Find the length of side x in simplest radical form with a rational denominator

Given:

In a quadrilatral three angle are

Required:

Remaining angle i.e.

Explanation:

In a quadrilatral ABCD

Final Answer

Remaining Angle= 102

Answer:

102

Step-by-step explanation:

If you add all of the angles (175+29+54) it gives you 258. As you may already know, a quadrilateral's angles have to all equal 360 combined. When you subtract 360-258, you get 102. Hope this helped! :)

The Large Cardinal Project is a field of set theory.

Set theory deals with basic projects. Giant Numbers card attributes are a subset of Infinite Numbers card numbers. The most active set theorists believe that the most important fundamental axioms studied today are compatible with ZFC. Steele and Leber used a giant map to prove the left finite algebraic pyramid theorem (a(bc) = (ab)(ac)). The idea is to introduce the great cardinals to thinkers from the very beginning. It was a little bit good. By definition, a great cardinal is a hypothesis. This aims to show how to establish some basic facts about big numbers by generalizing the combinatorial features of natural numbers to sets of seconds. It is an investigation of important fundamental positions and the axioms of set theory. Numeric Tables and Sequences Overview Aggregates, classes, and numeric tags are not allowed. Some properties of natural numbers Uncountable generalizations.

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Given:

Use the formula:

solve the equation :

Answer:

[tex]\textsf{Exact form}: \quad x=-7 +\sqrt{49+e^3}[/tex]

[tex]\textsf{Decimal form}: \quad x=1.312\; \sf (3\:d.p.)[/tex]

Step-by-step explanation:

Given equation:

[tex]\ln x + \ln (x+14)=3[/tex]

[tex]\textsf{Apply the product law} \quad \ln x + \ln y=\ln xy:[/tex]

[tex]\implies \ln (x(x+14))=3[/tex]

[tex]\implies \ln (x^2+14x)=3[/tex]

[tex]\textsf{Apply the log law} \quad e^{\ln x}=x:[/tex]

[tex]\implies e^{\ln (x^2+14x)}=e^3[/tex]

[tex]\implies x^2+14x=e^3[/tex]

Subtract e³ from both sides to form a quadratic equation:

[tex]\implies x^2+14x-e^3=e^3-e^3[/tex]

[tex]\implies x^2+14x-e^3=0[/tex]

Quadratic Formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

Therefore:

Substitute these values into the quadratic formula and solve for x:

[tex]\implies x=\dfrac{-14 \pm \sqrt{14^2-4(1)(-e^3)} }{2(1)}[/tex]

[tex]\implies x=\dfrac{-14 \pm \sqrt{196+4e^3} }{2}[/tex]

[tex]\implies x=\dfrac{-14 \pm \sqrt{4(49+e^3)} }{2}[/tex]

[tex]\implies x=\dfrac{-14 \pm \sqrt{4}\sqrt{49+e^3} }{2}[/tex]

[tex]\implies x=\dfrac{-14 \pm 2\sqrt{49+e^3} }{2}[/tex]

[tex]\implies x=-7 \pm \sqrt{49+e^3}[/tex]

Solutions:

[tex]x=-7 +\sqrt{49+e^3}, \quad x=-7 -\sqrt{49+e^3}[/tex]

Decimal form:

[tex]x= 1.312, \quad x=-15.312[/tex]

As logs of negative numbers cannot be taken, the only solution is:

[tex]x=-7 +\sqrt{49+e^3}\\\\x=1.312\;\sf (3\;d.p.)[/tex]

Answer:

C

Step-by-step explanation:

Let f(y)=x.

[tex]x=\frac{1}{3}-\frac{1}{21}y \\ \\ x-\frac{1}{3}=-\frac{1}{21}y \\ \\ y=-21x+7 \\ \\ f^{-1}(x)=-21x+7[/tex]

Object dilation for image 1 is 30 cm, image 2 is 21 cm, image 3 is 8 cm, and image 4 is 2 cm.

Dilation is a conversion, which is utilized to resize the thing. Dilation is operated to create things bigger or shorter.

For image 1, Dilation for the given side of polygon A is 10 × 3 = 30cm for polygon B.

Therefore, the dilation for the unknown side of polygon B would be 15 × 3 = 45cm.

For image 2, The dilation for the given side of triangle A is 7 × 3 = 21cm for triangle B.

Therefore, the dilation for the unknown side of triangle B would be 18 ÷ 3 = 6cm for triangle A.

For image 3, Dilation for the given side of triangle A is 12 × 4 = 48cm.

Therefore, the dilation for the unknown sides would be 32 ÷ 4 = 8cm for the left side of triangle A and 8 × 4 = 24 for the right side of triangle B.

For image 4, The dilation for the given side of square A is 2 × 2 = 4cm in square B.

Therefore, the dilation for the unknown side of square A would be 4 ÷ 2 = 2cm for square A.

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The given limit has its value as 2/3.

The most important calculus rule is known as the L' Hospital's Rule (L'Hôpital's rule). With the help of derivatives, this rule assesses limits involving indeterminate forms. The L'Hospital rule is a general method for evaluating indeterminate forms like∞ / ∞  or /. Calculus derivatives' limits for indeterminate forms are determined using L'Hospital's rule. The L Hospital rule can be applied numerous times.

This guideline recommends differentiating the numerator and denominator by an equal number of times until the confusing or problematic phrase is eliminated for easy understanding.

Since the limit is of the 0/0 type when both the numerator and denominator have h=0, the L Hospital rule can be applied in this situation.

Once the numerator has been differentiated, we obtain Numerator = 2((1/3) + h)

Once the denominator has been differentiated, we obtain Denominator = 1.

As a result of the denominator's complicated factor being eliminated, the limit can now be set.

As a result, the limit at h = 0 has a value of = 2((1/3) + 0)]/1 = 2/3.

As a result, when h=0, the value of the stated limit is 2/3.

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We can see that point S is at (2,4), therefore we have to move the point five units down in order to place the point S at (2,-1). The answer would be option C. 5 units.

Answer:

11,280

Step-by-step explanation:

so first you write the equation 97*57. then you multiply them, ( 7*7=49; 5*7= 35, now 9*7= 63; 5*9= 45) and the answer is 11,280

I might be wrong in my calculations because the calculator says the answer is 5,529 so yeah the answer is either 11,280 or 5,529.

Hope this helps

The maximum value of P = 11.

Given: P = -x + 6y

In this question we have to first solve the given system of equations.

Ignore the greater or lesser than sign that is:

y = -2x+ 4 -------- 1

And y = x + 1 ---------  2

On solving these two equations we get;

0= -3x + 3

⇒ -3x = -3

⇒ x= 1

Substituting the value of x in equation 2 we get

y = x+ 1

= 1 + 1 = 2

Thus y = 2 and x = 1

So on putting these values in P = -x + 6y we get

P = - 1 + 6× 2

P = - 1 + 12 = 11

Therefore P= 11.

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Answer:

DONT WORRY ITS FIFTY PERCENT

Answer:

1) 81/ 64

2)DNE(undefined), and

3)529/64

Step-by-step explanation:

1) 8√x + 7 = 16

8√x = 16 - 7 = 9

√x  = 9/8

x = (9/8 )² =  81/ 64

2) √7x+4−3=0

√7x + 1 = 0

√7x =  -1

as the square root is always positive, it is impossible.

3)  8√5x−7=16

8√5x = 16 + 7 = 23

√5x = 23/8

5x = (23/8)²  =  529/64

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From the diagram

Final answer = 3.124m

The slope of a straight line is given by the following expression:

By looking at the graph we have two locate two pairs of coordinates: Coordinate 1 (2,0) Coordinate 2 (-4,0).

Now we replace on the slope formula, having:

Pair of coordinates, coordinate 1 (2,0) coordinate 2 (3,2)

Three statements are correct and ∠FDE and ∠EDC are supplementary angles .

What is an example of a supplementary angle?

A) True, ∠BDF and ∠FDE are making linear pair .

C) True, ∠FDE and ∠EDC are supplementary angles .

D) True, ∠ABG and ∠GBD are complementary angles.

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Answer:

Between 30 and 33 mph or, simply

Range: [30,33]

Step-by-step explanation:

A Range is all possible values of a certain variable or piece of information commonly notated by a minimum and maximum. In this example, our variable is the speed traveled by drivers in a road. We are provided a minimum of 30 mph as this is the speed limit, and told that drivers may speed up to a maximum of 3 mph faster ( or 33 mph).

Therefore, our minimum would be 30, maximum would be 33, and Range would be [30, 33].

Brackets are used here because both our minimum and maximum values are included in the range.

HOPE THIS HELPS!!

Explanations:

8 - ( -3d + 2)

Open up the brackets:

The negative (-) sign outside the bracket will multiply both -3d and 2 one by one.

The equation then becomes:

8 + 3d - 2

Collect like terms:

8 and 2 are similar, they can come together. The equation becomes

8 - 2 + 3d

6 + 3d

Note that 3 is a common factor of 6 and 3, the equation finally becomes:

3 ( 2 + d)

nswer

The side of EFGH that corresponds with CD is GH.

xplanation

One of the key points for two figures to be similar is that the angles are the same.

Since parallelograms have opposite angles equal, and adjacent angles sum up to give 180 degrees. We know that ABC

Angle = 180 - 523 = 127

And this makes the similarity makes the order of similarity here to be

BCD = EFGH

o,

dD = GH

Hope this Helps!!!

Answer:-15y+-16z+4

Step-by-step explanation:

-y-16y+9z-25z+4

-15y+-16z+4

Answer:

corresponding!!!!!!

Step-by-step explanation:

Corresponding angle is an angle that are one the same side of the transversal lines :))

Hope this helps!!!

The value of a = -10, b = -0.2, c = 0.25

What is an equation?

An equation is a formula that is used to express the equality of two expressions with the help of = sign. In other words, it is an mathematic statement that made two expressions equal. There are different type of equation and we are here dealing with linear equation.

Given equation are,

a) 1/5a = -2

cross multiplying.

a = -2(5)

a = -10

b) 8+b = 7.8

Subtracting,

b = 7.8 - 8

b = 0.2

c) -0,5 = -2c

Dividing,

c = -0.5/-2

c = 0.25

Hence the solution of each equation, is solved above.

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The value of h is 13.3 cm

Let the triangle be ABC where

AB = 18 cm

AC = h cm

∠ABC = 48°

Since, ∠ACB = 90°, therefore the given triangle is a right angle triangle.

We know that

Sinθ = Perpendicular / Hypotenuse

Put θ = 48, we get

Sin 48 = [tex]\frac{h}{18}[/tex]

The value of Sin 48 is 0.74

0.74 × 18 = h

h = 13.3 cm

Therefore the value of h is 13.3 cm

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Answer: D = 39, D = -12 + 51

Step-by-step explanation:

1) Write an equation based off the prompt

D = -12(Spent cash) + 51(Remaining cash)

2) Solve D

D = 39

Explanation

We are given the following:

We are required to determine the converse, inverse, and contrapositive statements of a conditional statement and also determine whether the statement is true or false.

This is achieved thus:

We know that if P and Q are two simple statements, then

Implication (Conditional): P → Q

Converse: Q → P

Inverse: ~ P → ~ Q

Contrapositive: ~ Q → ~ P

We also know that an implication is false if the antecedent is true and the consequent is false.

Therefore, we have:

ive n statement: I

Let P: A toy block is a clover

Let Q: A toy block is red.

The given statement is true. This is because both statements are true.

Converse: If a toy block is red, then the toy block is a clover.

This statement is false. This is because it is not true for all cases.

Inverse: If a toy block is not a clover, then the toy block is not red.

This statement is true.

Contrapositive: If a toy block is not red, then the toy block is not a clover.

This statement is true.

Hence, the answers are:

His answer is incorrect

The correct answer is:

This is the square of (2x - 3)

Given (2x - 3)

The square of this is:

His answer of 4x² - 9 is incorrect.

A) none of these

B) only mean because if we replace 32 by 16 sum will decrease and so mean will decrease

C) both mean and median because when we remove some value os starting total sum will decrease and hence mean decrease

median will change because after remove some values total number will decrease and hence value will change

d)Negative skewed

Measures of central tendency are the values that characterize a data set by indicating the data's central location. Mean, Median, and Mode are the three primary metrics for determining central tendency.Mean is the product of the sum of all observations and the total number of observations.

An ordered set's median is its middle or centre value.

The most frequent value in a data set is called the mode.

Given that :32, 38, 42, 42, 43, 44, 46, 46, 47, 47, 49, 49, 51, 51, 51, 51, 52, 53, 53, 53, 53, 53

32, 38, 42, 42, 43, 44, 46, 46, 47, 47, 49, 49, 51, 51, 51, 51, 52, 53, 53, 53, 53, 53

mean = [tex]\frac{sum of observation}{number of observation}[/tex]

mean = [tex]\frac{1046}{22}[/tex]

= 47.54

The median is calculated by sorting the scores into numerical order, dividing the total by two, rounding the result up to get the median position, or using an even number of scores, averaging the median position's value with the following position's value.

here n = 22 which is even

median =[tex]\frac{\frac{n}{2}term +(\frac{n}{2}+1 )term }{2}[/tex]

[tex]\frac{\frac{22}{2}term +(\frac{22}{2}+1 )term }{2}\\ = \frac{11 term + 12 term}{2}[/tex]

= 49

Organize the numbers in a set in whatever order—from lowest to highest or highest to lowest—and then tally the frequency with which each number appears in the group. The mode is the one that shows up most frequently.

mode = 53 as it is repeated more times.

A) none of these

B) only mean because if we replace 32 by 16 sum will decrease and so mean will decrease

C) both mean and median because when we remove some value os starting total sum will decrease and hence mean decrease

median will change because after remove some values total number will decrease and hence value will change

d)Negative skewed

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The expression equivalent to 3(−2.4s − 3.8) is -7.2s - 11.4

An expression is said to be algebraic if it contains integer variables, constants, and algebraic operations ( subtraction, addition, multiplication, exponentiation by an exponent that is a rational number and division )

By using multiplication we can see that the expression  3(−2.4s − 3.8) is equivalent to the expression -7.2s - 11.4.

Now let us solve the other problems.

1. total cost of 3 friends = 9.73 × 3 = 29.19

cost of jalapeno poppers = 29.19 - 19.95 = $ 9.24

2. The required expression is -6/7k -7 + 5 + 1/2k = 5 over 14 times k plus negative 2

4.The expression for the dessert is : 3(10.35) + d = 43.05; d = 12.00

5. Expression is equivalent to 3(−4.5b − 2.1) − (6b + 0.6) is −19.5b − 6.9

Hence the requires expression is given by -7.2s - 11.4

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The expression equivalent to 3(−2.4s − 3.8) is -7.2s - 11.4 might as well just answer thx for the points :)

The equation of line containing vertices (8,4) is y = 4.

Y = mx+b, where m is the slope and b is the y-intercept, is the formula for the slope-intercept form (the point where the line crosses the y-axis). Using y=mx+b to graph a line is typically simple. The standard form and the point-slope form are other formats for linear equations.

Equation of line in slope - intercept form is

y = mx + c

where m= slope

c = y - intercept

As it is given that equation of line is horizontal,

this implies

x = 0

y = m (0) + c

y = c

Now, the given coordinates are (8,4)

Slope of the equation equals 0 As the line is horizontal.

⇒ y = 0 (8) + 4

⇒ y = 4

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Answer:

45

Step-by-step explanation: