To use the law of sines, which of the following statements must be true?

A. At least one side length and opposite angle pair must be known.
B. At least two angles must be known.
C. The triangle must be a right triangle.
D. All three side lengths must be known.

Answer:

See below

Step-by-step explanation:

Answer

Denomination

10              5             1           0.75      Change

5                0             0            0            0.25

4                 1              4          0.75

These are the only 2 ways I see of paying the parking pass. The tens can't drop down to 3 because the rest will never add up to 19.95

The opposite of 0 is 0, the opposite of 7 is -7 and the opposite of 6 is -6.

If we consider a number x, then the opposite of the number x will be equal to -x. In a number line the opposite of a number lying on the positive side always lies on the negative side of number line. Also, the opposite of a number -x is the x that is the number itself. It is given in the question that we need to find opposite of 0, 7 and 6.

Let x = 0, opposite of x is -x.

=> -x = -0

=> -x = 0

Now, let x = 7, opposite of x is -x

=> -x = -7

Now, let x = 6, opposite of x is -x

=>-x = -6

Thus, the opposite of the numbers 0, 7 and 6 are 0, -7 and -6 respectively.

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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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3842 and 2642 are the two numbers.

What is linear equations?
Linear equations are a subset of first order equations. One homogeneous variable of degree one constitutes a linear equation in one variable (i.e., only one variable). A linear equation could contain multiple variables. When a linear equation comprises two variables, for instance, linear equations in two variables are utilized. A mathematical statement known as an equation contains an algebraic expression and the equal symbol (=). It is the equation for a straight line. The equation is shown to be valid when values are substituted for the unknown values in the solutions of linear equations. When there is just one variable, there is just one answer.

How to Solve?
Solving a linear equation involves determining the answer to a linear equation with one, two, three, or more variables. The answer to a linear equation is the value or values of the variable(s) that are part of the equation. There are six main ways to resolve linear equations. For the purpose of solving linear equations, these methods include the Graphical Method, Elimination Method, Substitution Method, Cross Multiplication Method, Matrix Method, and Determinants Method.

Let the greater of the two numbers be "x" and the smaller one be "y".
Given, x - y = 1200 --(i) & x + y = 6484 --(ii)
Adding (i) and (ii), we get, 2x = 7684 ⇒ x = 3842
Subtracting (i) from (ii), we get, 2y = 5284 ⇒ y = 2642
Thus, the greater number of the two numbers is 3842 and the smaller number is 2641.

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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! :)

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

Answer: [tex]5d^3 -17cd^2 -2c^2 d+8c^3[/tex]

Step-by-step explanation:

Expanding the parentheses,

[tex]8c^3 +c^2 d-9cd^2 +5d^3 -3cd^2 d-8cd^2[/tex]

Combining like terms yields [tex]5d^3 -17cd^2 -2c^2 d+8c^3[/tex].

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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From the diagram

Final answer = 3.124m

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:

DONT WORRY ITS FIFTY PERCENT

INFORMATION:

We have the next subtraction

And we must solve it

STEP BY STEP EXPLANATION:

To solve a subtraction of two expressions, we must multiply the second expression by -1 and then add up the first expression and the result of the multiplication.

1. Multiply the second expression by -1

2. Add up the first expression and the result of the multiplication. We must add similar terms

Finally, the result of the subtraction is 2y = 14

ANSWER:

aA. 2y = 14

If Jacob ran 10 miles in 80 minutes at that he will run the distance of 18.75 miles in [tex]2\frac{1}{2}[/tex] hours

Number of miles that Jacob will run in 80 minutes = 10 miles

Number of miles that Jacob will run in 1 minutes = Number of miles that Jacob will run in 80 minutes/ 80

= 10/80

= 0.125 miles

We know,

1 hour = 60 minutes

[tex]2\frac{1}{2}[/tex] hours = 2.5×60

= 150 minutes

Number of of miles that Jacob will run in 150 minutes = Number of miles that Jacob will run in 1 minutes × 150

= 0.125×150

= 18.75 miles

Hence, if Jacob ran 10 miles in 80 minutes at that he will run the distance of 18.75 miles in [tex]2\frac{1}{2}[/tex] hours .

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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]

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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The equation of the line will be y = -2x + 3.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

Given that the equation of the line that passes through the points (0,3) and (2,-1).

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

First calculate the slope of the line:-

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( -1 - 3 ) / ( 2 - 0 )

Slope = -2

The y-intercept will be:-

y = mx + c

3 = 0 + c

c = 3

Equation of the line:-

y = mx + c

y = -2x + 3

Therefore, the equation of the line will be y = -2x + 3.

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Using the similar triangle principle, the height of Dixon in feet is 6 feet.

Ariadne's shadow is 15 feet long and Dixon's shadow is 18 feet long.

Ariadne is 5 feet tall.

The height of Dixon can be found using similar triangle principle.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

Therefore, using the similar triangle theory,

Let

x = height of Dixon

Hence,

shadow length of  Ariadne / Ariadne height = Dixon shadow length / Dixon height

shadow length of  Ariadne = 15 ft

Ariadne height  = 5 feet

Dixon shadow length = 18 feet

15 / 5 = 18 / x

cross multiply

15 × x = 18 × 5

15x = 90

divide both sides by 15

15x / 15 = 90 / 15

x = 6 ft

Therefore, Dixon height is 6 feet.

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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!!

The volume of the figure that is composed of two rectangular prisms is: 146 cubic in.

The volume of a rectangular prism = (length)(width)(height).

The figure can be decomposed into two rectangular prisms. Find the volume of each of the prisms.

Volume of rectangular prism 1:

Length of the prism = 8 in.

Width of the prism = 7 in.

Height of the prism = 1 in.

Volume of rectangular prism 1 = (8)(7)(1) = 56 in.³

Volume of rectangular prism 2:

Length of the prism = 10 in.

Width of the prism = 9 in.

Height of the prism = 1 in.

Volume of rectangular prism 1 = (10)(9)(1) = 90 in.³

Volume of the figure = 90 + 56 = 146 cubic in.

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Answer:

600

Step-by-step explanation:

[tex]R(1)=400 \\ \\ R(2)=1000 \\ \\ R(2)-R(1)=600[/tex]

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:

1 is the awnsewer

Step-by-step explanation:

1

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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EXPLANATION

The first equation is a line with the following slope-intercept form:

Subtracting -4x to both sides:

Dividing both sides by 4:

Simplifying:

The slope is -1 and the y-intercept is -2

Applying the same reasoning to the second equation we get:

3

Now, we can write and graph both linear equation

Answer:

Slope-intercept form:  y = mx + b

(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)

y = 1.5x - 7            m = 1.5     b = -7

(y = (1.5)x + (-7) ----> y = 1.5x - 7)

y = -1.5x - 4         m = -1.5      b = -4

y = -3x + 4           m = -3       b = 4

y = 3x          m = 3        b = 0

y = 7        m = 0     b = 7

(y = (0)x + 7  ---> y = 7)

Step-by-step explanation:

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.

Answer:

B

Step-by-step explanation:

using the rule of radicals

• [tex]\sqrt[n]{x}[/tex] ÷ [tex]\sqrt[n]{y}[/tex] = [tex]\sqrt[n]{\frac{x}{y} }[/tex], then

32[tex]\sqrt[8]{18y}[/tex] ÷ 8[tex]\sqrt[8]{3y}[/tex]

= [tex]\frac{32}{8}[/tex] ×[tex]\sqrt[8]{\frac{18y}{3y} }[/tex] ( cancel 18y and 3y by 3y )

= 4 × [tex]\sqrt[8]{6}[/tex]

= 4[tex]\sqrt[8]{6}[/tex]