What are the potential solutions to the equation?

Answer:

The other two angles are 22° , 22°

Step-by-step explanation:

To find the other angles, we can use angle sum property of triangle.

      The given angle 136° cannot be base angles. Let the base angles be x.

x + x + 136 = 180°

   2x + 136 = 180°

Subtract 136 from both sides,

            2x = 180 - 136

            2x = 44°

Divide both sides by 2,

              x = 44 ÷ 2

                \(\sf \boxed{x = 22^\circ}\)

Answer:42

Step-by-step explanation:

\(\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=15\pi \end{cases}\implies 15\pi =2\pi r\implies \cfrac{15\pi }{2\pi }=r\implies \cfrac{15}{2}=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{15}{2} \end{cases}\implies A=\pi \left( \cfrac{15}{2} \right)^2\implies A=\cfrac{225\pi }{4}\implies A=56.25\pi\)

Answer:

The answer is 2

Step-by-step explanation:

2 x ? x 3 x 2 x 2 = 48

6 x 4 x ? = 48

24 x ? = 48

24 ÷ 24 x ? = 48 ÷ 24

? = 2

Answer:

x = 17

Step-by-step explanation:

Subtract 6x from both sides:

2x - 18 = 16

Add 18 on both sides to isolate the variable:

2x = 18 + 16

2x = 34

Divide by 2: x = 17

Answer:

LCL = 59.26 to two decimal places

Step-by-step explanation:

Here, we want to estimate the LCL of the population mean with 90% confidence

We proceed as follows;

Given alpha = 0.1, then Z(0.05)=1.645 (from standard normal table), s = 15

Mathematically;

LCL =x_bar -Z*s/√( n)= 62 - (1.645 * 15)/√81

LCL = 62- (24.675)/9 = 59.2583

LCL = 59.26 to two decimal places

The equations classified according to the number of solutions are given as follows:

We solve the equation, hence:

4(2z - 1) = 8z - 4

8z - 4 = 8z - 4

Equivalent, hence they have infinitely many solutions.

-2(3n - 4) = -6n - 4

-6n + 8 = -6n - 4

0 = -12, which is false, hence it has no solutions.

-3(3q + 4) = -6q + 12

-9q - 12 = -6q + 12

3q = -24

q = -8.

One solution.

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\(\text{One of the expressions can be the simplified version}\\\\\text{Simplify:}\\\\-f-5(2f-3)\\\\\text{Use the distributive property}\\\\-f-10f+15\\\\\text{Combine like terms}\\\\\boxed{-11f+15}\\\\\text{That expression is equivalent to the expression listed in the question}\)

Answer:

11f+5

Step-by-step explanation:

khan

Answer:

\(\sqrt[2]{3^7}\)

Step-by-step explanation:

\(\sqrt[2]{3^7}\)

The top number is the power and the bottom of the fraction is the root

This is the rectangular equation described by the parameter equation x = t1/3 and y = t – 4.

Elimination of the parameter means to rewrite the equations in terms of only x and y. To do this, substitute t from one equation into the other equation. Here, the two equations are:x = t1/3 and y = t – 4Substitute t from the first equation into the second equation:y = (x^3) – 4Now the equation is in terms of x and y only.

This is the rectangular equation described by the parameter equation x = t1/3 and y = t – 4.The rectangular equation, y = (x^3) – 4 can be plotted on a graph. It is a cubic equation. The graph will look like a curve that passes through the point (0, -4) and continues to move towards infinity. The graph will be symmetric to the origin because the equation involves an odd power of x.

If the equation involved an even power of x, the graph would be symmetric to the y-axis. The graph will never touch the x-axis or y-axis, it will only approach them.In conclusion, the rectangular equation y = (x^3) – 4 is derived from the two parameter equations, x = t1/3 and y = t – 4. The graph of this equation is a cubic curve that is symmetric to the origin. The curve passes through (0, -4) and approaches the x and y-axes but never touches them.

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The statement X = Y + Yxy is True.

The equation given is:

X = Y + Yxy

To find x = (X- Y) / Yy we have to substitute the value of x in X = Y + Yxy as

X = Y + Yxy

X = Y + Yy (X-Y) / Yy

To solve for x, we can rearrange the equation as:
X = Y +  X - Y

X = X

Thus, the statement is True.

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Ans4863

Step-by-step explanation:

Answer:

slope intercept form

Step-by-step explanation:

Answer:

Slope intercept form

m - slope

b - y intercept

Answer:

68% of the data points lie between 10 and 18.

Step-by-step explanation:

one standard deviation to left of mean = 14 - 4 =10

one standard deviation to right of mean = 14 + 4 = 18

68% of data is in this region.

so the answer is 68% of the data points lie between 10 and 18.

Answer:

24.5

Step-by-step explanation:

add all numbers together =245

divide by numbers in set of data (10)

Answer:

Hope I helped!~

Step-by-step explanation:

To find the equation of the line, we can use the slope-intercept form of the equation:

y = mx + b

where m is the slope of the line and b is the y-intercept.

Using the two data points given, we can calculate the slope:

m = (11.25 - 8.35) / (1995 - 1993) = 1.95

To find the y-intercept, we can use one of the data points:

8.35 = 1.95(1993) + b

b = -3884.65

So the equation of the line is:

y = 1.95x - 3884.65

To predict the price of a box of two pieces on July 1, 1999, we can substitute x = 6 (since 1999 is 6 years after 1993) into the equation:

y = 1.95(6) - 3884.65

y = 11.7 - 3884.65

y = -3872.95

This gives us a negative price, which obviously does not make sense. It is likely that the price of a box of two pieces was not linearly increasing during this time period, or that there were other factors influencing the price. Therefore, we cannot use this equation to accurately predict the price of a box of two pieces on July 1, 1999.

Answer:

Step-by-step explanation:

Let the initial salary be x.

Set equation and solve for x:

Answer:

The original salary is $11641.18.

Step-by-step explanation:

The equation will be,

→ x + (x × 2)/100 = 11874

Now the original salary will be,

→ x + (x × 2)/100 = 11874

→ x + 0.02x = 11874

→ 1.02x = 11874

→ x = 11874/1.02

→ x = 11641.1764706

→ [ x = 11641.18 ]

Hence, original salary is $11641.18.

Answer:

The equation for the line is y = 2/5x + 24/5

Step-by-step explanation:

If you need the exact points, go to m4thway and plug that equation in.

Answer:

Jordan, Its been 5 hours, whats the answer?

Step-by-step explanation:

There can be only 1 triangle formed by the given information.

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.

Given that, ABC can be formed if C=60∘, c=17√3 and a=34

Using the sine law for triangle,

A/sina = B/sinb = C/sinc

34/sina = 17√3/sin60°

⇒ sina = 90°

Since, The triangle ABC is a right triangle,

Hence, There can be only 1 triangle formed by the given information.

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Answer:

-x - 3y

Step-by-step explanation:

\(=2x-5y+7+3x+2y-4+2x-8x-3 \\ \\ =-x-3y \)

5 "Always." Consecutive angles of a rectangle are always congruent.

6 "Never." A parallelogram is not always a square.

7 "Sometimes." In a rhombus, the diagonals are always perpendicular bisectors of each other, but they are not always congruent.

8 "Always." A rectangle has congruent sides, but not necessarily all four sides.

9 Given: ABCD is a parallelogram

To prove: AABC = ACDA

Proof:

AB || DC (definition of parallelogram)

AD || BC (definition of parallelogram)

∠ABC = ∠CDA (alternate interior angles)

AC = AC (reflexive property)

∠BCA = ∠DAC (alternate interior angles)

Therefore, AABC = ACDA (ASA congruence theorem)

10 Given: TRAP is an isosceles trapezoid

To prove: AAPR ARTA

TR = AP (definition of isosceles trapezoid)

∠APT = ∠ATR (alternate interior angles)

∠PAR = ∠RTA (alternate interior angles)

∠PAR = ∠APT (angles at a point)

Therefore, AAPR ARTA (AA congruence theorem)

Consecutive angles of a rectangle are always congruent. This is a property of rectangles that is true for every rectangle.

A square is a specific type of parallelogram that has all four sides congruent and all four angles right angles.

A rectangle has two pairs of opposite sides that are congruent, but the adjacent sides may have different lengths. This is a defining characteristic of rectangles, and it is always true for every rectangle.

The ASA congruence theorem states that two triangles are congruent if two angles and the included side of one triangle are congruent to the two angles and the included side of the other triangle. In this case, ∠ABC and ∠CDA are congruent by (3), AC is congruent by (4), and ∠BCA and ∠DAC are congruent by (5). Therefore, AABC = ACDA by the ASA congruence theorem.

The AA congruence theorem states that two triangles are congruent if two angles of one triangle are congruent to two angles of the other triangle, and the side between those angles is congruent in both triangles

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Answer:

Se pueden hacer 5040 permutaciones con la palabra COLUMNA.

Explanation:

La palabara COLUMNA posee 7 letras, por lo que debemos hacer permutación sin repetición.

La formula es:

P_^{n}: n!

Donde n son todos los elementos.

The universal statement is ∀x ¬ P(x). The existential statement is ∃x ¬ P(x) and the existential statement in English is "there exists someone who is not good at sports".

In the universal statement, the negation symbol ¬ in front of the predicate P(x) means "not good at sports." So, ∀x ¬ P(x) can be read as "for all x in the universe of discourse, x is not good at sports."

In the existential statement, the negation symbol ¬ in front of the predicate P(x) means "not good at sports." So, ∃x ¬ P(x) can be read as "there exists x in the universe of discourse such that x is not good at sports."

Therefore, the statement "Not everyone is good at sports" can be represented in symbols as ∀x ¬ P(x) as a universal statement and as ∃x ¬ P(x) as an existential statement. The existential statement can be rephrased as "there exists someone who is not good at sports."

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The complete question is -

consider the following statement: Not everyone is good at sports. for the following questions, let the universe of discourse be the set of all people. P(x) be the predicate x is good at sports.

1. write the statement as a universal statement.

a. ∀x ¬ P(x)

b. ¬ ∀x ¬ P(x)

c. ¬  ∃x ¬ P(x)

d. ¬ ∀x(P(x))

2. write the statement as an existential statement.

a.  ∃x ¬ P(x)

b. ¬ ∃xP(x)

c. ¬ (∃xP(x))

d.  ∃xP(x)

3. write the existential statement in English.

a. there exists someone who is not good at sports

b. there exists someone who is good at sports

c. there does not exist someone who is good at sports

d. there does not exist someone who is not good at sports.

Answer:

y = 10

Step-by-step explanation:

2y+30 = 3y+20

3y-2y= 30-20

y = 10

Answer:

\((2y30) = ( 3y + 20)\)

so its 10 bc 30-20

The cosine value is given as follows:

\(\cos{\theta} = \frac{4\sqrt{23}}{23}\)

The tangent value is given as follows:

\(\tan{\theta} = -\frac{\sqrt{7}}{4}\)

First we must obtain the secant value, according to the identity presented as follows:

\(\sec^2{\theta} = 1 + \tan^{2}{\theta}\)

Replacing the tangent into the expression, we have that:

\(\sec^2{\theta} = 1 + \frac{7}{16}\)

\(\sec^2{\theta} = \frac{23}{16}\)

\(\sec{\theta} = \frac{\sqrt{23}}{4}\)

The secant is positive, as the angle is in the fourth quadrant, where the cosine is positive.

The cosine is then given as follows:

\(\cos{\theta} = \frac{1}{\sec{\theta}}\)

\(\cos{\theta} = \frac{4}{\sqrt{23}} \times \frac{\sqrt{23}}{\sqrt{23}}\)

\(\cos{\theta} = \frac{4\sqrt{23}}{23}\)

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Answer:

C=2.54i

Step-by-step explanation:

The dependent variable is the value that is affected when we change the independent variable—it depends on the independent variable. So, we write equations with the dependent variable by itself.

The phrase "given" can mean "depend on". For example, if we want to find x given y, then the value of xxx depends on the value of y. In other words, xxx would be the dependent variable, and y would be the independent variable.

Hint #22 / 3

Kingsley wants to write an equation he can use to convert any given length in inches to centimeters. This means that inches (i)left parenthesis, i, right parenthesis is the independent variable, and centimeters (c) parenthesis, c, right parenthesis is the dependent variable.

Kingsley should write his equation with the dependent variable ccc by itself.

Hint #33 / 3

Kingsley should write his equation as c=2.54ic=2.54ic, equals, 2, point, 54, i.

Kingsley must multiply the measure in centimeters by 1 / 2.54 to get a unit conversion equation in inches.

Kingsley knows the conversion rate between inches and centimeters and wants to derive a formula. Both the inch and the centimeter are length units and we can represent it by the following ratio:

y / x = 2.54         (1)

Where:

Then, we clear the variable x in (1) to find the unit conversion formula:

x = y / 2.54        (2)

Kingsley must multiply the measure in centimeters by 1 / 2.54 to get a unit conversion equation in inches.

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\( \sf \longrightarrow \: 5 \bigg( \: n - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{n}{1} - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10 \times n - 1 \times 1}{1 \times 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10n - 1}{ 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: \frac{50n - 5}{ 10} = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =1(10) \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =10 \\ \)

\( \sf \longrightarrow \: \: 100n - 10=10 \\ \)

\( \sf \longrightarrow \: \: 100n =10 + 10\\ \)

\( \sf \longrightarrow \: \: 100n =20\\ \)

\( \sf \longrightarrow \: \:n = \frac{2 \cancel{0}}{10 \cancel{0}} \\ \)

\( \sf \longrightarrow \: \:n = \frac{1}{5} \\ \)

Answer:-

To solve the equation \(\sf 5(n - \frac{1}{10}) = \frac{1}{2} \\\) for \(\sf n \\\), we can follow these steps:

Step 1: Distribute the 5 on the left side:

\(\sf 5n - \frac{1}{2} = \frac{1}{2} \\\)

Step 2: Add \(\sf \frac{1}{2} \\\) to both sides of the equation:

\(\sf 5n = \frac{1}{2} + \frac{1}{2} \\\)

\(\sf 5n = 1 \\\)

Step 3: Divide both sides of the equation by 5 to isolate \(\sf n \\\):

\(\sf \frac{5n}{5} = \frac{1}{5} \\\)

\(\sf n = \frac{1}{5} \\\)

Therefore, the solution to the equation \(\sf 5(n - \frac{1}{10})\ = \frac{1}{2} \\\) is \(\sf n = \frac{1}{5} \\\), which corresponds to option (d).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Option B) The statement does not make sense because the sum of the probabilities of Jonas winning and not winning the race must equal = 1

Since the above question says that the probability of Jonas winning the race is = 0.6

And the question says that the probability of Jonas losing the race is = 0.5

If we sum up the probabilities of winning and losing,

Probability = 0.4 + 0.5

= 0.9

Hence, the above situation is not possible because the probability must be = 1.

According to the phenomenon of Probability,

Let us consider two probabilities that are

The winning probability is given = x

The Losing probability is given =  y

So, x + y = 1 ( must be 1 )

Therefore, Option B) The statement does not make sense because the sum of the probabilities of Jonas winning and not winning the race must equal = 1

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Decide whether the following statement makes sense (or clearly true) or does not make sense (or is clearly false). Explain your reasoning. The probability that Jonas will win the race is 0.6 and the probability that he will not win is 0.5. Choose the correct answer below.

A. The statement makes sense because it is true that the probability of Jonas not winning the race is

B. The statement does not make sense because the sum of the probabilities of Jonas winning and not winning the race must equal to 1.

C. The statement makes sense because the probability of Jonas winning the race will always be between 0 and 1.

D. The statement does not make sense because the probability of Jonas winning the race cannot be greater than the probability of him not winning the race.

7.
We are given:
abcissa(x-coordinate) of given point: -6
let's say the ordinate(y-coordinate) of the given point is y
distance of the given point from (1,3) = √74

we can rewrite the given information as:
the distance between the points (-6,y) and (1,3) is √74

finding y:
we know that in order to find the distance between any two points, we use the distance formula, which goes as follows:
distance = \(\sqrt{(x_1-x_2)^2 + (y_1 - y_2)^2}\)

from the data we are given, let's say that:
(x₁, y₁) = (-6, y)
(x₂, y₂) = (1, 3)
(you can use them interchangably, there is no restriction on which point gets to be labelled as 1)

plugging this in the distance formula, we get:
distance  = \(\sqrt{(-6-1)^2 + (y - 3)^2}\)
we are also given that the distance is √74,

√74 = \(\sqrt{(-7)^2 + (y - 3)^2}\)

squaring both sides to get rid of the square root

74 = (-7)² + (y - 3)²
74 = 49 + y² + (3)² -2(y)(3)         (using the "square of sum" identity)
74 = 49 + y² + 9 - 6y
74 = 58 + y² - 6y
y² - 6y + 58 - 74 = 0                   (subtracting 74 from both sides)
y² - 6y - 16 = 0
y² - 8y + 2y - 16 = 0                   (splitting the middle term)
y(y - 8) + 2(y - 8) = 0
(y + 2)(y - 8) = 0
which means that:
y + 2 = 0    ,     y - 8 = 0
y = -2 , y = 8
These are the two possible values of y

8.
We are given:
points A and B
A: (3, y)
B: (6, 2)
distance between A and B = 5 units
finding possible values of y
here, we will use the distance formula again to find the value of y
distance formula: \(\sqrt{(x_a-x_b)^2 + (y_a - y_b)^2}\)
plugging the given values, we get:
5 = \(\sqrt{(3-6)^2 + (y - 2)^2}\)
25 = (3 - 6)² + (y - 2)²              (squaring both sides)
25 = (-3)² + (y - 2)²
25 = 9 + y² + (2)² - 2(y)(2)
25 = 9 + y² + 4 - 4y
y² - 4y + 9 + 4 - 25 = 0            (subtracting 25 from both sides)
y² - 4y - 12 = 0
y² - 6y + 2y - 12 = 0                 (splitting the middle term)
y(y - 6) + 2(y - 6) = 0
(y + 2)(y - 6) = 0

y + 2 = 0   ,    y - 6 = 0
y = - 2  ,   y = 6
These are the two possible values of y