Help with math problem please

This is the same as writing y = sqrt(4(x+5)) - 1

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

Explanation:

The given graph appears to be a square root function.

The marked points on the curve are:

Reflect those points over the line y = x. This will have us swap the x and y coordinates.

Recall the process of reflecting over y = x means we're looking at the inverse. The inverse of a square root function is a quadratic.

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Let's find the quadratic curve that passes through (1,-4), (3,-1) and (5,4).

Plug the coordinates of each point into the template y = ax^2+bx+c.

For instance, plug in x = 1 and y = -4 to get...

y = ax^2+bx+c

-4 = a*1^2+b*1+c

-4 = a+b+c

Do the same for (3,-1) and you should get the equation -1 = 9a+3b+c

Repeat for (5,4) and you should get 4 = 25a+5b+c

We have this system of equations

Use substitution, elimination, or a matrix to solve that system. I'll skip steps, but you should get (a,b,c) = (1/4, 1/2, -19/4) as the solution to that system.

In other words

a = 1/4, b = 1/2, c = -19/4

We go from y = ax^2+bx+c to y = (1/4)x^2+(1/2)x-19/4

----------

Next we complete the square

y = (1/4)x^2+(1/2)x-19/4

y = (1/4)( x^2+2x )-19/4

y = (1/4)( x^2+2x+0 )-19/4

y = (1/4)( x^2+2x+1-1 )-19/4

y = (1/4)( (x^2+2x+1)-1 )-19/4

y = (1/4)( (x+1)^2-1 )-19/4

y = (1/4)(x+1)^2- 1/4 - 19/4

y = (1/4)(x+1)^2 + (-1-19)/4

y = (1/4)(x+1)^2 - 20/4

y = (1/4)(x+1)^2 - 5

The equation is in vertex form with (-1,-5) as the vertex. It's the lowest point on this parabola. Placing it into vertex form allows us to find the inverse fairly quickly.

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The last batch of steps is to find the inverse.

Swap x and y. Then solve for y.

y = (1/4)(x+1)^2 - 5

x = (1/4)(y+1)^2 - 5

x+5 = (1/4)(y+1)^2

(1/4)(y+1)^2 = x+5

(y+1)^2 = 4(x+5)

y+1 = sqrt(4(x+5))

y = sqrt(4(x+5)) - 1

I'll let the student check each point to confirm they are on the curve y = sqrt(4(x+5)) - 1.

You can also use a tool like GeoGebra to verify the answer.

The height of the upper end of the handrail above the floor is approximately 3.467726 meters.

To calculate the height of the upper end of the handrail above the floor, we can use trigonometry and the given information about the length of the handrail and the angle of inclination.

Let's break down the problem into two right triangles:

The first right triangle is formed by the handrail, the floor, and a vertical line connecting the lower end of the handrail to the floor. The vertical line represents the height of the lower end above the floor, which is given as 0.7m.

The second right triangle is formed by the handrail, the floor, and a horizontal line parallel to the floor, connecting the upper end of the handrail to the floor. This horizontal line represents the height we need to calculate.

Now, let's apply trigonometric ratios to find the height of the upper end of the handrail above the floor.

In the first right triangle:

Opposite side = height of the lower end = 0.7m

Hypotenuse = length of the handrail = 5.4m

Using the sine function:

sin(angle) = Opposite / Hypotenuse

sin(40°) = 0.7 / 5.4

Now, let's solve for the sin(40°):

sin(40°) ≈ 0.64279

Multiplying both sides of the equation by 5.4:

0.64279 * 5.4 ≈ 3.467726

So, the length of the vertical line in the second right triangle (representing the height of the upper end of the handrail above the floor) is approximately 3.467726 meters.

Therefore, the height of the upper end of the handrail above the floor is approximately 3.467726 meters.

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Therefore, BC is equal to 4 cm.

To solve this problem, we can use the Angle Bisector Theorem and the Pythagorean Theorem.

Let's start by applying the Angle Bisector Theorem. According to the theorem, the ratio of the segments of the hypotenuse formed by the altitude is equal to the ratio of the corresponding sides of the triangle.

In triangle ABC, we have:

AD/DB = AC/CB

Given that AD = 8 cm, we need to find DB. Let's denote DB as x.

8/x = AC/CB

Since AC is the altitude, it can be determined by applying the Pythagorean Theorem in right triangle ACH.

AC^2 = AH^2 + HC^2

AC^2 = (AB - BH)^2 + HC^2

AC^2 = (BC - 4)^2 + HC^2

Now, let's apply the Pythagorean Theorem in right triangle BCH.

BC^2 = BH^2 + HC^2

BC^2 = 4^2 + HC^2

Since AC = BC - 4, we can substitute these expressions into the equation:

(BC -4)^2 + HC^2 = BC^2

Expanding and simplifying this equation, we get:

BC^2 - 8BC + 16 + HC^2 = BC^2

Simplifying further, we have:

-8BC + 16 + HC^2 = 0

Now, let's substitute the value of HC = AD - AH = 8 - 4 = 4 into the equation:

-8BC + 16 + 4^2 = 0

-8BC + 16 + 16 = 0

-8BC + 32 = 0

-8BC = -32

BC = -32 / -8

BC = 4

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The solution to the system of inequalities in interval notation is [-2, 1].

Based on the information provided in the image below, we have the following system of inequalities;

-12 < 3x - 6

-3 ≥ 3x - 6

By adding 6 to both sides of the equation (inequality), we have;

-12 < 3x - 6

-12 + 6 < 3x - 6 + 6

-6 < 3x

-2 < x

x > -2 (flip)

-3 ≥ 3x - 6

-3 + 6 ≥ 3x - 6 + 6

3 ≥ 3x

1 ≥ x

x ≤ 1

Therefore, the solution to the system of inequalities is given by:

-2 < x ≤ 1

In interval notation, we have [-2, 1].

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The forecasted level of output for the 15th year would be 14/15000.

To forecast the level of output for the 15th year, we need to analyze the given information about the firm's total production of cars at the end of ten years of operation and its production during the first year.

According to the information provided, the firm's total production of cars at the end of ten years of operation is 14/1500. However, the production of logo cars during the first year is not specified. We need this information to accurately forecast the level of output for the 15th year.

If we assume that the production of logo cars during the first year is constant throughout the ten-year period, we can use the given information to estimate the average annual production. Since we have 14/1500 as the total production over ten years, we can calculate the average annual production as (14/1500) / 10.

(14/1500) / 10 = 14/15000

Therefore, the estimated average annual production is 14/15000.

Now, to forecast the level of output for the 15th year, we can assume that the average annual production remains constant. Therefore, the forecasted production for the 15th year would be the same as the average annual production.

Hence, the forecasted level of output for the 15th year would be 14/15000.

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Answer:

25/9

Step-by-step explanation:

3 1/3 ÷ 1 1/5

3 1/3 = 10/3

1 1/5 = 6/5

10/3 ÷ 6/5 = 10/3 x 5/6 = 50/18 = 25/9

So, the answer is 25/9

To simplify the expression (2x-3)(5x^2-2x+7), we can use the distributive property.

First, multiply 2x by each term inside the second parentheses:

2x * 5x^2 = 10x^3

2x * -2x = -4x^2

2x * 7 = 14x

Next, multiply -3 by each term inside the second parentheses:

-3 * 5x^2 = -15x^2

-3 * -2x = 6x

-3 * 7 = -21

Combine all the resulting terms:

10x^3 - 4x^2 + 14x - 15x^2 + 6x - 21

Now, combine like terms:

10x^3 - 19x^2 + 20x - 21

So, the simplified expression is 10x^3 - 19x^2 + 20x - 21.

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Navern Corporation's manufacturing cycle efficiency (MCE) for its elevators is approximately 11.36%.

Value-added time is the time spent on activities that directly add value to the product.

Value-added time: Process time = 5 days (the process of manufacturing the elevators)

Total cycle time: Wait time + Inspection time + Process time + Move time + Queue time

= 12 days + 12 days + 5 days + 6 days + 9 days

= 44 days

MCE = (Value-added time / Total cycle time) * 100

= (5 days / 44 days) * 100

≈ 11.36%

Therefore, Navern Corporation's manufacturing cycle efficiency (MCE) for its elevators is approximately 11.36%.

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First, we can simplify each expression:

(10⁰x10¹x1¹⁰) = 10¹¹

(10x10¹) = 100

(10⁰+10¹+1¹⁰) = 1 + 10 + 1,000,000,000 = 1,000,000,011

(10⁰+10¹x1¹⁰) = 10¹⁰

Now we can arrange them in increasing order:

10¹¹ < 10¹⁰ < 100 < 1,000,000,011

So the correct order from smallest to largest is:

(10⁰x10¹x1¹⁰) (10⁰+10¹x1¹⁰) (10 x 10¹) (10⁰+10¹+1¹⁰)

or

(10¹¹) (10¹⁰) (100) (1,000,000,011)

Answer: The expression, 3v^4, means that the variable, v, is multiplied by itself 4 times (v * v * v * v) and then is multiplied after by the coefficient 3.

Step-by-step explanation:

Exponent indicates the number of times a number needs to be multiplied by itself.

For example if your given x^2

that simply means that the variable, x, is being multiplied by itself twice:

x * x

if your given 2z^9

that means that the variable, z, is first multiplied by itself nine times and after that it is multiplied by the coefficient, two.

Answer:

y= -x²-4x+2

Step-by-step explanation:

write in vertex form

a(x-h)²+k

in our case h = -2 and k= 6

y=a(x+2)²+6

now we just need to solve for a. we know that when x= 1 y = -3. plug these values in and solve for a

-3= a(1+2)²+6

-9=9a

a= -1

thus the formula is -(x+2)²+6

generally, teachers want things in standard form, so expand the exponent and simplify.

-(x²+4x+4)+6

y= -x²-4x+2

Answer:

[tex]y = -x^2 - 4x + 2[/tex]

Step-by-step explanation:

The equation of a parabola in vertex form is:

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

where (h, k) is the vertex of the parabola.

In this case, the vertex is (-2, 6), so h = -2 and k = 6.

We also know that the parabola passes through the point (1, -3).

Plugging these values into the equation, we get:

[tex]-3 = a(1 - (-2))^2 + 6[/tex]

[tex]-3 = a(3)^2 + 6[/tex]

-9 = 9a

a = -1

Substituting a = -1 into the equation for a parabola in vertex form, we get the equation of the parabola:

[tex]y = -1(x + 2)^2 + 6[/tex]

This equation can also be written as:

[tex]y = -x^2 - 4x -4+6\\y=x^2-4x+2[/tex]

The missing coordinate in the ordered pair (5, ?) that satisfies the equation 4x - 3y = 18 is y = 2/3. Hence, the complete ordered pair is (5, 2/3).

To determine the missing coordinate in the ordered pair (5, ?) that satisfies the equation 4x - 3y = 18, we can substitute the given x-coordinate, which is 5, into the equation and solve for y.

Let's substitute x = 5 into the equation:

4(5) - 3y = 18

20 - 3y = 18

Now, we can solve for y by isolating it on one side of the equation:

-3y = 18 - 20

-3y = -2

Divide both sides of the equation by -3 to solve for y:

y = -2 / -3

y = 2/3

Therefore, the missing coordinate in the ordered pair (5, ?) that satisfies the equation 4x - 3y = 18 is y = 2/3. Hence, the complete ordered pair is (5, 2/3).

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Question

Following equation. 4x-3y=18 Determine the missing coordinate in the ordered pair (5,?) so that it will satisfy the given equation.

The values of p and q are 1 and 3, respectively.

Given the equation x^2-4x + 1 = (x-p)- q, we can compare the coefficients of the corresponding terms on both sides of the equation.

We compared the coefficients of the x^2 terms on both sides of the equation. The coefficient of the x^2 term on the left-hand side is 1, and the coefficient of the x^2 term on the right-hand side is 1. This means that the two terms are equal, and therefore p = 1.

We compared the coefficients of the x terms on both sides of the equation. The coefficient of the x term on the left-hand side is -4, and the coefficient of the x term on the right-hand side is -1. This means that the two terms are equal, and therefore q = 3.

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The ratios are both identical (three fifths and three fifths). Option A

The ratios of sin x° and cos y° are given as;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

In the question given above, the value of adjacent is 5 and the value of perpendicular is 12.

By using Pythagoras theorem, we can find the value of the hypotenuse.

Hypotenuse² = Adjacent² + Perpendicular²

Hypotenuse² = 5² + 12²

Hypotenuse² = 25 + 144

Hypotenuse² = 169 = 13²

Hypotenuse = 13

The value of sin X° will be;

sin X =  5/13

cos Y = 5/13.

sin X° = cos Y° = 5/13

Therefore, both the ratios of sin x° and cos y° are equal and their value is 5/13.

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Complete question:

Use the image below to answer the following question. What relationship do the ratios of sin x° and cos y° share?

A right triangle is shown. The two angles that are not 90 degrees are marked x and y. The leg across from angle y measuring 4, another leg across from angle x measuring 3, and the hypotenuse measuring 5

The ratios are both identical (three fifths and three fifths).

The ratios are opposites (negative three fifths and three fifths).

The ratios are reciprocals (three fifths and five thirds).

The ratios are both negative (negative five thirds and negative three fifths).

Answer:

total age = 84 years

Step-by-step explanation:

mean is calculated as

mean = [tex]\frac{total}{count}[/tex]

here count = 7 and mean = 12 , then

[tex]\frac{total}{7}[/tex] = 12 ( multiply both sides by 7 )

total = 7 × 12 = 84 years

Answer:

$2100

Step-by-step explanation:

40% of 1500 is 600

1500 + 600 = 2100

The selling price will be $2100

Answer: Read the solution

Step-by-step explanation:

A. For diagram A, triangles ANC and BDE are similar. Thus, we can use similarity ratios to find the length of AC. (x+1)/12 = (x+5)/15. 15x+15=12x+60. Thus 3x=45, and x=15. Since we need to find AC, AC = 15+1 = 16.

B. For diagram B, triangles SRT and VUT are similar. Again, using similarity ratios, (4x-1)/14=(x+2)/6 or 14x+28=24x-6. 10x=34, x=3.4.

To simplify the expression 14√27 - √3, we can simplify the radicals and then perform the subtraction:

First, let's simplify the radicals:

√27 = √(9 × 3) = √9 × √3 = 3√3

Now we can rewrite the expression:

14√27 - √3 = 14(3√3) - √3

Next, distribute the 14:

14(3√3) - √3 = 42√3 - √3

Finally, combine like terms:

42√3 - √3 = 41√3

So the simplified expression is 41√3.

The Lagrange interpolating polynomial of degree 1 is P₁(x) = (f₁ - fo)x + (foxo - f₁xo) / (x₁ - xo).

To derive the Lagrange interpolating polynomial of degree 1, let's consider two distinct points: (x₁, f₁) and (xo, fo). The Lagrange interpolating polynomial of degree 1 can be expressed as:

P₁(x) = L₁(x)f₁ + L₂(x)fo,

where L₁(x) and L₂(x) are the Lagrange basis polynomials defined as:

L₁(x) = (x - xo) / (x₁ - xo),

L₂(x) = (x - x₁) / (xo - x₁).

Substituting these expressions into P₁(x), we have:

P₁(x) = [(x - xo) / (x₁ - xo)]f₁ + [(x - x₁) / (xo - x₁)]fo.

Simplifying further:

P₁(x) = [f₁(x - xo) + fo(x - x₁)] / (x₁ - xo).

Expanding the numerator:

P₁(x) = [f₁x - f₁xo + fox - fox₁] / (x₁ - xo).

Finally, we can rearrange the terms to obtain the Lagrange interpolating polynomial of degree 1:

P₁(x) = (f₁ - fo)x + (foxo - f₁xo) / (x₁ - xo).

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The true statement about the set is n.

The correct answer choice is option A.

The intersection of two sets for instance, set A and B, denoted (n) is the set containing all elements of set A that also belongs to set B.

{6, 8, 10, 12} _ {5, 6, 7, 8, 9} = {6, 8}

Let

{6, 8, 10, 12} = set A

{5, 6, 7, 8, 9} = set B

A n B = {6, 8}

Therefore, the intersection of set A and set B, that is, the elements of set A that are also contained in B are {6, 8}

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Therefore, an appropriate confidence interval for μ30−μ60μ30​−μ60​ (the difference in mean body temperature) would be −0.796−0.796 to −0.404−0.404 (rounded to the appropriate decimal places).

To estimate the difference in the mean body temperature after exercising for 30 minutes versus 60 minutes, we can construct a confidence interval. Since the conditions for inference have been assumed to be met, we can proceed with the following steps:

   Calculate the difference in sample means: xˉ30−xˉ60=38.3−38.9=−0.6xˉ30​−xˉ60​=38.3−38.9=−0.6.

   Determine the standard error of the difference, which is given by the formula:

   SE=(s302n30)+(s602n60)SE=(n30​s302​​)+(n60​s602​​)

Substituting the values, we have:

SE=(0.27218)+(0.29224)≈0.100SE=(180.272​)+(240.292​)  ​≈0.100.

   Choose an appropriate confidence level. Let's say we want a 95% confidence interval.

   Using the standard error, calculate the margin of error, which is given by multiplying the critical value (corresponding to the chosen confidence level) by the standard error. For a 95% confidence level, the critical value is approximately 1.96.

   Margin of Error = 1.96 * 0.100 ≈ 0.196.

   Construct the confidence interval by subtracting and adding the margin of error to the difference in sample means:

   −0.6−0.196−0.6−0.196 to −0.6+0.196−0.6+0.196.

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The algebra class of 14 students in the Algebra 2 class of 23 students do not play basketball or baseball.

The number of students in a certain Algebra 2 class of 23 students who play basketball and baseball is 9, given that 7 of them play basketball and 2 of them play baseball.

The number of students in the class who do not play basketball or baseball is given by the number of students who do not play basketball plus the number of students who do not play baseball and the students who do not play basketball or baseball.

However, since each student is either playing basketball or baseball or neither, we can say that the total number of students who do not play basketball or baseball is given by the number of students in the class minus the total number of students who play basketball or baseball.

Thus, the number of students who do not play basketball or baseball is given by:

23 - 9 = 14

Therefore, 14 students in the Algebra 2 class of 23 students do not play basketball or baseball.

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When 'x' is 5, the Algebraic  expression 3x - 4 evaluates to 11.

To find the algebraic expression for "4 less than the product of 3 and some number," let's break it down step by step.

First, let's define the unknown number as 'x.' Since the problem states "the product of 3 and some number," we can express this as 3 * x or simply 3x.

Next, we want to subtract 4 from this product. The phrase "4 less than" indicates subtraction, so we subtract 4 from 3x. This can be represented as 3x - 4.

In summary, the algebraic expression for "4 less than the product of 3 and some number" is 3x - 4, where 'x' represents the unknown number.

To calculate the value of this expression for a specific value of 'x,' you substitute that value into the expression and simplify. For example, if 'x' is 5, you would substitute 5 into the expression:

3(5) - 4

This simplifies to:

15 - 4 = 11

So, when 'x' is 5, the expression 3x - 4 evaluates to 11.

In general, the algebraic expression allows us to represent a mathematical relationship between quantities using symbols and operations. By substituting specific values into the expression, we can calculate the corresponding results.

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Note the complete question:

Algebraic expression for 4 less than the product of 3 and some number

What is the algebraic expression for "4 less than the product of 3 and some number?

Please help me understand the meaning of how to calculate.

Answer:

The common difference in the given sequence is 5.

Step-by-step explanation:

The common difference in the sequence is 5 because they all add by 5 each time for example 5 + 5= 10 and 10+5=15

The original price of the wool suit was $795.

Let's denote the original price of the wool suit as "P."

We know that the suit was discounted by 20%, which means the discounted price is 80% (100% - 20%) of the original price.

Given that the discounted price is $636, we can set up the following equation:

0.8P = $636

To find the original price, we need to solve for P. We can do this by dividing both sides of the equation by 0.8:

P = $636 / 0.8

P = $795

Therefore, the original price of the wool suit was $795.

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Answer:

Kirsten makes $12.50 per hour

Step-by-step explanation:

The total is $432.50

$5 is taken out of her paycheck, so that will be negative.

35 hours is the time she spent working.

The unknown variable we are looking for is the amount she makes in one hour.

Setting up the equation, we get:

$432.50 = $35x - $5

where x is the amount she makes every hour

Solve for x:

$437.50=$35x

$437.50 / $35 = x

Therefore, x = $12.50

The scaled triangle will be larger than the initial size by a factor 2.

The scaled square will be smaller than the initial side by a factor 4

Dilation refers to a transformation that changes the size of a geometric figure without altering its shape.

Dilation involves scaling an object by a certain factor, that might result in  enlarging or reducing its dimensions uniformly in all directions.

Based on the given diagram, the new length and size of the object is calculated as follows;

For the triangle, (measure the length with ruler)

For the square; (measure the length with ruler)

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The test score that is an outlier is 60. Option A

A data point that dramatically deviates from the dataset's main pattern or trend is referred to as an outlier.

From the information given, we have that;

The score are;

60, 69, 79, 80, 86, 86, 86, 89, 90, and 100.

We can see that the outlier is 60.

This is due to the fact that all of the other scores, which range from 69 to 100, are considerably higher and closer in value.

The score of 60, however, is considerably lower than the others pupils.

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