A rectangle has a length of (x+4)cm and a width of (3x-1)cm. It’s perimeter is 78cm
Calculate the value of x

Writing the equation for g in the form y = ax² + bx + c is x² + 8x + 14

The equation of the transformation is written as follows

the parent function f(x) = x²

a translation left 4 units

f(x) = (x + 4)²

down 2 units

f(x) = (x + 4)² - 2

expanding the equation

f(x) = (x + 4)(x + 4) - 2

f(x) = x² + 8x + 16 - 2

f(x) = x² + 8x + 14

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Hello!

A

B    C

AC² = AB² + BC²

AC² = 5² + 3²

AC² = 34

AC = √34

AC ≈ 5.83

Answer:

Step-by-step explanation:

I Hope This Help

Answer:

hERE

Step-by-step explanation:

Answer:

Surface area of prism = 1301 cm²

Step-by-step explanation:

A triangular pyramid has 3 rectangular sides and 2 triangular sides.

Now, we are told that the triangular side is isosceles.

This means that two of the rectangular sides which share a side with the equal side of the triangle are equal as well as the 2 triangular sides.

Surface area of prism = 2(area of triangular face) + 2(area of rectangle sharing one side with the equal side of the triangle) + (area of rectangle sharing side with the unequal side of the triangle).

Area of triangle = ½ × base × height

Area of triangle = ½ × 9 × 13 = 58.5 cm²

Since height of prism is 32 cm, then;

area of rectangle sharing one side with the equal side of the triangle = 32 × 14 = 448 cm²

area of rectangle sharing side with the unequal side of the triangle = 32 × 9 = 288 cm²

Thus;

Surface area of prism = 2(58.5) + 2(448) + 288

Surface area of prism = 1301 cm²

The given statement is True.

Because the one-tailed test provides more power to detect an effect in one direction by not testing the effect in the other direction.

In statistics, power is defined as the likelihood of correctly rejecting a null hypothesis. In other words, avoiding a type II error. There are many ways to increase the power of a study to ensure that significant effects are not missed and incorrect conclusions are not drawn.

The main difference between one-tailed and two-tailed tests is that one-tailed tests will only have one critical region whereas two-tailed tests will have two critical regions. If we require a 100(1−α) 100 ( 1 − α ) % confidence interval we have to make some adjustments when using a two-tailed test.

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Answer:

10:50 AM

Step-by-step explanation:

since she started at 9:05, and we know there are 60 minutes in 1 hour. we can add them up together which gives us 10:05, then we add .45 which gives us 10:50. hope this helps!

Answer:

9) 127 °

10) 67°

11) 100°

12) 118°

Step-by-step explanation:

adjacent angles in parallelograms are supplementary (their sum is 180°)

opposite angles are congruent

Answer:

the answer is positive 10

Step-by-step explanation:

The poverty line is determined by the level of income needed to cover basic needs.

The poverty line is a threshold used to measure poverty and determine eligibility for various assistance programs. It represents the minimum income level required for individuals or households to meet their basic needs, such as food, shelter, clothing, and healthcare. The specific calculation of the poverty line varies from country to country and is often adjusted for factors like family size and location. To determine the poverty line, policymakers and researchers consider factors such as the cost of living, household expenses, and prevailing social standards. They assess the minimum income necessary to provide a decent standard of living and ensure that individuals and families are not living in extreme deprivation. The poverty line is not based on estimates from middle- or high-income households or surveys completed solely on the elderly. Instead, it is designed to reflect the income level below which individuals or households are considered to be living in poverty, indicating the need for targeted interventions and support to improve their economic well-being.

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Answer:

question 5 is letter C. \(\frac{3}{4}\) in/week

question 6 is -4

Step-by-step explanation:

5. he does 3 in 4 weeks

divide 3 by 4

and you get how much he does in one week

which is .75

convert that decimal to a fraction and you get 3/4

6. the y-intercept is -4

hope this helps a little

Step-by-step explanation:

21:18=7:6

42:36=7:6

63:54=7:6

The two types of control charts for variables are the X-bar chart and the R-chart.

Control charts are widely used in statistical process control to monitor and analyze the variability and stability of processes over time. They are used for variables data, which are measurements or observations that can be quantified.

1. X-bar Chart: The X-bar chart is used to monitor the central tendency or average of a process. It tracks the sample means over time to detect any shifts or trends. It helps in assessing whether the process is in control or if there are any systematic variations from the target value.

2. R-chart (Range chart): The R-chart is used to monitor the variability or dispersion within a process. It tracks the ranges (the difference between the highest and lowest values) of samples over time. By analyzing the range values, it helps in understanding whether the process is stable and consistent or if there are any unusual variations or outliers.

Together, the X-bar chart and the R-chart provide valuable insights into process performance and allow for early detection of any deviations or abnormalities, helping organizations maintain quality standards and take appropriate corrective actions when necessary.

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The ball traveled approximately \(26.27\) units in total.

To calculate the distance the ball traveled, we can use the distance formula between two points in a Cartesian coordinate system.

Distance = \(\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1} )^{2} }\)

Let's calculate the distance between Player A and Player B first:

Distance_AB =

\(\sqrt{((16-2)^{2}+(9-4)^{2}) }\)

\(= \sqrt{(14^{2}+5^{2} ) } \\= \sqrt{(196 +25)} \\= \sqrt{221} \\= 14.87\)

Now, let's calculate the distance between Player B and Player C:

Distance_BC =

\(\sqrt{ ((25 - 16)^2 + (16 - 9)^2)}\\= \sqrt{ (9^2 + 7^2)}\\= \sqrt{(81 + 49)}\\= \sqrt{130}\\=11.40\)

Finally, we can calculate the total distance traveled by adding the distances AB and BC:

Total distance = Distance_AB + Distance_BC

\(= 14.87 + 11.40 \\= 26.27\)

Starting from Player A at \((2, 4),\) it was thrown to Player B at \((16, 9),\) covering a distance of about \(14.87\) units. From Player B, the ball was then thrown to Player C at \((25, 16),\) covering an additional distance of approximately \(11.40\) units.

Combining these distances, the total distance the ball traveled was approximately \(26.27\) units.

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Resolviendo una simple ecuación con porcentajes, veremos que el número total de estudiantes es 17,727,273

Sabemos que en un dado año, 22% del numero total de estudiantes universitarios estaban matriculados a tiempo parcial, y hay un total de 3,900,000 estudiantes matriculados a tiempo parcial.

Sí definimos N como el numero total de estudiantes, entonces el 22% de N es igual a 3,900,000, entonces podemos escribir la ecuación:

(22%/100%)*N = 3,900,000

0.22*N = 3,900,000

N = 3,900,000/0.22 = 17,727,273

Ese es el numero total de estudiantes.

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Answer:  729

Step-by-step explanation:  what we are seeing here is known as exponents, how exponents work is that you have to multiply a number a certain times, depending on the power of #.

3^2 = 9 because simplified, its 3 * 3

3^4 = 81 because simplified, its 3 * 3 * 3 * 3

now the solution would be 9 * 81, which equals 729

-----

hope this helps

The person is willing to supply fewer hours of labor at wage rate w1 than at w2 and more hours of labor at wage rate w3 than at w2.

What is fewer hours (w1)?

"Fewer hours (w1)" refers to a condition where an individual is willing to offer a reduced amount or a lesser number of hours of labor in response to a specific wage rate denoted as w1. It implies a decrease in the quantity of labor supplied relative to other wage rates, such as w2 or w3.

Typically, the labor supply curve has an upward slope, indicating that as the wage rate increases, individuals are more willing to supply labor or work more hours. This is because higher wages incentivize individuals to allocate more of their time to work in order to earn more income.

Therefore, if we assume a conventional labor supply curve, we can infer that at a higher wage rate (w3) compared to a lower wage rate (w2), the individual would be willing to supply more hours of labor. Conversely, at a lower wage rate (w1) compared to w2, the individual would be willing to supply fewer hours of labor.

It is important to note that the actual relationship between wage rates and labor supply can be influenced by various factors such as individual preferences, market conditions, and other economic factors. Therefore, a specific labor supply curve graph or more information would be needed to provide a more accurate and specific explanation.

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The solution of the compound inequality is 4 ≤ x ≤ 6.

The solution of the compound inequality is calculated as follows;

The given inequality equation;

2 + x ≤ 3x – 6 ≤ 12

Break down the compound inequality into two equations as;

2 + x ≤ 3x – 6

add 6 to both sides of the equation;

2 + 6 + x ≤ 3x

8 + x ≤ 3x

Subtract x from both sides of the equation;

8 ≤ 2x

4 ≤ x

Another solution of the inequality is determined as;

3x – 6 ≤ 12

3x ≤ 12 + 6

3x ≤ 18

x ≤ 18/3

x ≤ 6

The solution = 4 ≤ x ≤ 6

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The complete question is below:

Which best describes the solution set of the compound inequality below?

2 + x ≤ 3x – 6 ≤ 12

a: 4 ≤ x ≤ 9

b: 4 ≤ x ≤ 6

c: –2 ≤ x ≤ 2

d: –2 ≤ x ≤ 3

The proportion used to find the value of a is a/18 = 16/a

Proportion is a mathematical comparison between two numbers. According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

Given are three similar triangles, (refer to attached figure to separately see the similar triangles)

We know that, similar triangle have corresponding sides in equal ratio,

Therefore,

a/18 = 16/a

Hence, the proportion used to find the value of a is a/18 = 16/a

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Answer:

Sorry

Step-by-step explanation:

This is hard i tried but dont understand

Answer:

1) y= -2×+5/5

2) y=-6×+7/4

Answer:

\(\\\sf7x^3 - 2x^2 - 5\)

Step-by-step explanation:

\(\\\sf(6x^3 + 3x^2 - 2) + (x^3 - 5x^2 - 3)\)

Remove parenthesis.

6x^3 + 3x^2 - 2 + x^3 - 5x^2 - 3

Rearrange:

6x^3 + x^3 + 3x^2 - 5x^2 - 2 - 3

Combine like terms to get:

----------------------------------------

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Answer:

7x³ - 2x² - 5

Step-by-step explanation:

(6x³ + 3x² - 2) + (x³ - 5x² - 3)

Remove the round brackets.

= 6x³ + 3x² - 2 + x³ - 5x² - 3

Put like terms together.

= 6x³ + x³ + 3x² - 5x² - 2 - 3

Do the operations.

= 7x³ - 2x² - 5

____________

hope this helps!

The rate at which the volume of the cone is changing is -5235.98 inches³/s when the radius of the circular cone is 50 inches and the height is 10 inches.

The formula for the circular cone can be given as;

V = 1/3 πr²h

Now we take the derivative with respect to time as follows;

V = 1/3 πr²h

dV/dt = 1/3π d/dt(r²h)

dV/dt = 1/3π [2r(dr/dt) × h + r²(dh/dt)]

Now we substitute the values in this equation as follows;

dV/dt = 1/3π [2 × 50 × 5 × 10 + (50²) (-4)]

dV/dt = 1/3π [ 5000 - 10000]

dV/dt = 1/3π [-5000]

dV/dt = -5235.98

Hence the negative sign indicates that the volume is decreasing over time and the rate of change is calculated to be -5235.98 inches³/s.

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The given conditions to write an equation for the line passing through (−9,2) and parallel to the line whose equation is y = −3x+ 2.

There are many different methods to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically include one or more variables.

More than one variable may be present in a linear equation. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.

\($$We have the equation of a parallel line and a point which it passes through. To write the equation of the line in point-slope form, we will use the following formula:y−y1=m(x−x1)We know that the slope of parallel lines are same and we are given the equation for parallel line, y=−3x+2$$\)

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Answer:

what math is this???????

The sequence a₁ = (3^n + 5^n)^(1/n) converges to 5. The limit of the sequence as n approaches infinity is 5. This means that as n becomes larger and larger, the terms of the sequence get arbitrarily close to 5.

Let's examine the expression (3^n + 5^n)^(1/n). As n gets larger, the dominant term in the numerator is 5^n, since it grows faster than 3^n. Dividing both the numerator and denominator by 5^n, we get ((3/5)^n + 1)^(1/n). As n approaches infinity, (3/5)^n approaches 0, and 1^(1/n) is equal to 1.

Therefore, the expression simplifies to (0 + 1)^(1/n), which is equal to 1. Multiplying this by 5, we obtain the limit of the sequence as 5.

In conclusion, the sequence a₁ = (3^n + 5^n)^(1/n) converges to 5 as n approaches infinity.

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The solution of the word problem is -2. Julio's number is -2

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation

Let Julio's number be x

If you subtract 12 from Julio's number, you will have:

x-12

When you multiply the difference by -7, you will have:

-7(x-12)

Given that the result is -98. That means:

-7(x-12) = -98

Solve for x:

-7(x-12) = -98   (Expand the parenthesis)

-7x + 84 = 98

-7x = 98-84

-7x = 14

x = 14/(-7)

x = -2

Thus, Julio's number is -2

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Answer:

7

Step-by-step explanation:

hey there,

< Here's how you do subtraction in fractions!

Make sure you find a least common denominator. Here, it's given to you to be 15. Usually, you can just multiply the two denominators but then it would be quite large at times, so you kind of just have to guess.

How did they go from  \(\frac{4}{5} x-\frac{1}{3} x\)  to \(\frac{?}{15} x\)?

Well, they used a least common denominator. 5 was multiplied by 3 to create 15, and 3 was multiplied by 5. But when you multiply the bottoms, you have to multiply the tops of the fraction too (the numerators).

So 4/5x was multiplied by 3. Denominator turned out to be 15, and now the top is 4x3 = 12. So the fraction is 12/15.

1/3x, on the other hand, was multiplied by 5. Denominator was also 15 so they're the same, and top is 1x5 = 5. So the fraction is 5/15.

Now, let's put them together.

\(\frac{12}{15}x-\frac{5}{15} x\)

When subtracting x, the x just stays there, so if it was 10x-4x, the answer would've been 6x. So now let's subtract!

12-5 = 7, and the denominator stays the same.

The answer is \(\frac{7}{15} x\). So the numerator, or answer to your question, would be 7.

Hope this helped! Feel free to ask anything else.

The function that relates x and y was found to be:

y = -0.736x + 30.391

It's required to find the value of y when x = 8:

y = -0.736 (8) + 30.391

Operating:

y = -5.888 + 30.391

y = 24.503

Rounding to one decimal place:

y = 24.5

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\(2x - 6 = 8\)

Add sides 6

\(2x - 6 + 6 = 8 + 6\)

\(2x = 14\)

Divide sides by 2

\( \frac{2x}{2} = \frac{14}{2} \\ \)

\(x = 7\)

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The correct answer is (( B )) .

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The quality control manager at Sony uses systematic sampling to estimate the percentage of defects in a manufacturing batch of music CDs. Therefore, the quality control manager can estimate that approximately 20% of the entire manufacturing batch of music CDs may have defects based on the systematic sample she obtained.

Systematic sampling involves selecting items from a population at regular intervals. In this case, the quality control manager selects every 16th music CD starting from the ninth. This method ensures that every CD has an equal chance of being selected, providing a representative sample of the batch.

By using systematic sampling, the quality control manager obtains a sample of 140 music CDs. She can then examine these CDs to determine the number of defective ones. Let's assume she finds 28 defective CDs in the sample.

To estimate the percentage of defects in the manufacturing batch, the quality control manager can use the formula:

Defect percentage = (Number of defective CDs / Sample size) *100

Substituting the values, we have \((\frac{28}{140}) * 100 = 20%\).

Therefore, the quality control manager can estimate that approximately 20% of the entire manufacturing batch of music CDs may have defects based on the systematic sample she obtained. This estimation provides valuable information for assessing the quality of the batch and taking necessary actions for improvement.

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Answer:

f(-3)=1

Step-by-step explanation:

u can see at x=-3 y=1

Answer:

1

Step-by-step explanation:

f(-3) means the same as x = -3

Look at the graph of the x axis  -3 and the point you see there is (-3, 1)

So the y axis or the answer is 1 for that coordinate.

f(-3) = 1

Hope it helped!