruent triangles based on the SAS theorem.

On the other hand, if all three corresponding side lengths are congruent to each other, then the triangles are congruent by the SSS theorem.

The proof that can be used to show that the two triangles are congruent by SAS is shown below:

Statement                                 Reasons                                  

1. ∠L ≅ ∠Q, LM ≅ QP,              1. Given

MN ≅PN, NL ≅ NQ

2. ΔLMN ≅ ΔQPN                    2. SSS

Based on the given information we are given, another way of writing this proof can be:

Statement                                 Reasons                                  

1. ∠L ≅ ∠Q, LM ≅ QP,              1. Given

MN ≅PN, NL ≅ NQ

2. ΔLMN ≅ ΔQPN                    2. SAS

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Answer:

56

Step-by-step explanation:

Answer:

In 2010, the average selling price was $700, and in 2012, the average selling price was $560.

The correct reason for the similarity of triangles ADC and CBA is given as follows:

SSA.

The similarity theorems are listed as follows:

In this problem, we have that:

Two sides and an angle not between them, hence they are congruent by the SSA theorem.

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The value of t for the given triangle angle will be equal to 1.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given the three angles of the triangle are 111,34, and 35t. The value of t will be calculated as,

35t + 111 + 34 = 180

35t = 180 - 111 - 34

35t = 35

t = 1

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1 is the root of the equation cosx = x² in the interval  [0, pi]/

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The given equation is cosx = x²

cosx-x²=0

y(x)=cosx-x²

y(0)=1

y(π)=-1-π²

y(π)<0<y(0) and y is continuous, there must be a value of x in [0, pi]

where

cosx−x²=0.

Hence, 1 is the root of the equation cosx = x² in the interval  [0, pi].

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option B is correct. 10/9 is greater than 1, the product of  [tex]3\frac{2}{3}[/tex] and ​10/9​ is greater than ​3 is the statement,

Multiplication is a method of finding the product of two or more numbers

We need to find the product of [tex]3\frac{2}{3}[/tex] and 10/9.

Firstly let us convert the mixed fraction  [tex]3\frac{2}{3}[/tex] to the improper fraction.

11/3 is the simplified form of  [tex]3\frac{2}{3}[/tex]

11/3×10/9

110/27

4.1

As we observe the 10/9 is greater than 1, the product of  [tex]3\frac{2}{3}[/tex] and ​10/9​ is greater than ​3.

Hence, the statement 10/9 is greater than 1, the product of  [tex]3\frac{2}{3}[/tex] and ​10/9​ is greater than ​3.

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the answer to the expression 8.3-4 1/5 (6.1+1/2)is -19.42

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

The given expression

8.3-4 1/5 (6.1+1/2)

=8.3-4 1/5 (6.6)

=8.3-(6.6*21/5)

=-19.42

Hence the answer is -19.42

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Answer: The number of trials is limited to two.

Answer:

reflection over the y-axis

Step-by-step explanation:

Answer:

C?

Step-by-step explanation:

Answer:

To apply the distributive property using the greatest common factor (GCF) to write an equivalent expression for 0.3x - 2.7, we need to find the GCF of the coefficients of the terms in the expression. In this case, the GCF is 0.3, so we can write the expression as 0.3(x - 9). This is an equivalent expression to 0.3x - 2.7, because multiplying 0.3 by the difference of x and 9 produces the same result as subtracting 2.7 from 0.3x.

Step-by-step explanation:

The correct answer is:  [D]:  " [tex]\frac{(1.2)^2^4}{(1.4)^1^8}[/tex]  "

Step-by-step explanation:

Given:  ( 1.4³ / 1.2⁴)⁻⁶ ;

Note the following properties of exponents:

1)    [tex]a^-^b = \frac{1}{a^b}[/tex] ;  { [tex]a\neq 0[/tex] } ;  and:

2)   the  'power of a fraction' rule:
 [tex](\frac{a}{b})^c} =\frac{a^c}{b^c}[/tex] ;  [tex]b\neq 0[/tex] '

As such:
[tex](\frac{1.4^3}{1.2^4})^{-6}[/tex]  ;

=  1  ÷ ( [tex]\frac{1.4^3}{1.2^4})^{6}[/tex] ;

=  [tex]\frac{1}{1}[/tex]   ÷ ( [tex]\frac{1.4^3}{1.2^4})^{6}[/tex] ;;

=  [tex]\frac{1}{1}[/tex]   ÷   [tex]\frac{1.4^(^3^*^6^)}{1.2^(^4^*^6^)}[/tex] ;

Note the follow property of exponents:
" [tex](\frac{a}{b})^c = \frac{a^c}{b^c}[/tex] " ;  {" b ≠ 0 "}.

⇒ =   [tex]\frac{1}{1}[/tex]   ÷ [tex]\frac{1.4^(^1^8^)}{1.2^(^2^4^)}[/tex]

Note:  Dividing by a fraction or a number; is the same as multiplying by the reciprocal (invert) of that number.

   =   [tex]\frac{1}{1}[/tex]   *  [tex]\frac{1.2^(^2^4^)}{{1.4^(^1^8^)}}[/tex] ;

   =     "  [tex]\frac{1.2^(^2^4^)}{{1.4^(^1^8^)}}[/tex]  "  ;

which corresponds to:
Answer choice:  [D]:   " [tex]\frac{1.2^(^2^4^)}{{1.4^(^1^8^)}}[/tex] " .
____________
Hope this is helpful!  Best of luck!

____________

Answer:

29

he area of the pool is 34 ft * 48 ft = <<34*48=1632>>1632 ft2.

Thus, the total area of the pool and the border strip is 1632 ft2 + 344 ft2 = <<1632+344=1976>>1976 ft2.

Hence, the border strip is 1976 ft2/34 ft = <<1976/34=58>>58 ft long.

Therefore, the border strip can be 58 ft/2 = <<58/2=29>>29 ft wide. Answer: {29}.

After solving the angles, the measure of angle x is 145°.

When two straight lines or rays intersect at a single endpoint, an angle is created.

The vertex of an angle is the location where two points come together.

The Latin word "angulus," which means "corner," is where the term "angle" originates.

The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation.

A geometrical shape called an angle is created by connecting two rays at their termini.

In most cases, an angle is expressed in degrees.

(Refer to the image attached below)

We can see that ∠ABC is a straight angle.

∠ABC = ∠ABD + ∠DBC where ∠ABD is x.

Now, solve for x as follows:

∠ABD + ∠DBC = ∠ABC

x + 35 = 180

x = 180 - 35

x = 145°

Therefore, after solving the angles, the measure of angle x is 145°.

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Answer:

17/6 divided by 5/3 is equal to 17/6 * 3/5, which simplifies to 51/30.

Answer:

green line or "b"

Step-by-step explanation:

we can set this up into the slope intercept form

y=mx+b

where m is the slope and b is y intercept

12=3x+4y

-3x -3x

-3x+12=4y

/4.  /4.  /4

-3/4x+3=y

we can see the only line with a negative slope and a y intercept at 3 is the green line or "b"

hopes this helps please mark rainliest

The value of x = -84/17, y= 24/17 and z = 9/17

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

x -2y + z= -6

x- 5z= -12

-x+ 6y + 4z = 3

Put x= -12+ 5z in equation 1 and 3

-12+ 5z - 2y + z= -6

6z - 2y = 6

3z - y= 3............(a)

and, 12 - 5z + 6y + 4z = 3

6y - z = -9.......(b)

Solving a and b we get

6(3z- 3) - z = -9

18z - 18 - z= -9

17z = 9

z= 9/17

and, y= 3(9/17) - 3 = 24/17

and, x = -12 + 120/17= -84/17

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In solving the equation, the student did the division wrong, and 29.4/4.2 = 7 which is correct.

Multiplication is the opposite of division.

If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group.

Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.

So, the equation is:

4.2p = 29.4

Let's solve as follows:

4.2p = 29.4

p = 29.4/4.2

p = 7

So, the value of p comes to 7.

Where in the image, the value of p is 123.48 which is wrong as the division is not done properly.

Therefore, in solving the equation, the student did the division wrong, and 29.4/4.2 = 7 which is correct.

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The Number of Soccer Balls is 16 and the Number of T-Shirts is 68

What is Linear Equation in Two Variables?

A linear equation in two variables is one that is stated in the form         ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

Let,

Number of Soccer Balls = x

Number of T-Shirts = y

Equation 1:

x + y = 84 -----------(i)

Equation 2:

25x + 9.5y = 1046 ----------(ii)

Multiplying Equation 1 by 25

25x + 25y = 2100 ---------(iii)

Substracting Equation2 from Equation 1

15.5y = 1054

y = 68

So, x = 16

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Reason:

x and y are the legs.

[tex]5\sqrt{2}[/tex] is the hypotenuse.

The hypotenuse is always opposite the 90 degree angle.

The hypotenuse is always the longest side of any right triangle.

Answer:

  D(6, -2)

Step-by-step explanation:

You want the coordinates of point E in ∆DEF congruent to ∆ABC after, it has been translated 4 units to the right.

The triangle names tell us that point E is the image of point B after the translation.

Moving a point to the right 4 units adds 4 to its x-coordinate.

  B(2, -2) ⇒ E(2+4, -2) = E(6, -2)

The Length is 5 inches and the Breadth is 15 inches

What is Perimeter?

A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. The circumference of a circle or an ellipse is its perimeter. There are various practical applications for calculating the perimeter.

Solution:

Perimeter of Rectangle = 2*(Length + Breadth)

According to the question

Breadth = 3*Length

Perimeter = 40

40 = 2*(Length + 3*Length)

20 = 4*Length

Length = 5 inch

Breadth = 15 inch

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The total distance walked in each case is given below;

Jada's pet turtle walked 10 feet, and then half that length again

Total distance = 10 + (1/2 of 10)

= 10 + (1/2 × 10)

= 10 + 5

= 15 feet

Jada's pet baby brother walked 3 feet, and then half that length again

Total distance = 3 + (1/2 of 3)

= 3 + (1/2 × 3)

= 3 + 1.5

= 4.5 feet

Jada's pet hamster walked 4.5 feet, and then half that length again

Total distance = 4.5 + (1/2 × 4.5)

= 4.5 + 2.25

= 6.75 feet

Jada's pet robot walked 1 foot, and then half that length again

Total distance = 1 foot + (1/2 × 1)

= 1 + 0.5

= 1.5 feet

A person walked x feet, and then half that length again

Total distance = x + (1/2 × x)

= x + 1/2x

= 1.5x feet

In conclusion, the total distance is calculated by adding the initial distance and additional distance

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The coordinates of point C is (-2, 12)

The segment OC is perpendicular to the chord AB.

The midpoint of a line segment is given as,

x = (a + c)/2

y = (b + d) / 2

Where (x, y) is the midpoint and (a, b) and (c, d) are the two endpoints.

We have,

Points A(-6,10) and B(2,14) lie on circle O with its center at (2,4).

C is the midpoint of the chord AB.

Now,

The coordinates of C = (x, y).

x = (-6 + 2) / 2 = -4/2 = -2

y = (10 + 14) / 2 = 24/2 = 12

(x, y ) = (-2, 12)

The relationship between chord AB and segment OC.

The segment OC is perpendicular to the chord AB.

Thus,

The coordinates of C is (-2, 12)

The relationship between segment OC and chord AB is that segment OC is perpendicular to chord AB.

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The solutions for the given equation is x=0, x=-4 and x=3.

The given functions are f(x)=2x³+9x²+13x+12 and g(x)=3x³+10x²+x+8.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Now, f(x)-g(x)

= 2x³+9x²+13x+12-(3x³+10x²+x+8)

= 2x³+9x²+13x+12-3x³-10x²-x-8

= -x³-x²+12x+4

Graph the cubic using its end behavior and a few selected points.

Rises to the left and falls to the right

Plot (-2, -16), (-1, -8), (0, 4), (1, 14) and (2, 16)

Given f(x)-g(x)=4

-x³-x²+12x+4=4

⇒ -x³-x²+12x=0

⇒ -x(x²+x-12)=0

⇒ x=0 and x²+x-12=0

⇒ x=0 and x²+4x-3x-12=0

⇒ (x+4)(x-3)=0

⇒ x=0, x=-4 and x=3

Therefore, the solutions for the given equation is x=0, x=-4 and x=3.

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Answer:

To find the value of the quartiles, we need to first find the median of the data set. The median is the middle value of the data set, or the value that separates the lower half of the data from the upper half. In this data set, the median is 2.5, as it is the middle value when the data is arranged in ascending order.

Once we have the median, we can find the first and third quartiles. The first quartile, also known as Q1, is the median of the lower half of the data set, and the third quartile, also known as Q3, is the median of the upper half of the data set. In this data set, the lower half of the data is {1.3, 1.5, 1.7, 2, 2.5}, and the upper half of the data is {2.7, 2.9, 3, 3.1}. The median of the lower half is 1.7, and the median of the upper half is 2.9.

Therefore, the value of the quartiles is Q1 = 1.7, Q2 = 2.5, and Q3 = 2.9.

Option C, Q1 = 1.7; Q2 = 2.5; Q3 = 2.9, is the correct answer.

Step-by-step explanation:

Answer:

2.95

Step-by-step explanation:

The statement that is true about the self-serve frozen yogurt store is;

Option C: The yogurt sales had a decreasing trend in the last four months of 2011

From the attached file, we see a pie chart, a graph and a table.

Now, let us access the given options;

a) The percentage that prefer chocolate = 38%

Percentage that prefer vanilla and strawberry combined = 22% + 30% = 52%.

Thus, the given statement is wrong

b) From the graph curve, we see that;

Number of units sold in November = 3000 units

Number of units sold in August = 6000 units

Difference is 3000 units and not 4000 units and so the statement is wrong.

c) We see that for the last four months the curve showed a decreasing slope which means a decreasing trend of units sold.

d) This is not correct because the median number of ounces sold from 3 to 4pm was not more than the median number of ounces sold from 7 to 8pm on the stem leaf plot.

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Step-by-step explanation: When you divide the 2 by 9, you get like 0.222222 (and it repeats forever), then since the 2 is less than 5, you round down, so it would be 0.22 after rounding. I hoped this helped!