Lesson 17

Using the info given, solve for the missing value of the right triangle. Round each angle to the nearest degree, each length to the nearest tenth, & each trigonometric value to four decimal places, if necessary.
Hypotenuse = 14.5 meters
Opposite side = 6.3 meters
θ = ?

Answer:

Step-by-step explanation:

Isolate by the x from one side of the equation.

|x-3|=5

x-3=-5 and x-3=5

1. x-3=-5

Add 3 from both sides.

x-3+3=-5+3

Solve.

-5+3=(-2)

x=-2

2. x-3=5

Add 3 from both sides.

x-3+3=5+3

Solve.

5+3=8

x=8

Therefore, the correct answer is x=-2 or x=8.

By solving system of linear equation we get Cost for 1 cheeseburger $5 and 1 cups of lemonade $2

A system of linear equations is a collection of two or more linear equations that have the same variables. A linear equation is an equation in which the highest power of the variable is 1. In other words, the equation is a straight line when graphed.

Here is an example of a system of linear equations:

3x + 2y = 19

2x + 4y = 18

This is a system of equations problem, where we can use the information provided to set up two equations and then solve for the unknown variables. Let x be the cost of one cheeseburger and y be the cost of one cup of lemonade.

From the information provided, we know that:

3x + 2y = 19 (the cost of 3 cheeseburgers and 2 cups of lemonade is $19)

2x + 4y = 18 (the cost of 2 cheeseburgers and 4 cups of lemonade is $18)

To find the cost of one cheeseburger and one cup of lemonade, we can solve this system of equations. One way to do this is by substitution.

3x + 2y = 19

we get

[tex]x=\frac{19-2y}{3}[/tex]

substituting x in equation 2x+4y=18

we get

 [tex]2(\frac{19-2y}{3})+4y=18[/tex]

[tex]38 - 4y + 12y = 54\\8y = 16\\y = 2[/tex]

substituting y in equation 3x+2y=19

[tex]3x+2(2)=19\\3x=19-4\\3x=15\\x=5[/tex]

The cost of one cup of lemonade is $2

The cost of one cheeseburger is $5

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Answer:

Other words for subtraction:

taking away

withdrawal

abstraction

removal

discounting

Step-by-step explanation:

The total number of muffins in 4 boxes by the arithmetic equation is (4 × 10) + (4 x 3) = 52.

The series where the common difference between any two next words stays constant is known as an arithmetic sequence. Let's review what a sequence is. A collection of numbers that follow a pattern is called a sequence.

Every term in an arithmetic sequence is created by adding a specified number (either positive, negative, or zero) to the term before it.

the number of boxes of muffins is 4

The muffins in each box is 13

so the total number of muffins in 4 boxes is 4 x 13

⇒ 4 x (10 + 3)

⇒ (4 x 10) + (4 x 3) = 52

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Answer: x>18.64

Step-by-step explanation:

x+6.56-6.56>25.2-6.56

x>18.64

Answer:

1 / 27 cm^3

Step-by-step explanation:

Given,

side = 1 / 3 cm

To find : Volume ( cube ) = ?

Formula : -

Volume ( cube ) = ( side )^3

Volume ( cube )

= ( 1 / 3 )^3

= 1^3 / 3^3

= 1 / 27

= 1 / 27 cm^3

The required graph of the function of h(x) is shown, where h(x) =  |x| + |x + 2|.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
In the graph, functions f and g are absolute functions,
f = |x|
g = |x + 2|

So,
h(x) = f + g

Now substitue the functions,

h(x) = |x| + |x + 2|

Thus, the required graph of the function of h(x) is shown.

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Answer:

there is not enough info but i think it would be (5,11)

Step-by-step explanation:

divide

Answer:

[tex]y=\dfrac{11}{4}x[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]

Choose two (x, y) points from the given table:

Substitute them into the slope formula:

[tex]\implies \dfrac{22-11}{8-4}=\dfrac{11}{4}[/tex]

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

Substitute point (4, 11) and the found slope into the point-slope formula and rearrange to slope-intercept form:

[tex]\implies y-11=\dfrac{11}{4}(x-4)[/tex]

[tex]\implies y-11=\dfrac{11}{4}x-11[/tex]

[tex]\implies y=\dfrac{11}{4}x[/tex]

The weight of the jar after solving equation simultaneously is w=0.

A set of two or more first-degree equations with two or more connected unknowns is known as a system of linear equations.

A system of equations is solved by determining the value of each unknown until the system's equations are all satisfied. That is, it is necessary to find the values of the unknowns so that, when substituted, they will produce the suggested solution in both equations.

j+w=1.5

2j+w=3

Simultaneously solving gives

w=0

the weight of jar is 0.

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Answer:

a. 12.50%

b. 87.50%

c. 37.50%

d. 12.50%

Step-by-step explanation:

The quadratic equation that models the situation is

h(t) = - 4.9t² + 60.

A quadratic equation is a equation that is of the form -

y = f{x} = ax² + bx + c

Given is that the function h(t) = - 4.9t² + h₀ gives the height (h), in meters, of an object (t) secs after it falls from an initial height h₀. The table shows data for a pebble that fell from a cliff as -

TIME (t)     HEIGHT (h)

1                   55.1

2                  40.4

3                  15.9

The given function is -

h(t) = - 4.9t² + h₀

For the point (1, 55.1), we can write as follows -

55.1 = - 4.9 x 1 x 1 + h₀

h₀ = 55.1 + 4.9

h₀ = 60

So, we can write the function as -

h(t) = - 4.9t² + 60

Therefore, the quadratic equation that models the situation is

h(t) = - 4.9t² + 60.

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Answer:

c on edge

3.5

Step-by-step explanation:

Answer: 3.75 ft

Step-by-step explanation:

30/8=3.75

So since area is A= L*W

8*3.75=30 ft2

Answer:

[tex]\implies \boxed{\red{\sf ( x +1)^2 = \dfrac{1}{4}}} [/tex]

Step-by-step explanation:

Given :-

And we need to write the equation by completing the square. Here's the step by step explanation .

Step 1: Make the coefficient of x² as 1 :-

[tex]\implies \dfrac{4x^2}{4} + \dfrac{8x}{4} + \dfrac{3 }{4}= 0 [/tex]

Step 2: Rewrite the equation :-

[tex]\implies x^2 + 2x +\dfrac{3}{4}= 0 [/tex]

Step 3: Add 1² to both sides :-

[tex]\implies x^2 + 2x + 1^2+\dfrac{3}{4}= 0 + 1^2 [/tex]

Step 4: Rewriting in whole square form:-

[tex]\implies ( x +1)^2 = 1 - \dfrac{3}{4} [/tex]

Step 5: Simplify the RHS :-

[tex]\implies ( x +1)^2 = \dfrac{4- 3}{4} [/tex]

Step 6: The required form of equⁿ :-

[tex]\implies ( x +1)^2 = \dfrac{1}{4} [/tex]

Hence the equation by rewriting it by completing the square is ( x + 1)² = 1/4 .

Answer:

Question 1: 29

Question 2: 50

Question 3: AD≅BC

Step-by-step explanation:

question 1: Since it's a parallelogram opposite sides are equal.

4x+5=5x-1   add one to both sides

4x+6 =5x subtract 4x from both sides

6 = x

So AD is equal to 5(6) - 1 = 30-1 =  29=AD

Question 2: Since diagonals in a parallelogram bisect each other AE = EC

So...

5x+5 = 8x- 7 add 7 to both sides

5x+12 = 8x subtract 5x from both sides

12=3x divide both sides by 3

4=x

AC= 5(4) + 5 + 8(4) - 7

AC= 20 + 5 + 32 - 7

AC= 50

Question 3: Lines can only be congruent, represented by ≅, not equal which is represented by =. Values can be equal.

By using the elimination method you get the answer  line AD ≅ line BC

Answer:

-9/10

Step-by-step explanation:

The slope of line C is [tex]m=\frac{8-(-2)}{3-(-6)}=\frac{10}{9}[/tex].

The slope of any line perpendicular to line C is the negative (opposite) reciprocal of this slope.

The slope of line F is [tex]-\frac{9}{10}[/tex].

Therefore , the solution to the given problem is the equation of the midline is: y = M+m /2 .

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

Here,

The midline equation is y = M+m /2

when a function has: o a max M AND a min m or o (if it does not have extrema) a bound above M and a bound below m, where M is the minimum bound above and m is the maximum bound below.

When one of the following conditions is true for a function, even though it has a bound below, there is no midline (even if it has a bound above)

It is solely constrained from above (or below)

Any line is midline if a function has the values (-∞, +∞)

Therefore , the solution to the given problem is the equation of the midline is: y = M+m /2 .

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Answer:

1. The rational, game-theoretic solution to this game is:

H. The proposer suggests a 50/50 division (so each player would get $30), and the responder accepts.

2.  No. When this game is played with real people, the result does not typically match the game-theory prediction discussed in Part 1.

Step-by-step explanation:

Players in a game respond with different strategies, which are usually unknown to the second player.  While people are expected to act rationally, most times, they do not.  They are propelled by different rationality and preferences.  Therefore, players' game strategies are unpredictable.

Answer:

[tex]1\frac{7}{8}[/tex]

Step-by-step explanation:

Answer:

1.875

Step-by-step explanation:

Convert the whole number 3, and you get 15/4

complete the process, and you get 1.875 aka 1 7/8

Answer:

yup soooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo

Step-by-step explanation:

well this is how i do it. add everything then divide by 2 becuase triangle is half of square

The total displacement made by her to go from home to the school is given by the sum of the distances of P to Q, Q to R and then R to S.

The total displacement is obtained as the distance that she walks to go to the school from her home.

The check-points that she passes to go to the school are given as follows:

Hence the total displacement is given by the sum of each of these distances.

These distances are calculated using the formula for the distance between two points, given as follows:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

In which [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of each point.

The problem is incomplete, hence the answer is given in general terms.

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Answer:

0.22

Step-by-step explanation:

Since 5 rounds up, it would be 0.22

Answer:

0.22 Is the answer.

I wish you luck on your assignments.

If the probability of s1 = .6 the value above node degree 4 will be 320, as determined by the solution.

The area of mathematics known as probability deals with numerical descriptions about how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

S1 probability = 0.6

F's likelihood is 0.40.

If the probability of S1 is given a value of 0.6, then

Probability of S2 then equals 0.4.

Using the table equation's payoff values as an exception.

EV=Σ

Each decision's expected value is calculated.

EV(Node 8) = 0.6 * 100 + 0.4 * 300

= 180

EV(Node 9) = 0.6 * 400 + 0.4 * 200= 320

We chose the best value for node 4 from nodes 8 and 9.

The ideal option for node 9 is the line complicated branch with EV(node 8) = 180.

The ideal anticipated value is determined to be 320.

Node 4's EV is 320.

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Answer:

Step-by-step explanation:

12 divided by four plus 2 x 6+4

assuming that the question is:

12 : 4 + 2 x 6 + 4 =

3 + 12 + 4 =                     (remember PEMDAS)

19

Answer:

4

Step-by-step explanation:

a p e x  its correct

Answer:

It would be 1%

Step-by-step explanation:

First of all, note that any of the cans with the batch have the same chance at being defective, so ingore that. However, note the chance that each one is defective:

10%

So if you picked up any can, it would have a 10% chance of being defective. With this, by picking up two cans, you would do:

0.1 * 0.1 = 0.01

To find the chance of both cans being defective, being 1% for both of the selected cans being defective.

Answer:

I think it's 28 square units

A'(-2, -3) would result if A (2, -3) was reflected over the x axis. Point (2,3)'s representation under the x-axis is (2,-3). from the y-axis P image (-a,b).

Changing the sign of the value on the opposite axis, in this case the y-value, is all that is required to reflect a point such as (-2,3) across the x-axis in a question. As a result, this location has a y-value of 3. A positive number, this. A negative sign produces a result of -3.

While the Y coordinate remains the same when you reflect across the Y-axis, the X coordinate changes sign. Determining the reflection of (2, 3) across the Y-axis is therefore (-2, 3). The Y-coordinate of each point must be negative while reflecting across the X axis, but the X value must remain constant.

Therefore the correct answer is option a ) A'(-2, -3)

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Answer:

[tex]25 + 12x + 14 + 12x = 159 \\ 39 + 24x = 159 \\ 24x = 120 \\ x = 5[/tex]

they will earn a combined $ 159 in 5 days

I think that it is the last one

Hope this helps

Answer: D

Step-by-step explanation: