x+y+2x=1,x-y+z=-5,3x+y+z=3.​

Answer:

x=-24

Step-by-step explanation:

2/3*1/2x = 2/6x
2/3*12=8
1/2*1/3x=1/6x
1/2*14=7
2/6x+8=1/6x+7-3
2/6x+8=1/6x+4
Takeaway 1/6x both sides to make x on one side
1/6x+8=4
take away 8 both sides to make x on its own
1/6x=-4
divide 1/6 both sides
x=-24
Hope this helps, (brainliest pleasee thanks)

To find the value of the cosine of angle M in triangle AMNO, we can use the Law of Cosines. The Law of Cosines states that in a triangle with sides [tex]\displaystyle a[/tex], [tex]\displaystyle b[/tex], and [tex]\displaystyle c[/tex], and angle [tex]\displaystyle C[/tex] opposite side [tex]\displaystyle c[/tex], the following equation holds:

[tex]\displaystyle c^{2} =a^{2} +b^{2} -2ab\cos( C)[/tex]

In triangle AMNO, we have the following information:

[tex]\displaystyle AM=17[/tex] (side [tex]\displaystyle a[/tex])

[tex]\displaystyle MN=15[/tex] (side [tex]\displaystyle b[/tex])

[tex]\displaystyle AN=8[/tex] (side [tex]\displaystyle c[/tex])

Angle M = 90 degrees

We can apply the Law of Cosines to find the value of [tex]\displaystyle \cos( M)[/tex]:

[tex]\displaystyle AN^{2} =AM^{2} +MN^{2} -2\cdot AM\cdot MN\cdot \cos( M)[/tex]

Substituting the given values:

[tex]\displaystyle 8^{2} =17^{2} +15^{2} -2\cdot 17\cdot 15\cdot \cos( M)[/tex]

Simplifying:

[tex]\displaystyle 64=289+225-510\cdot \cos( M)[/tex]

[tex]\displaystyle 64=514-510\cdot \cos( M)[/tex]

Rearranging the equation:

[tex]\displaystyle 510\cdot \cos( M) =514-64[/tex]

[tex]\displaystyle 510\cdot \cos( M) =450[/tex]

Dividing both sides by 510:

[tex]\displaystyle \cos( M) =\frac{450}{510}[/tex]

Simplifying:

[tex]\displaystyle \cos( M) =\frac{15}{17}[/tex]

Therefore, the value of the cosine of angle M in triangle AMNO, to the nearest hundredth, is approximately [tex]\displaystyle 0.88[/tex].

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

Answer:

In the given equation, V(r) represents the volume of the air inside a basketball when the radius of the basketball is r.

Step-by-step explanation:

The function V(r) represents the volume of the basketball when the radius is r. So, the correct interpretation is that V(r) represents "the volume of the basketball when the radius is r."

★ Apply Phythagoras Theorem:-

[tex] \sf \longrightarrow \: {(adjacent \: side)}^{2} + {(opposite \: side)}^{2} = {(hypotenuse)}^{2} [/tex]

[tex] \sf \longrightarrow \: {(9)}^{2} + {(opposite \: side)}^{2} = {(17)}^{2} [/tex]

[tex] \sf \longrightarrow \: 81 + {(opposite \: side)}^{2} = {(17)}^{2} [/tex]

[tex] \sf \longrightarrow \: 81 + {(opposite \: side)}^{2} = 289[/tex]

[tex] \sf \longrightarrow \: {(opposite \: side)}^{2} = 289 - 81[/tex]

[tex] \sf \longrightarrow \: {(opposite \: side)}^{2} = 208[/tex]

[tex] \sf \longrightarrow \: opposite \: side= \sqrt{ 208}[/tex]

[tex] \sf \longrightarrow \: opposite \: side=14.422[/tex]

Answer:

he spent 2hours 50minutes snowboarding

the time he spent skiing and snowboarding minus the time he skied

5hours minus 2hours 10minutes

Answer:  Choice C.   [tex]\displaystyle \boldsymbol{-\frac{\sqrt{5}}{3}}[/tex]

===================================================

Work Shown:

Part 1

[tex]\sin^2(\theta)+\cos^2(\theta) = 1\\\\\cos^2(\theta) = 1-\sin^2(\theta)\\\\\cos(\theta) = -\sqrt{1-\sin^2(\theta)} \ \ \text{ ..... cosine is negative in Q2}\\\\\cos(\theta) = -\sqrt{1-\left(\frac{2}{3}\right)^2}\\\\\\cos(\theta) = -\sqrt{1-\frac{4}{9}}\\\\[/tex]

Part 2

[tex]\cos(\theta) = -\sqrt{\frac{9}{9}-\frac{4}{9}}\\\\\cos(\theta) = -\sqrt{\frac{9-4}{9}}\\\\\cos(\theta) = -\sqrt{\frac{5}{9}}\\\\\cos(\theta) = -\frac{\sqrt{5}}{\sqrt{9}}\\\\\cos(\theta) = -\frac{\sqrt{5}}{3}\\\\[/tex]

0.225 can be expressed as the fraction  1/200.

To convert 0.225 to a fraction, we need to understand the place value of each digit. In this case, the digit 2 is in the hundredths place (2/100), the digit 2 is in the thousandths place (2/1000), and the digit 5 is in the ten-thousandths place (5/10000).

Next, we can simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator. In this case, the GCD of 2, 100, 1000, and 10000 is 2.

Now, we divide both the numerator and denominator by 2 to simplify the fraction. The numerator becomes 1 (2 divided by 2) and the denominator becomes 5000 (10000 divided by 2).

Further simplification is possible by dividing both the numerator and denominator by 5. The numerator becomes 1 (1 divided by 1) and the denominator becomes 1000 (5000 divided by 5).

Again, we can divide both the numerator and denominator by 5. The numerator remains 1 and the denominator becomes 200 (1000 divided by 5).

Therefore, 0.225 can be expressed as the fraction 1/200.

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The correct statement about the mean is:

The mean equals the sum of all observations divided by the number of observations.

The mean is a commonly used measure of central tendency. It is calculated by summing up all the observations and then dividing the sum by the total number of observations. It provides an average value that represents the typical value of the data set.

To calculate the mean, it is not necessary to order the observations from least to most. The order of the observations does not affect the mean calculation.

The mean is not necessarily a whole number. It can be a decimal or a fraction, depending on the data set and the values of the observations. The mean represents the balance point of the data set and can take on any real number value.

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Answer:

  (c)  y = 2b/(2a -c)x -2bc/(2a -c)

Step-by-step explanation:

Given the equation of line BD in point-slope form you want the simplified equation.

  y -0 = (2b/(2a -c))(x -c)

The equation is simplified by using the distributive property to eliminate parentheses.

  [tex]y-0=\dfrac{2b}{2a-c}(x -c)\\\\\\y=\dfrac{2b}{2a-c}x-\dfrac{2b}{2a-c}c\\\\\\\boxed{y=\dfrac{2b}{2a-c}x-\dfrac{2bc}{2a-c}}\qquad\text{matches choice C}[/tex]

<95141404393>

Answer:

f(x) = 4x² - 2x + 11

f'(x) = 8x - 2

m = f'(3) = 8(3) - 2 = 24 - 2 = 22

41 = 22(3) + b

41 = 66 + b

b = -25

y = 22x - 25

For a collection of numbers to be considered a sequence, it is essential that they have a law of formation, are ordered in a specific manner, and can be either finite or infinite.

B: They have a law of formation:

A sequence is a set of numbers arranged in a specific order according to a rule or pattern. The numbers in a sequence are not random but follow a specific law of formation.

This law can be a mathematical formula, a recursive relationship, or any other systematic pattern that determines the values of the sequence. Without a well-defined law of formation, a collection of numbers cannot be considered a sequence.

C: They are ordered:

In a sequence, the numbers are arranged in a specific order or sequence. The order of the numbers is crucial and defines the pattern and structure of the sequence.

Each number in the sequence has a unique position or index that determines its place in the sequence. The order of the numbers allows us to identify the next number or predict the pattern of the sequence. Without the concept of order, the numbers would simply be a set of unrelated elements and not a sequence.

A: They may or may not be infinite:

Sequences can be finite or infinite. A finite sequence has a specific number of terms, and once the pattern or rule is established, the sequence ends.

On the other hand, an infinite sequence continues indefinitely, and its terms extend infinitely in one direction or both directions. Whether a sequence is finite or infinite depends on the context and the specific rule or pattern that governs its formation.

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Note: the translated question is:

To have a sequence it is essential that the numbers that form it:

A: be infinite

B: they have a law of formation C: they are ordered

Answer:

  (a)  10, $2088.81

  (b)  see attached

  (c)  B. increases at a slower rate

Step-by-step explanation:

Given the cost function g(x) = -1736.7 +1661.4·ln(x) for the average dollar cost of health insurance in year x after 2000, you want the cost in 2010, a graph for the years 2006 to 2015, and a description of the shape of the curve.

The value of x is years after 2000, so for the year 2010, the value of x is ...

  x = 2010 -2000 = 10

Substituting 10 for x in the function will give the cost in 2010. That is ...

  g(10) = -1736.7 +1661.4·ln(10) ≈ 2088.81

The cost in 2010 is about $2088.81.

The second attachment shows a graphing calculator's rendition of the graph. We note it has positive slope everywhere, but does not intersect the lines y=1000 or y=3000. This eliminates choices A, C, and D, leaving choice B for the graph.

The logarithm function has positive and decreasing slope. The function here is a scaled and shifted version of the logarithm function, but it still has positive and decreasing slope. That is, ...

 the average cost increases at a slower rate as time goes on

<95141404393>

The period of the trigonometric function is -2π/3.

To determine the period of the trigonometric function based on the given information, we need to consider the pattern of the graph and identify the interval over which it repeats.

Given that the maximum point is at (-π, 7.7) and the minimum point is at (-1/3π, -6.7), we can observe that the graph completes one full oscillation between these two points.

The distance between the maximum and minimum points corresponds to half of the period. Therefore, the full period of the function can be found by doubling this distance.

The distance between (-π, 7.7) and (-1/3π, -6.7) can be calculated as follows:

Δx = -1/3π - (-π) = π/3π - π = -π/3

Since the full period is twice this distance, we multiply by 2:

2 * (-π/3) = -2π/3

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The equation of the normal line to the curve x^2y^2 = 4 at the point (-1,-2) is y = x - 1.

To find the tangent line and normal line to the curve x^2y^2 = 4 at the point (-1,-2), we need to determine the derivative of the curve equation with respect to x and evaluate it at the given point.

First, let's differentiate the equation x^2y^2 = 4 implicitly with respect to x using the chain rule:

2x * (y^2) + 2y * (2xy * dy/dx) = 0

Simplifying the equation, we have:

2xy^2 + 4xy(dy/dx) = 0

Now, let's find the value of dy/dx at the point (-1,-2). Substitute x = -1 and y = -2 into the equation:

2*(-1)(-2)^2 + 4(-1)*(-2)(dy/dx) = 0

Simplifying further:

8 + 8(dy/dx) = 0

8(dy/dx) = -8

dy/dx = -1

We have found the derivative dy/dx at the point (-1,-2), which is -1. This represents the slope of the tangent line to the curve at that point.

Using the point-slope form of a line, we can write the equation of the tangent line as:

y - y₁ = m(x - x₁)

Substituting the values of (-1,-2) and dy/dx = -1 into the equation, we have:

y - (-2) = -1(x - (-1))

y + 2 = -1(x + 1)

y + 2 = -x - 1

y = -x - 3

Therefore, the equation of the tangent line to the curve x^2y^2 = 4 at the point (-1,-2) is y = -x - 3.

To find the normal line, we know that the slope of the normal line is the negative reciprocal of the slope of the tangent line. Therefore, the slope of the normal line is 1.

Using the point-slope form of a line again, we can write the equation of the normal line as:

y - y₁ = m'(x - x₁)

Substituting the values of (-1,-2) and m' = 1 into the equation, we have:

y - (-2) = 1(x - (-1))

y + 2 = x + 1

y = x - 1

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The missing statement 4 of the two column proof of AD ║ BC is:

Statement 4: m∠1 + m∠4 = 180°

The complete two column proof to show that AD || BC is as follows:

Statement 1: AD ║ DC

Reason 1: Given

Statement 2: m∠2 = m∠4

Reason 2: Given

Statement 3: ∠1 and ∠3 are supplements

Reason 3: Same side interior angles theorem

Statement 4: m∠1 + m∠4 = 180°

Reason 4: Def. of Supplementary angles

Statement 5: m∠1 + m∠2 = 180°

Reason 5: Substitution

Statement 6: ∠1 and ∠2 are supplements

Reason 6: Def. of Supplementary angles

Statement 7: AD ║ BC

Reason 7: Converse same side interior angles thm

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Answer:

D.

Step-by-step explanation:

To find the number of customers Sam's Swimming Pool Cleaning has, we need to calculate the total revenue generated by the business and divide it by the weekly charge per customer.

Total revenue = 52 x $25 x number of customers

We know that the annual gross profit is $88,400. So, we can set up an equation to find the number of customers:

$88,400 = 52 x $25 x number of customers - $48,000

$88,400 + $48,000 = 52 x $25 x number of customers

$136,400 = $1,300 x number of customers

Number of customers = $136,400/$1,300

Number of customers = 105

Therefore, Sam's Swimming Pool Cleaning has 105 customers. The correct answer is D.

Sam’s Swimming Pool Cleaning have 105 customers.

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is:

To get how many customers Sam has, write an equation that will relate to the gross profit. Let n be the customers. Since for 52 weeks, Sam charges $25 per week per person, multiply n by the number of weeks and the charge. The equation is written as $88,400 = 52 weeks x $25 per week x n persons. Divide $88,400 by the product of 52 weeks and the $25 charge. The answer will be 105.

Therefore, Sam’s Swimming Pool Cleaning have 105 customers.

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The value of tan(80°) × tan(10°) + sin(70°) + sin(20°) ​= 2.28171276

Trigonometry is the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). These six trigonometric functions in relation to a right triangle are displayed in the figure.

Given:

tan(80°) × tan(10°) + sin(70°) + sin(20°)

Using Trigonometric identity

sin (A · B) = sin A cos B - cos A sin B

So, tan(80°) × tan(10°) + sin(70°) + sin(20°)

[tex]\rightarrow \tan (80 \times 10)=1[/tex]

[tex]\rightarrow\sin(70^\circ+20^\circ)=1.28171276[/tex]

[tex]\rightarrow 1.28171276+1=\bold{2.28171276}[/tex]

Hence,  tan(80°) × tan(10°) + sin(70°) + sin(20°) = 2.28171276

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The opposite of -5 can be represented by situations such as a temperature increase of 5 degrees and a financial gain of $5. Additionally, it can also represent a distance traveled of 5 miles and a weight gain of 5 pounds.

The opposite of -5 is 5. The opposite of a number represents the number with the opposite sign. Here are three situations that can be represented by the opposite of -5:

Situation 1: Temperature Change

If the temperature is currently -5 degrees Celsius and it undergoes a change in the opposite direction, it means it increases by 5 degrees. Therefore, the opposite of -5 represents a temperature increase of 5 degrees.

Situation 2: Financial Gain

Suppose you owe someone $5, and you receive the opposite of that amount. The opposite of owing $5 would be gaining $5. So, the opposite of -5 represents a financial gain of $5.

Additional situations that can be represented by the opposite of -5:

Situation 3: Distance Traveled

If a car has traveled -5 miles, indicating it has moved in the opposite direction, the opposite of that distance would be 5 miles. So, the opposite of -5 represents a distance traveled of 5 miles.

Situation 4: Weight Gain

Imagine someone loses 5 pounds (which can be represented as -5). The opposite of losing 5 pounds would be gaining 5 pounds. Thus, the opposite of -5 represents a weight gain of 5 pounds.

In each of these situations, the opposite of -5 denotes a change in the opposite direction or the reverse of the initial value.

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Answer:    -8 ≥ x

Step-by-step explanation:

Let x be the number, we set up an inequality:

-183 ≥ 9 + 24x    [we use ≥ to present "at least"]

-192 ≥ 24x

  -8 ≥ x

By conducting a statistical test with the provided data and using a significance level of 0.05 and a critical value of 0.811, the educator can determine whether the number of absences significantly affects the final grade of the students.

To analyze the relationship between the number of absences and the final grade of students, an educator collected data from a sample. The obtained data reveals that for 10 absences, the corresponding final grade was 70. In order to determine whether the number of absences significantly impacts the final grade, a statistical test is needed.

The information provided, "Test at α = 0.05, XCV = 0.811," suggests that the educator is referring to a significance level (α) of 0.05 and the critical value (XCV) associated with this level is 0.811.

To conduct a hypothesis test, the educator needs to set up the null (H0) and alternative (Ha) hypotheses. In this case, the null hypothesis would assume that the number of absences does not have a significant effect on the final grade. The alternative hypothesis would assume that the number of absences does have a significant effect on the final grade.

Using the obtained data, the educator would perform the statistical test, such as a correlation analysis or a regression analysis, to determine the strength and significance of the relationship between absences and final grade.

If the test statistic (such as the correlation coefficient or regression coefficient) exceeds the critical value, the null hypothesis would be rejected, suggesting that the number of absences does have a significant impact on the final grade.

The educator can then interpret the results, considering factors such as the direction and strength of the relationship. Additionally, they may explore other variables or factors that could be influencing the final grade and further refine their analysis.

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Reason:

The order of ABCD and EFGH is important. This is because the letters pair up based on their position.

D and H pair up because they're the last letters of ABCD and EFGH respectively. Similar polygons have congruent corresponding angles.

Take note of how the angles are marked to indicate which angles pair up.

D = H

4x = 100

x = 100/4

x = 25

Answer:

25 is the answer by matching the equial sides

Step-by-step explanation:

100°/4=X

25=X

Answer:

I wish you good luck in finding your answer

Answer: 115

Step-by-step explanation:

The proof to show that FA = RN should be completed with the following step and reasons;

Step                                                        Reason_______

FR = AN                                                   Given

RA = RA                                   Reflexive property of Equality

FR + RA = AN + RA                 Addition Property of Equality

FR + RA = FA                         Segment Addition Postulate

AN + RA = RN                        Segment Addition Postulate

FA = RN                                 Transitive Property of Equality

In Geometry, the Segment Addition Postulate states that when there are two end points on a line segment (F) and (N), a third point (A) would lie on the line segment (RN), if and only if the magnitude of the distances between the end points satisfy the requirements of these equations;

FR + RA = FA.

AN + RA = RN.

This ultimately implies that, the Segment Addition Postulate is only applicable on a line segment that contains three collinear points.

By applying the Segment Addition Postulate to the given end points, we can logically deduce that line segment FA is equal to line segment RN based on the steps and reasons stated in the two-column proof shown above.

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The equations of the asymptotes of the hyperbola are y = (5/9)x - 79/9 and y = -(5/9)x + 79/9.

To find the equations of the asymptotes of the hyperbola defined by the equation:

[tex]-25x^2 + 81y^2 + 100x + 1134y + 1844 = 0[/tex]

We can rewrite the equation in the standard form by isolating the x and y terms:

[tex]-25x^2 + 100x + 81y^2 + 1134y + 1844 = 0[/tex]

Rearranging the terms:

[tex]-25x^2 + 100x + 81y^2 + 1134y = -1844[/tex]

Next, let's complete the square for both the x and y terms:

[tex]-25(x^2 - 4x) + 81(y^2 + 14y) = -1844\\-25(x^2 - 4x + 4 - 4) + 81(y^2 + 14y + 49 - 49) = -1844\\-25((x - 2)^2 - 4) + 81((y + 7)^2 - 49) = -1844[/tex]

Expanding and simplify

[tex]-25(x - 2)^2 + 100 - 81(y + 7)^2 + 3969 = -1844\\-25(x - 2)^2 - 81(y + 7)^2 = -1844 - 100 - 3969\\-25(x - 2)^2 - 81(y + 7)^2 = -4913[/tex]

Dividing both sides by -4913:

[tex](x - 2)^2/(-4913/25) - (y + 7)^2/(-4913/81) = 1[/tex]

Comparing this equation to the standard form of a hyperbola:

[tex](x - h)^2/a^2 - (y - k)^2/b^2 = 1[/tex]

We can determine that the center of the hyperbola is (h, k) = (2, -7). The value of [tex]a^2[/tex] is (-4913/25), and the value of [tex]b^2[/tex] is (-4913/81).

The equations of the asymptotes can be found using the formula:

y - k = ±(b/a)(x - h)

Substituting the values we found:

y + 7 = ±(√(-4913/81) / √(-4913/25))(x - 2)

Simplifying:

y + 7 = ±(√(4913) / √(81)) × √(25/4913) × (x - 2)

y + 7 = ±(√(4913) / 9) × √(25/4913) × (x - 2)

Rationalizing the denominators and simplifying:

y + 7 = ±(5/9) ×(x - 2)

Finally, rearranging the equation to isolate y:

y = ±(5/9)x - 10/9 - 7

Simplifying further:

y = ±(5/9)x - 79/9

In light of this, the equations for the hyperbola's asymptotes are y = (5/9)x - 79/9 and y = -(5/9)x + 79/9.

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Answer:

[tex]\boxed{y=\dfrac{5}{9}x-\dfrac{73}{9}}\;\; \textsf{and} \;\;\boxed{ y=-\dfrac{5}{9}x-\dfrac{53}{9}}[/tex]

Step-by-step explanation:

First, rewrite the given equation in the standard form of a hyperbola by completing the square.

Given equation:

[tex]-25x^2+81y^2+100x+1134y+1844=0[/tex]

Arrange the equation so all the terms with variables are on the left side and the constant is on the right side:

[tex]-25x^2+100x+81y^2+1134y=-1844[/tex]

Factor out the coefficient of the x² term and the coefficient of the y² term:

[tex]-25(x^2-4x)+81(y^2+14y)=-1844[/tex]

Add the square of half the coefficient of x and y inside the parentheses of the left side, and add the distributed values to the right side:

[tex]-25(x^2-4x+4)+81(y^2+14y+49)=-1844-25(4)+81(49)[/tex]

Factor the two perfect trinomials on the left side and simplify the right side:

[tex]-25(x-2)^2+81(y+7)^2=2025[/tex]

Divide both sides by the number of the right side so the right side equals 1:

[tex]\dfrac{-25(x-2)^2}{2025}+\dfrac{81(y+7)^2}{2025}=\dfrac{2025}{2025}[/tex]

      [tex]\dfrac{-(x-2)^2}{81}+\dfrac{(y+7)^2}{25}=1[/tex]

        [tex]\dfrac{(y+7)^2}{25}-\dfrac{(x-2)^2}{81}=1[/tex]

As the y²-term is positive, the hyperbola is vertical (opening up and down).

The standard equation of a vertical hyperbola is:

[tex]\boxed{\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1}[/tex]

Therefore, comparing this with the rewritten equation:

The formula for the equations of the asymptotes of a vertical hyperbola is:

[tex]\boxed{y=\pm \dfrac{a}{b}(x-h)+k}[/tex]

Substitute the values of h, k, a and b into the formula:

[tex]y=\pm \dfrac{5}{9}(x-2)-7[/tex]

Therefore, the equations for the asymptotes are:

[tex]\boxed{y=\dfrac{5}{9}x-\dfrac{73}{9}}\;\; \textsf{and} \;\;\boxed{ y=-\dfrac{5}{9}x-\dfrac{53}{9}}[/tex]

Answer : Focus is (0,3)

To find the focus of the parabola defined by the equation (y - 3)² = -8(x - 2), we can compare it with the standard form of a parabolic equation: (y - k)² = 4a(x - h).

In the given equation, we have:

(y - 3)² = -8(x - 2)

Comparing it with the standard form, we can determine the values of h, k, and a:

h = 2

k = 3

4a = -8

Solving for a, we get:

4a = -8

a = -8/4

a = -2

Therefore, the vertex of the parabola is (h, k) = (2, 3), and the value of 'a' is -2.

The focus of the parabola can be found using the formula:

F = (h + a, k)

Substituting the values, we get:

F = (2 + (-2), 3)

F = (0, 3)

Therefore, the focus of the parabola defined by the equation (y - 3)² = -8(x - 2) is at the point (0, 3).

Answer:

Focus = (0, 3)

Step-by-step explanation:

The focus is a fixed point located inside the curve of the parabola.

To find the focus of the given parabola, we first need to find the vertex (h, k) and the focal length "p".

The standard equation for a sideways parabola is:

[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]

where:

If p > 0, the parabola opens to the right, and if p < 0, the parabola opens to the left.

Given equation:

[tex](y-3)^2=-8(x-2)[/tex]

Compare the given equation to the standard equation to determine the values of h, k and p:

The formula for the focus is (h+p, k).

Substituting the values of h, p and k into the formula, we get:

[tex]\begin{aligned}\textsf{Focus}&=(h+p,k)\\&=(2-2,3)\\&=(0,3)\end{aligned}[/tex]

Therefore, the focus of the parabola is (0, 3).

a)In a typical week, Maybelle will earn a total of: $600 + $250 = $850

b) Her total earnings for the week would be: $600 + $300 = $900

c)  Her paycheck will be reduced by $100.

d) Her wage earnings should remain the same assuming she still works at least 40 hours per week.

To calculate Maybelle's earnings in a typical week, we first need to determine the minimum number of hours she works. Since she earns $15 per hour for at least 40 hours per week, her minimum wage earnings are:

$15 x 40 = $600

In addition to her wage earnings, Maybelle earns a commission of 10% for each pair of shoes she sells. Since she is expected to sell $2,500 worth of shoes every week, her commission earnings are:

$2,500 x 0.10 = $250

b) If Maybelle sells $3,000 worth of shoes in one week, her commission earnings would be:

$3,000 x 0.10 = $300

On top of her wage earnings of $600 (based on working at least 40 hours at $15 per hour)

c) If customers return $1,000 worth of shoes the next week, Maybelle's commission earnings will not be affected. However, her wage earnings will be reduced by the amount of the returned shoes, which is $1,000 x 0.10 = $100.

d) With an economic downturn and sales slump, Maybelle's earnings from commission will likely decrease since she will sell fewer shoes. However, her total earnings will likely decrease due to the decrease in commission earnings.

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The correct Option is A. The measure of angle HGF is 20°.

Quadrilateral EFGH is an isosceles trapezoid with bases EH and FG.

The measure of angle HGF is (9y + 3)°, and the measure of angle EFG is (By + 5)°.

To find the measure of angle HGF, we need to solve for the value of y.

Since EFGH is an isosceles trapezoid, the opposite angles are congruent.

Therefore, the measure of angle EFG is also (9y + 3)°.

To find the value of y, we can set the two expressions equal to each other: (9y + 3)° = (By + 5)°.

Next, we can solve for y by isolating it.

We subtract 3° from both sides: 9y = By + 2.

To get y by itself, we subtract By from both sides: 9y - By = 2.

Finally, we can factor out y: y(9 - B) = 2.

To solve for y, we divide both sides by (9 - B): y = 2 / (9 - B).

Now that we have the value of y, we can substitute it back into the expression for angle HGF: (9y + 3)°.

Thus, the measure of angle HGF is (9(2 / (9 - B)) + 3)°.

Therefore, The correct Option is A.

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Answer:

Step-by-step explanation:

To find the time it takes for the turtle to reach the pond, we can use the formula:

Time = Distance / Speed

Given that the turtle travels at a speed of 1/12 mile per hour and the distance to the pond is 5/6 mile, we can substitute these values into the formula:

Time = (5/6) / (1/12)

To simplify this, we can multiply the numerator by the reciprocal of the denominator:

Time = (5/6) * (12/1) = (5 * 12) / 6 = 60 / 6 = 10

Therefore, it will take the turtle 10 hours to reach the pond.

Answer:

x = 0.39 or

x = -1.72

Step-by-step explanation:

The quadrateic formula is:

[tex]x = \frac{-b\pm\sqrt{b^2 - 4ac} }{2a}[/tex]

eq: 3x² + 4x - 2

which is of the form ax² + bx + c = 0

where a = 3, b = 4 and c = -2

sub in quadratic formuls,

[tex]x = \frac{-4\pm\sqrt{4^2 - 4(3)(-2)} }{2(3)}\\\\=\frac{-4\pm\sqrt{16 + 24} }{6}\\\\=\frac{-4\pm\sqrt{40} }{6}\\\\=\frac{-4\pm2\sqrt{10} }{6}\\\\=\frac{-2\pm\sqrt{10} }{3}\\\\=\frac{-2+\sqrt{10} }{3} \;or\;=\frac{-2-\sqrt{10} }{3}\\\\=0.39 \;or\; -1.72[/tex]

The correct combination is option a) 1 twenty, 3 tens, and 5 singles, which allows us to make change for $55 without making change for a twenty dollar bill.

The correct answer is a) 1 twenty, 3 tens, 5 singles.

To make change for $55 using exactly nine bills without making change for a twenty dollar bill, we need to avoid using any combination that includes a twenty dollar bill.

Option a) includes 1 twenty, 3 tens, and 5 singles. The total value of these bills is 20 + 3(10) + 5(1) = $55. This combination allows us to make the exact change for $55 without including a twenty dollar bill.

Option b) includes 4 tens, 2 fives, and 5 singles. The total value of these bills is 4(10) + 2(5) + 5(1) = $55. Although this combination also makes the exact change for $55, it includes four tens, which can be exchanged for a twenty dollar bill.

Option c) includes 2 twenties, 1 ten, and 6 singles. The total value of these bills is 2(20) + 10 + 6(1) = $57. This combination exceeds $55 and also includes two twenty dollar bills, making change for a twenty dollar bill.

Option d) includes 2 twenties, 2 fives, and 5 singles. The total value of these bills is 2(20) + 2(5) + 5(1) = $55. However, this combination includes two twenty dollar bills, making change for a twenty dollar bill.

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