A triangle with a height of 12in.²has an area of 36 in.² how long is the base of the triangle

Answer:

-4x

Step-by-step explanation:

Answer:

x = -4

Step-by-step explanation:

The axis of symmetry is the vertical line that makes a mirror image on the left and right for a vertical parabola

It goes through the vertex and is the x coordinate

x = -4

As per the given details, f(-3) = 8, (b) f(-1) = -2, and (c) f(1) = UNDEFINED.

To locate the function values, substitute values of x into the function f(x) and evaluate the expression.

f(-3):

As, x = -3 and x < -1, we'll use the first part of the function: f(x) = -4x - 4.

f(-3) = -4(-3) - 4

      = 12 - 4

      = 8

Therefore, f(-3) = 8.

f(-1):

Again as, x = -1, we'll use the second part of the function: f(x) = x² + 2x - 1.

f(-1) = (-1)² + 2(-1) - 1

     = 1 - 2 - 1

     = -2

Therefore, f(-1) = -2.

f(1):

Since x = 1 and x > -1, we'll use the first part of the function: f(x) = -4x - 4.

Since x = 1 does not satisfy the condition x < -1, the function value is undefined (UNDEFINED) for f(1).

Therefore, (a) f(-3) = 8, (b) f(-1) = -2, and (c) f(1) = UNDEFINED.

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The angles R and U of the two triangles are equal, the ratio of the sides is RS/UW = RT/UV.

A triangle is a three-sided polygon which is one of the basic shapes in geometry. It is a closed figure formed by three line segments which are connected end-to-end. Each side of a triangle is called an edge, and each corner is called a vertex. The angles of a triangle are the interior angles which are formed by the intersection of two edges. Triangles come in many different types depending on the length of the sides and the size of the angles. The three most common types of triangles are equilateral, isosceles, and scalene.

Proof:
The two triangles, RST and UWV, are similar triangles because the angles R and U are equal. According to the similarity theorems, if two angles of one triangle are equal to two angles of a second triangle, then the two triangles are similar.

Since the two triangles are similar, their sides are proportional. The proportionality can be expressed as:

RS/UW = RT/UV

The proof is completed by applying the Angle-Angle Similarity Postulate which states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

This implies that the proportionality of the sides of the two triangles can be expressed as a ratio of the sides. Since the angles R and U of the two triangles are equal, the ratio of the sides is RS/UW = RT/UV.

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Graph of each objective function using linear programming.

Here,

Putting the equation equal to 420 and plotting the graph by finding the value of A and By putting A=0 and finding B then putting B=0 and finging A.

For example putting A=0 in 7A+10B=420 will yield  (0,42) and Putting B=0 will yield (60, 0). plotting theses points on graph and joining them to generated the line.

Repeating thin step for each objective function and plotting the graph.

7A + 10B = 420 is labelled as a.

6A+4B = 420 is labelled as b.

-4A + 7B = 420 is labelled as c .

The graph of each function is attached below.

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Answer:

Answer (e)

Step-by-step explanation:

Note that this graph has a zero at x = 1 and a vertical asymptote at x = -4.  Only Answer (e) corresponds to that.  Try letting x = 1.  y is zero, correct?  Try letting x = -4.  y is undefined, correct?

The health club has 2 employees who work on lead generation. Each employee contacts leads for 20 hours a week and is paid $20 per hour. Approximately 8% of the leads become members and pay a one-time fee of $100. Material costs are $190 per week, and overhead costs are $1,100 per week. To analyze the productivity of the operation, we need to calculate the multifactor productivity in fees generated per dollar of input. The owner is also considering purchasing a new software program that would allow each employee to contact 20 more leads per week, but it would increase material costs by $260 per week. We need to calculate the new multifactor productivity if the software is purchased and determine how it would affect productivity.

a. To calculate the multifactor productivity, we need to determine the total fees generated and the total input costs. The total fees generated per week can be calculated as 8% of the total number of leads contacted multiplied by the one-time fee of $100, which is (0.08 * 200) * $100 = $1,600. The total input costs per week are the sum of employee wages, material costs, and overhead costs, which is (2 employees * 20 hours/week * $20/hour) + $190 + $1,100 = $2,490. Therefore, the multifactor productivity is $1,600 / $2,490 = 0.64.

b. If the owner purchases the software program and each employee can contact 20 more leads per week, the total number of leads contacted per week by both employees will be 2 * (200 + 20) = 440. The new material costs per week will be $190 + $260 = $450. The overhead costs remain the same at $1,100. The total input costs per week become (2 employees * 20 hours/week * $20/hour) + $450 + $1,100 = $1,650. The new multifactor productivity is $1,600 / $1,650 = 0.97.

c. The new multifactor productivity after purchasing the software program has increased to 0.97 from the previous value of 0.64. The change in productivity can be calculated as ((0.97 - 0.64) / 0.64) * 100 = 51.6%. Therefore, purchasing the software program would increase productivity by approximately 51.6%.

By analyzing the multifactor productivity and the impact of purchasing the software program, the owner can make an informed decision about whether the investment is worthwhile considering the potential increase in productivity.

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Answer:

9x8=72      72-8=64  64x9=576

Step-by-step explanation:

Answer:

Nine times the difference of 8 and a number = 9(x-8)

The prime of the set  is  mathematically given as

A' {e,h,i,j,k}

This is further explained below.

Generally, Mathematically speaking, "set theory" refers to the study of well-defined groups, or "sets," of individual things that are collectively referred to as "members" or "elements" of the set. Because sets are the only topic of discussion in pure set theory, the only sets that may be taken into account are those that include other sets as members.

Assigned the letter A (A prime), The components that are included in the Universal set but are absent from Set A are denoted by the letter A'.

In conclusion, the prime of the set  is  mathematically given as

A' {e,h,i,j,k}

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CQ

Let U={e,f,g,h,i,j,k} and A={f,g}

find A'

Answer:

Try A

Step-by-step explanation:

Answer:

6 times............ I think

Answer:

Chord

Step-by-step explanation:

Notice that the highlighted part is the line segment that joins the points J and E on the circle, which is known as a chord.

The 86th percentile is 45.72 (rounded to 2 decimal places).

To solve the given questions, we will assume that births are uniformly distributed across the 52 weeks of the year, following a uniform distribution from 1 to 53.

a. The mean of a uniform distribution can be calculated using the formula:

  Mean = (a + b) / 2,

  where a is the minimum value (1) and b is the maximum value (53).

  Mean = (1 + 53) / 2 = 54 / 2 = 27.

b. The standard deviation of a uniform distribution can be calculated using the formula:

  Standard Deviation = (b - a) / √12,

  where a is the minimum value (1) and b is the maximum value (53).

  Standard Deviation = (53 - 1) / √12 = 52 / √12 ≈ 15.0111 (rounded to 4 decimal places).

c. The probability that a person will be born at the exact moment that week 48 begins is 1/52 since there is only one specific moment corresponding to that week out of the 52 possible weeks.

d. To find the probability that a person will be born between weeks 5 and 9, we need to calculate the cumulative probability for week 9 and subtract the cumulative probability for week 5. Since the distribution is uniform, the probability for each week is 1/52.

  P(5 < z < 9) = P(z ≤ 9) - P(z ≤ 5) = 9/52 - 5/52 = 4/52 = 1/13.

e. The probability that a person will be born after week 35 can be calculated by subtracting the cumulative probability up to week 35 from 1. Again, since the distribution is uniform, the probability for each week is 1/52.

  P(x > 35) = 1 - P(x ≤ 35) = 1 - 35/52 = 18/52 = 9/26 ≈ 0.3462 (rounded to 4 decimal places).

f. P(x > 8 and x < 33) can be calculated by subtracting the cumulative probability up to week 33 from the cumulative probability up to week 8.

  P(8 < x < 33) = P(x ≤ 33) - P(x ≤ 8) = 33/52 - 8/52 = 25/52 ≈ 0.4808 (rounded to 4 decimal places).

g. To find the 86th percentile, we need to calculate the value below which 86% of the data falls. Since the distribution is uniform, we can calculate it as follows:

  86th percentile = a + (b - a) * 0.86,

  where a is the minimum value (1) and b is the maximum value (53).

  86th percentile = 1 + (53 - 1) * 0.86 = 1 + 52 * 0.86 ≈ 45.72 (rounded to 2 decimal places).

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Births are approximately Uniformly distributed between the 52 weeks of the year. They can be said to follow a Uniform distribution from 1 to 53 (a spread of 52 weeks). Round answers to 4 decimal places when possible a. The mean of this distribution is 27b. The standard deviation is 15.0111 c. The probability that a person will be born at the exact moment that week 48 begins is P(x-48)- 1/52d. The probability that a person will be born between weeks 5 and 9 is P(5 < z < 9)-452 e. The probability that a person will be born after week 35 s P(x> 35)-18/5f P> 8 ix33)g Find the 86th percentile.

The survival time of a 60kg deer without food at -20 degrees Celsius depends on various factors, including its age, sex, and physical condition. However, assuming the deer is healthy and has 5kg of fat, it could potentially survive for around 30 to 50 days without food.

The exact survival time can vary depending on several factors, such as the deer's level of physical activity, environmental conditions, and how much energy it is expending to stay warm in the cold temperature. Additionally, if the deer is able to find sources of water, this can also increase its chances of survival.

It's important to note that this is just an estimate and that the actual survival time may vary. If the deer is injured or sick, its chances of survival may be reduced, and it may not be able to survive as long without food.

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Complete Question

How many days could a 60kg deer survive without food at -20 degrees Celsius if it has 5kg of fat?

Answer:

\(\boxed{y = \dfrac{1}{4}x -4}\)

Step-by-step explanation:

The slope-intercept form of a line equation is y = mx + b\(\sf\\\\To\;find\;b, \;plug \;in \;the \;values\; of\; (4, - 3) \;which \;corresponds\; to\; x = 4, y = -3 \;into \;the \;above \;equation:\\== > - 3 = \dfrac{1}{4}\cdot 4 + b\\\\Switching\;sides,\\\dfrac{1}{4}\cdot 4 + b = -3\\\\Simplifying\\1 + b = -3\\\\b = -3 -1 = -4\\So\; the\; equation \;of \;the\; perpendicular\; line \;is: \boxed{y = \dfrac{1}{4}x -4}\)

A perpendicular line will have slope is  \(-\dfrac{1}{m}\)

The perpendicular line will have a slope which is the negative of the reciprocal of the first line

Here the line is 4x + y =3

This can be re-written as y = -4x + 3

Slope of this line is -4

\(\sf Reciprocal \; of-4 = -\dfrac{1}{4}\)

\(\sf Negative \; of \; reciprocal = -(-\dfrac{1}{4}) = \dfrac{1}{4}\)

\(\sf So\;slope\;of\;perpendicular\;line=\dfrac{1}{4}\\Equation \;of \;the \;perpendicular\; line\; is \;y = \dfrac{1}{4}x + b \;where \;b \;is \;the\; y\; intercept\)

Answer:

6) 9x-25+9x-25(sum of base angles)

9x-25+9x-25+104=180(sum of angles in a triangle)

collect like terms

9x+9x-25-25+104=180

18x-50+104=180

18x+54=180

18x=180-54

18x=126

divide both sides by 18

18x÷18=126÷18

x=7

\( \huge \underline{\boxed{ \color{cyan} \tt \dag \: Answer:}}\)

Total money spent on grocery = $40

Money spent on fruit = $18

Percentage of total she spent on fruit = ?

\(\tt Percentage \: of \: total \: she \: spend \: on \: fruit \\ =\tt \dfrac{Money \: spent \: on \: fruit}{Total \: money \: spent} \times 100\%\)

\( \tt : \implies percentage = \dfrac{18}{40} \times 100\% \\ \tt : \implies percentage = \dfrac{18}{4} \times 10\% \\ \tt : \implies percentage = \dfrac{9}{2} \times 10\% \\ \tt : \implies percentage = 9 \times 5\% \\ \tt : \implies percentage = 45\% \\ \)

\( \tt \color{fuchsia} Hence, \: answer \: is \: 45 \%.\)

Answer:

(12x+4)² and p²−6p+9

Step-by-step explanation:

From the given choices, we areto select the one that are squares of linear expressions

1) For the expression (12x+4)²

This is regarded as the square of 12x+4 since the expression 12x4 is enclosed in parenthesis

2) For the expression p^2−6p+9

Factorize;

p^2−6p+9

p^2−3p-3p+9

p(p-3)-3(p-3)

(p-3)(p-3)

(p-3)²

Hence p^2−6p+9 is a square of the expression p-3

This are the only two required expressions (12x+4)² and p²−6p+9

The inequality passing through (1, 4), (-2, -2), intersecting the y-axis at 2 units and intersects the x-axis at (-1, 0) to form shaded portions on the left side is y > 2x+2

An equation is an expression that shows the relationship between two or more variables and numbers.

An inequality shows the non equal comparison of two or more numbers and variables.

The inequality passing through (1, 4), (-2, -2), intersecting the y-axis at 2 units and intersects the x-axis at (-1, 0) to form shaded portions on the left side is y > 2x+2

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Translate vertex W to vertex M. Next, reflect WXY across the line containing line segment WX is MXY

The intersection of two lines, two line segments, or any suitable combination of rays, segments, and lines that results in two straight "sides" coming together at one point is known as an angle's vertex. 1. Translate vertex W to vertex M: Move point W to the right by 4 units, creating point M.

2. Reflect WXY across the line containing WX: Create a line perpendicular to WX, and reflect WXY across it. The resulting figure is MXY.

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The function f(x) has a greater maximum 7.

The given function is f(x)=-3x²+6x+4 and g(x) the function in the graph.

We need to check which function has the greater maximum.

The maximum value of a function is the place where a function reaches its highest point, or vertex, on a graph.

The first way is graphing. You can find the maximum value visually by graphing the equation and finding the maximum point on the graph. This is especially easy when you have a graphing calculator that can do the work for you.

The maximum for the function g(x) is 6.

From the graph given below, we can see that the maximum for the function f(x) is 7.

Therefore, the function f(x) has a greater maximum 7.

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Answer:

10ft by 12ft

Step-by-step explanation:

Step 1 : Find the area of the garden.

Area formula = length * width

Area = 8 * 12

Area = 96

Step 2 : Find 25% of 96.

96 divided by 4 = 24

Step 3 : Add that 25% (24) onto 96.

24 + 96 = 120

We now know that the new area of the garden is 120 \(feet^{2}\).

The new dimensions of the garden could be 10 times 12, since that equals 120. Therefore, the answer is 10ft by 12ft.

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There are no options.

\(\frac{1}{b^{4} }\)   <------------- only expression created by this rule.

Answer:

Step-by-step explanation:

The given expression should be typed as b^(-4), which indicates that variable b has the exponent -4.

Recall that:            

     1

------------- = a^(-n)

   a^n

                                        1

Therefore, b^(-4) =   --------------

                                     b^4

Given:

Number of employees are 5.

Probability that an employee will be late to work at a large corporation is 0.21.

The given data follows binomial distribution,

The probability that at least 3 employees are late is given as,

Answer: The probability that in a department of 5 employees at least 3 are late is 0.0659.

Answer:

1

1

1

2

2

2

2

Step-by-step explanation:

The z-score of an appliance that failed after 64 months is 2.

To find the z-score:

The given parameters are:

The z-score is then computed as follows:

We have the following for an appliance that stopped working after 64 months:

So, the equation becomes:

Compare and contrast the differences:

Calculate the quotient:

Therefore, the z-score of an appliance that failed after 64 months is 2.

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Using a confidence level of 95%, the margin of error for the mean GRE score of graduate students is approximately 14.15. The upper bound of the confidence interval is 314.15, and the lower bound is 285.85. This means we are 95% confident that the true population mean GRE score falls between these two values.

To calculate the margin of error, we use the formula:

Margin of Error = Z * (Standard Deviation / √n)

In this case, the standard deviation is 47 and the sample size (n) is 50. The Z-value for a 95% confidence level is approximately 1.96. Plugging in these values, we get:

Margin of Error = 1.96 * (47 / √50) ≈ 14.15

This means that the sample mean of 300 is expected to be within 14.15 points of the true population mean GRE score.

The confidence interval is then constructed by adding and subtracting the margin of error from the sample mean:

Confidence Interval = (Sample Mean - Margin of Error, Sample Mean + Margin of Error)

= (300 - 14.15, 300 + 14.15) = (285.85, 314.15)

Interpreting the confidence interval, we can say that we are 95% confident that the true population mean GRE score for graduate students falls within the range of 285.85 to 314.15. This means that if we were to repeat the sampling process and calculate the sample mean GRE scores multiple times, approximately 95% of the confidence intervals obtained would contain the true population mean.

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