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The quadratic equation is solved and intersect at the points (4, 1) and (-1, 16)

Given data ,

To find the intersection points of the two functions, we can set them equal to each other and solve for x:

x² - 6x + 9 = -x² + 17

Bringing all the terms to one side:

2x² - 6x - 8 = 0

Dividing by 2:

x² - 3x - 4 = 0

We can factor this quadratic equation as:

(x - 4)(x + 1) = 0

So the solutions are:

x = 4 or x = -1

To find the corresponding values of y, we can substitute each value of x into either of the original equations

y = x² - 6x + 9

When x = 4:

y = 4² - 6(4) + 9 = 1

So one intersection point is (4, 1).

When x = -1:

y = (-1)² - 6(-1) + 9 = 16

So the other intersection point is (-1, 16).

Hence , the two functions intersect at the points (4, 1) and (-1, 16)

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Answer:

Let's use "K" to represent Kevin's current age, and "M" to represent his mother's current age.

According to the problem, if you triple Kevin's age, the result is 1 less than his mother's age:

3K = M - 1

We can simplify this equation by adding 1 to both sides:

3K + 1 = M

This equation tells us that if we add 1 to three times Kevin's age, we get his mother's age. We can use this equation to solve for Kevin's age if we know his mother's age, or we can use it to solve for his mother's age if we know Kevin's age.

Answer:

198 ft^2

Step-by-step explanation:

l = 3

w = 3

h = 15

2(3*3) + 4(3*15) = 18 + 180

18 + 180 = 198 ft^2

3.5= 35/10

35/10= 7/2

which is equal to 3 1/2

Therefore: 3 1/2 and 7/2

If lines m and n are parallel, then the value of x must be 4.

If lines m and n are parallel, then the measures of the angles in the correspondent quadrants must be the same ones.

Here we can see that the two angles are in the third quadrant, thus, these angles have the same measure. Then we can write this as:

6x² = 96

Now we can solve this for x, we will get:

x² = 96/6

x² = 16

x = √16

x = 4

That is the value of 4.

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The correct options are rectangular prism, square pyramid.

When a shape has a rectangular cross-section, it means that if the shape is cut perpendicular to its base, the resulting cut will be a rectangle. So, the only shapes that will have a rectangular cross section are those whose base is a rectangle or a shape that can be inscribed within a rectangle.

The shapes that have rectangular cross sections when they are cut perpendicular to the base are:

Rectangular prism

Square pyramid

Therefore, the correct options are rectangular prism, square pyramid.

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Complete question:

the value of the test statistic is approximately 5.19.we can get the answer by using formula .

what is statistic  ?

A statistic is a numerical value or measure that is calculated from a sample of data, and is used to describe or make inferences about a population. Statistics are used in various fields, including business, economics, social sciences, and natural sciences, to analyze data

In the given question,

To test the claim that the percentage of residents who favor construction is more than 49%, we can use a one-sample z-test. The test statistic can be calculated as:

z = (p - P) / √(P * (1 - P) / n)

where:

p = the sample proportion (0.53)

P = the hypothesized population proportion under the null hypothesis (0.49)

n = the sample size (800)

Substituting the given values into the formula, we get:

z = (0.53 - 0.49) / √(0.49 * 0.51 / 800) ≈ 5.19

Rounding the test statistic to two decimal places, we get:

z ≈ 5.19

Therefore, the value of the test statistic is approximately 5.19.

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For the drug used to treat asthma in a clinical trial:

Part 1:

The test is right-tailed because the alternative hypothesis is that less than 9% of treated subjects experienced headaches.

Part 2:

The test statistic is z = 0.64, rounded to two decimal places (given in the calculator display).

Part 3:

The P-value is 0.7401, rounded to four decimal places (also given in the calculator display).

Part 4:

The null hypothesis is Upper H₀: p ≥ 0.09. We conclude that there is not sufficient evidence to support the claim that less than 9% of treated subjects experienced headaches.

Part 5:

We fail to reject the null hypothesis because the P-value is greater than the significance level, α=0.01.

Part 6:

The final conclusion is: D, There is not sufficient evidence to support the claim that less than 9% of treated subjects experienced headaches.

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The raw x-value associated with a Z-score of 0.21 for the given distribution is 145.89.

To compute the raw x-value associated with a Z-score of 0.21 for a distribution with a population mean, μ, of 144 and a population standard deviation, σ, of 9, we can use the formula for standardizing a variable:

Z = (x - μ) / σ

Rearranging the formula to solve for x, we get:

x = Zσ + μ

Substituting the given values, we get:

x = 0.21(9) + 144

Simplifying the expression, we get:

x = 145.89

A Z-score represents the number of standard deviations a value is from the mean, and it can be used to standardize values from different distributions. By standardizing values, we can compare them on a common scale and make more meaningful statistical inferences.

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The left-handed students in the music program are option A 15 students.

A table that shows the frequencies of two category variables is known as a two-way frequency table. It is a method for succinctly and clearly organising and displaying data for two variables. One variable is represented by the table's rows, while the other variable is represented by the table's columns. The frequency of each combination of categories is displayed in the table's cells. To examine the relationship between the two variables and to spot patterns and trends in the data, a two-way frequency table can be employed. To summarise and analyse data, it is frequently used in statistics, the social sciences, and other disciplines.

From the given table the number of students that are in music program and left handed is given by the intersection of the row and column of the two.

Thus, he left-handed students in the music program are 15.

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the approximate difference in the mean circumferences of the Earth and the Moon is about 29153.88 kilometers.

A circle is a particular type of ellipse in mathematics or geometry where the eccentricity is zero and the two foci are congruent.

A circle is also known as the location of points that are evenly spaced apart from the centre. The radius of a circle is measured from the centre to the edge. T

he line that splits a circle into two identical halves is its diameter, which is also twice as wide as its radius.

A circle is a fundamental 2D form whose radius is quantified. The interior and exterior parts of the aircraft are separated by the circles.

The formula for the circumference of a circle is:

C = 2πr

where C is the circumference, π (pi) is a constant approximately equal to 3.14, and r is the radius.

The difference in the mean circumferences of the Earth and the Moon can be found by subtracting the circumference of the Moon from the circumference of the Earth.

The circumference of the Earth is:

C earth = 2π * 6371.0 km = 40075.04 km (rounded to two decimal places)

The circumference of the Moon is:

C moon = 2π * 1737.5 km = 10921.16 km (rounded to two decimal places)

The difference in the mean circumferences of the Earth and the Moon is:

C earth - C moon = 40075.04 km - 10921.16 km ≈ 29153.88 km

Therefore, the approximate difference in the mean circumferences of the Earth and the Moon is about 29153.88 kilometers.

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We can set up the equation :

0.9x = 110 ,

where x is the unknown number. To solve for x, we can divide both sides by 0.9 :

x = 110 ÷ 0.9

x = 122.22 (rounded to two decimal places)

So the unknown number is approximately 122.22.

To find 9% of that number, we can multiply 122.22 by 0.09 :

0.09 × 122.22 = 11.00 (rounded to two decimal places)

Therefore, 9% of the number is approximately 11.

Answer:

$52.50

Step-by-step explanation:

1500 * 3.5% = 52.50

Answer:

$52.5 for the first year

Step-by-step explanation:

You can derive a decimal from a percentage by dividing by 100.

For example, 1% is 0.01

3.5% is 0.035

You can also move the decimal point back 2 places, but that's cringy.

So the problem says how much interest she will have to pay after one year, when the interest rate is 3.5%.

Therfore, we must multiply:

1500 by 3.5%

We stated that 3.5% is 0.035, so we can replace that

1500 * 0.035

Plug that into a caluclator and we get.....

$52.5 for the first year

ANSWER CHOICE 1

Phew! That was a long problem! May I please have Brainliest?

The given trigonometric expression sin⁻¹(-3√(2)/2) in radians is approximately -2.2143 radians.

As we know that sin⁻¹(x) = -cos⁻¹(x) + π/2, which is the angle in the fourth quadrant whose cosine is 3sqrt(2)/2.

We have:

cos²θ + sin²θ = 1

Since sine is negative and cosine is positive, we know that:

sinθ = -sqrt(1 - cos²θ)

Substituting cosθ = 3√(2)/2, we get:

sinθ = -√(1 - (3√(2)/2)²) = -√(1 - 9/8) = -√(1/8) = -√(2)/2

Therefore, sin^(-1)(-3sqrt(2)/2) = -cos^(-1)(3sqrt(2)/2) + π/2.

Since cosine is positive in the fourth quadrant, we have:

cos⁻¹(3√(2)/2) = π/4

Substituting this value, we get:

sin⁻¹(-3√(2)/2) = -π/4 + π/2 = π/4

Therefore, sin⁻¹(-3√(2)/2) in radians is approximately -2.2143 radians.

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The length of wire used for the square is 0.25 meters and the length of wire used for the circle is 1 meter. To maximize the total area, the wire should be cut in half, with each piece having a length of 1 meter.

To minimize the total area of both figures and minimize the length of wire used, the wire should be cut in half, giving each piece a length of 1 meter.

For the square frame, we know that each side of the square is equal to the length of wire used to make it, so we can divide the 1 meter of wire in half to get 0.5 meters for each side of the square.

The perimeter of the circle is the length of wire used to make it, so we can use the remaining 1 meter of wire to find the radius of the circle:

2πr = 1

r = 1/(2π)

Using this radius, we can find the circumference of the circle and the length of wire used:

C = 2πr = 1 meter

Therefore, the length of wire used for the square is 0.5 meters and the length of wire used for the circle is 1 meter.

To maximize the total area, we need to cut the wire into two equal pieces, each with a length of 1 meter.

For the square frame, each side will have a length of 0.25 meters, which will give us a total area of 0.0625 square meters.

For the circle, the radius will be 1/(4π) meters, which will give us a circumference of 1/(2π) meters and a total area of π/(16) square meters.

Therefore, to maximize the total area, the wire should be cut in half, with each piece having a length of 1 meter.

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If John pours the partially filled bucket into an empty one, he would still have 29 full buckets and a bucket with 2/3 of its capacity filled.

In order to arrive at a solution, it is necessary to commence by reducing the fraction 1/1.5 into a more basic form.

Thus, we do this below:

1 ÷ 1.5 = 1 ÷ (3/2) = 1 × (2/3) = 2/3

So, John has 29 full buckets and another bucket that is 2/3 full.

If he pours the partially filled bucket into an empty one, he would still have 29 full buckets and a bucket with 2/3 of its capacity filled.

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John has 29 full buckets of water and another bucket that is 1/1.5 full. How many full buckets of water would he have if he pours the partially filled bucket into an empty one?

Answer:

x ≥ -5

Step-by-step explanation:

Since we see the dot is filled in, we know the sign is either ≤ or ≥. Then, we can see that x is greater than -5 as the arrow is pointing in the positive direction (to the right). Therefore, it would be x ≥ -5

The result of the row 1 multiplication by 1/4 is determined as  [¹/₂  0 ].

The resultant of the row multiplication in the surd is calculated by applying the following method;

row 1 in the given surds = [2 0]

To multiply row by 1/4, we will multiply each entity by 1/4 as shown below;

[2 0] x 1/4 = 1/4(2 0)

= [¹/₂  0 ]

Thus, the result of the row multiplication is determined by multiplying each entry in row 1, that 2, and 0 by 1/4.

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The formula for the linear function is f(p) = -50p + 1750. So, correct option is E.

To find the formula for the linear function from the given table, we need to determine the equation of a straight line that passes through the three given points. We can use the point-slope form of the equation of a straight line to solve for the slope and y-intercept.

Let's choose two of the given points, say (15, 1000) and (25, 500), to calculate the slope:

slope = (change in y)/(change in x)

= (500 - 1000)/(25 - 15)

= -50

Now, we can use the slope and one of the given points, say (15, 1000), to solve for the y-intercept using the point-slope form:

y - y₁ = m(x - x₁)

y - 1000 = -50(x - 15)

y - 1000 = -50x + 750

y = -50x + 1750

Therefore, the formula for the linear function is f(p) = -50p + 1750, which means that for each additional dollar increase in price per shirt, the number of shirts sold decreases by 50. Option (e) is the correct answer.

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The maximum voltage produced by the system is 12 volts.

The function given is:

[tex]v_{inst}(t) = 12 * sin(360 * 60 * 6.3 + 79)[/tex]

To find the maximum voltage produced by the system, we need to determine the maximum value of the sine function within the given range.

Let's focus on the argument of the sine function: 360 * 60 * 6.3 + 79.

First, calculate the value of the argument:

360 * 60 * 6.3 + 79 = 136080 + 79 = 136159

Now, substitute this value back into the sine function:

sin(136159)

The sine function has a periodicity of 360 degrees or [tex]2\pi[/tex] radians. Therefore, we can subtract multiples of 360 degrees from the argument without changing the value of the sine function. Let's find the nearest multiple of 360 degrees to 136159:

136159 ÷ 360 [tex]^\sim_\sim[/tex] 378.22

Since the quotient is not an integer, we can conclude that subtracting multiples of 360 degrees will not bring us closer to a maximum or minimum value of the sine function.

Therefore, to find the maximum voltage, we need to evaluate sin(136159) directly. However, calculating the sine function of such a large number is not practical or necessary. The sine function oscillates between -1 and 1, and the maximum value it can reach is 1.

So, regardless of the specific value of sin(136159), the maximum voltage produced by the system will be:

Maximum voltage = 12 * 1 = 12 volts.

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Answer:

100

Step-by-step explanation:

The number has the same digit in its hundreds place and its hundredths place. The digit in the hundreds place is 100 times greater than the digit in the hundredths place (https://ccssmathanswers.com/hundredth-place-in-decimals). Therefore, the value of the digit in the hundreds place is 100 times greater than the value of the digit in the hundredths place.

Therefore, the answer is 100.

Answer:

Step-by-step explanation:

To write the standard equation of a circle with its center in the fourth quadrant tangent to x=7, y=-4 and x=17, we can first find the center of the circle.

Since the center is in the fourth quadrant and tangent to x=7, y=-4 and x=17, the center must lie on the line x=12 (the midpoint between 7 and 17) and y=-4 (the point of tangency).

So the center of the circle is (12, -4).

Next, we need to find the radius of the circle. Since the circle is tangent to x=7 and x=17, the radius is the distance from the center to either x=7 or x=17.

The radius is thus 12 (the difference between 12 and 7) or 5 (the difference between 12 and 17).

So the standard equation of the circle is:

(x - 12)^2 + (y + 4)^2 = 25

Answer: each package weighs 3.25lb 

Step-by-step explanation:

looking at the weight of each package (3lb 4oz), we can convert the 4oz to pounds by dividing by 16oz/lb; 4/16 = 0.25lb 

The value of x in the circle is 4.2

From the question, we have the following parameters that can be used in our computation:

The circle

Using the intersecting chords equation, we have

(5x - 8) * 4 = (x + 1) * 10

When solved for x, we have

x = 4.2

Hence. the value of x is 4.2

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The value of x if the line BD is the perpendicular bisector of AC is 11.5

From the question, we have the following parameters that can be used in our computation:

The figure where the line BD is the perpendicular bisector of AC.

To calculate the value of x, we use the following equation by setting the line segments equal to each other

3(2x - 8) = 45

Divide both sides of the above equation by 3

2x - 8 = 15

So, we have the following equation

2x = 23

Divide both sides of the above equation by 2

x = 11.5

Hence, the calculated value of x is 11.5

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The fraction expression 2 1/2 - 4 1/4 when evaluated is -1 3/4

To solve 2 1/2 - 4 1/4, we need to convert the mixed numbers into improper fractions, then find a common denominator and subtract the two fractions.

First, we convert 2 1/2 and 4 1/4 into improper fractions:

2 1/2 = 5/2

4 1/4 = 17/4

Next, we find a common denominator. In this case, the smallest common denominator is 4:

5/2 = 10/4

17/4 = 17/4

Now we can subtract the fractions:

10/4 - 17/4 = -7/4

Finally, we can convert the resulting improper fraction back into a mixed number:

-7/4 = -1 3/4

Therefore, 2 1/2 - 4 1/4 = -1 3/4.

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12 - 2^2 x 2

---Remember: PEMDAS

---In this case exponents are first, then multiplication, then subtraction

12 - 4 x 2

12 - 8

4

Answer: 4

Hope this helps!

Answer: Since 1 and 2 have the same measure, angle CED is also equal to 1 and 2. Therefore, triangle CED and triangle CAB are similar by the Angle-Angle (AA) criterion.

Using the properties of similar triangles, we can set up the following proportion:

$\frac{CE}{CA}=\frac{CD}{CB}$

Substituting the given values:

$\frac{CE}{x+4}=\frac{x}{14}$

Cross-multiplying:

$14CE = x(x+4)$

$14CE=x^2+4x$

We also know that triangle ADE and triangle ABC are similar by the AA criterion. Therefore, we can set up the following proportion:

$\frac{DE}{AB}=\frac{AE}{AC}$

Substituting the given values:

$\frac{DE}{18}=\frac{AE}{x+4}$

Cross-multiplying:

$AE = 18\frac{DE}{x+4}$

Now, we can substitute the value of $AE$ in terms of $DE$ into the first equation:

$14CE=x^2+4x$

$14\frac{DE}{x+4}=x^2+4x$

$14DE=x^2+4x(x+4)$

$14DE=x^2+4x^2+16x$

$18x^2+16x-14DE=0$

We can now use the quadratic formula to solve for $x$:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-16\pm\sqrt{(16)^2-4(18)(-14DE)}}{2(18)}$

$x=\frac{-16\pm\sqrt{256+1008DE}}{36}$

Since $DC=x$, we can now use this equation to find the value of $DC$ for a given value of $DE$. For example, if $DE=5$, we have:

$DC=\frac{-16\pm\sqrt{256+1008(5)}}{36}$

$DC\approx 2.3$ or $DC\approx -3.1$

Since distance cannot be negative, we choose the positive solution:

$DC\approx 2.3$ units.

To find $DE$, we can substitute the value of $DC$ back into one of the earlier equations:

$\frac{CE}{x+4}=\frac{x}{14}$

$\frac{CE}{2.3+4}=\frac{2.3}{14}$

$CE\approx 1.34$ units

Now we can use the second similarity proportion to find $DE$:

$\frac{DE}{18}=\frac{AE}{x+4}$

$\frac{DE}{18}=\frac{18-1.34}{2.3+4}$

$DE\approx 3.64$ units

Therefore, $DC\approx 2.3$ units and $DE\approx 3.64$ units.

Step-by-step explanation: