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For k = 0 and k = 16, there are rational solutions to the quadratic equation [tex]x^{2} + kx + 4k = 0[/tex]

We are given a quadratic equation [tex]x^{2} + kx + 4k = 0[/tex]

An algebraic equation in x with a degree of 2 is known as a quadratic equation. It is written in the format [tex]a[/tex][tex]x^{2}[/tex] [tex]+ bx + c[/tex] = 0. To find out whether there exists two solutions, one solution, or no solution for a quadratic equation, we use the discriminant of the quadratic equation.

We will find the solutions to this quadratic equation with the help of discriminant formula

As we know from the equation that b = k, a = 1, and c = 4k.

[tex]b^2 - 4ac = 0[/tex]

[tex]k^2 - 4(4k) = 0[/tex]

[tex]k^2 - 16k = 0[/tex]

k (k-16) = 0

k = 0    or    k - 16 = 0

k = 0    or    k = 16

So, for k = 0 or k = 16 the equation [tex]x^{2} + kx + 4k = 0[/tex] has only one solution.

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The surface area of octagonal pyramid with height of 12 and a side length of 4.24 is 281.477 unit²

Height of octagonal pyramid = 12

Side length of octagonal pyramid = 4.14

The surface area of octagonal pyramid is  

SA = 2s²( 1 + √2) + 4sh

Here, s is side length of the octagonal pyramid = 4.14

h is height of the octagonal pyramid = 12

putting the values in the equation we get

SA = 2 × 4.14 ( 1 + √2 ) + 4 × 4.14 × 12

SA = 82.757 + 198.72

SA = 281.477

The surface area of octagonal pyramid is 281.477

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The angle in each quadrant with a common reference angle with 306° are

To find angles in each quadrant with a common reference angle with 306°, we first need to determine the reference angle for 306°.

Reference angle is the acute angle between the terminal side of an angle and the x-axis. We can find the reference angle for any angle θ by subtracting the nearest multiple of 180° from θ and taking the absolute value of the result. In this case:

|306° - 180°| = 126°

So, the reference angle for 306° is 126°.

Now, we can find an angle in each quadrant with a common reference angle of 126°:

1st quadrant: The angle with a reference angle of 126° in the 1st quadrant is simply 126°.

2nd quadrant: To find the angle with a reference angle of 126° in the 2nd quadrant, we need to subtract the reference angle from 180° (since all angles in the 2nd quadrant are between 90° and 180°).

180° - 126° = 54°

So, an angle with a reference angle of 126° in the 2nd quadrant is 54°.

3rd quadrant: To find the angle with a reference angle of 126° in the 3rd quadrant, we need to subtract the reference angle from 180° and then add 180° (since all angles in the 3rd quadrant are between 180° and 270°).

180° + 126° = 306°

So, an angle with a reference angle of 126° in the 3rd quadrant is 306°.

4th quadrant: To find the angle with a reference angle of 126° in the 4th quadrant, we need to subtract the reference angle from 360° (since all angles in the 4th quadrant are between 270° and 360°).

360° - 126° = 234°

So, an angle with a reference angle of 126° in the 4th quadrant is 234°.

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Answer:

Step-by-step explanation: The vertex is the point at the bottom if the parabola opens up and at the top if it opens at the bottom.

Answer:

8.19 units.

Step-by-step explanation:

I didn't use desmos, i completed the question with all steps and working and didn't require desmos. Hope this Helps. Question was solved using trignometric ratios.

Answer: x = -1, y = 6

Step-by-step explanation:

lets substitute the value of y from the first equation into the y in the second equation.

-2x + 4 = -3x + 3

4 - 3 = -3x + 2x

1 = -1x

x = -1

we know from before that y = -2x + 4

so y = -2(-1) + 4

y = 6

Given the scenerio in the picture about corn, the statement that is true looking at a significance level of 5% is The result is not statistically significant which implies that spraying the corn plants with the new type of fertilizer does increase the growth rate.

Looking at the statement "The result is not statistically significant,"this means that the p-value (probability value) of the test was greater than 0.05. It could have 0.15 oe 0.2.

When a test is greater than 0.05 or 5 % significance level, it shows that the what is happening to the corn (increase in growth rate) could have been as a result of chance alone.

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The sets of side lengths that could form a right triangle are 36-48-60 (option b) and 14-48-50 (option d).

To determine which of these sets of side lengths could form a right triangle, we will use the Pythagorean theorem (a² + b² = c²), where a and b are the shorter sides and c is the hypotenuse. Let's evaluate each option:

a) 4-7-10
Applying the Pythagorean theorem: 4² + 7² = 16 + 49 = 65, which is not equal to 10² (100). So, this set does not form a right triangle.

b) 36-48-60
Applying the Pythagorean theorem: 36² + 48² = 1296 + 2304 = 3600, which is equal to 60² (3600). So, this set does form a right triangle.

c) 6-10-14
Applying the Pythagorean theorem: 6² + 10² = 36 + 100 = 136, which is not equal to 14² (196). So, this set does not form a right triangle.

d) 14-48-50
Applying the Pythagorean theorem: 14² + 48² = 196 + 2304 = 2500, which is equal to 50² (2500). So, this set does form a right triangle.

In conclusion, the sets of side lengths that could form a right triangle are 36-48-60 (option b) and 14-48-50 (option d).

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A deposit of $2000 earning 4.2% simple interest for 3 years will have a balance of $2252. The estimated balance rounded to the nearest whole number is $2252.

To calculate the balance in the account after 3 years, we can use the formula

balance = principal x (1 + interest rate x time)

Plugging in the values, we get

balance = 2000 x (1 + 0.042 x 3)

balance = 2000 x (1 + 0.126)

balance = 2000 x 1.126

balance = 2252

Therefore, the balance in the account after 3 years is $2252.

As for the estimate, since the interest is simple, we can approximate it by multiplying the interest rate by the number of years and adding it to the principal. So, the estimate would be

estimate = principal x (1 + interest rate x time)

estimate = 2000 x (1 + 0.042 x 3)

estimate = 2000 x (1 + 0.126)

estimate = 2000 x 1.126

estimate = 2252

Rounding to the nearest whole number, the estimate is also $2252.

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The angles that belongs to the right angles category are:

KER must be a right angle because it is an angle formed between a tangent (KE) and a radius (AK) at the point of tangency (K). By the Tangent-Secant Theorem, it follows that the measure of the intercepted arc KR is equal to the measure of the angle ∠KER plus 90 degrees. Since KR is a diameter (and therefore a semicircle), its measure is 180 degrees. Therefore, ∠KER + 90 = 180, which implies that ∠KER = 90 degrees.

∠ARE must be a right angle because it is an inscribed angle that intercepts the diameter KR. By the Inscribed Angle Theorem, the measure of an inscribed angle is half the measure of its intercepted arc. Since KR is a diameter, the intercepted arc is the entire circle, which has a measure of 360 degrees. Therefore, ∠ARE = 360/2 = 180 degrees. Moreover, a diameter and a chord that contains the diameter must form a right angle at the point where they meet (in this case, point A). Hence, ∠ARE is a right angle.

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Image transcribed:

The figure below shows a circle with center A, diameter KR, and secants RE and RI. Which of the angles must be right angles? Select all that apply.

Q

E

R

K

D

∠KIR

∠ARD

∠KER

∠ARE

∠ERI

Answer:

Step-by-step explanation:

It's given that, Radius of the circle is 9 cm.

We know that Circumference of the circle is calculated as 2πr

where,

Substituting the required values,

Circumference = 2 × 3.14 × 9

= 6.28 × 9

= 56.52 cm

Hence the required circumference of the circle is 56.52 cm

The answer is not 9 > 6, as that is a comparison between two numbers, but rather g ≤ 6, as it sets a limit on the number of goldfish that can be in the tank.

The correct inequality that represents the situation is g ≤ 6. The problem states that the maximum number of goldfish that can live in a small tank is 6, meaning that the number of goldfish must be less than or equal to 6.

The symbol ≤ represents "less than or equal to", while the symbol > represents "greater than".

Therefore, the answer is not 9 > 6, as that is a comparison between two numbers, but rather g ≤ 6, as it sets a limit on the number of goldfish that can be in the tank.

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Answer:

k = 1

Step-by-step explanation:

We can use the table for g(x) = f(kx) to find the value of k.

Notice that when x = -2, we have g(-2) = f(k(-2)) = f(-2k) = 64. Similarly, when x = 2, we have g(2) = f(k(2)) = f(2k) = 64.

Using the fact that f(x) is a quadratic function, we can see that its axis of symmetry passes through the vertex at (0, 0), which means that the x-coordinate of the vertex is 0. This tells us that the coefficient of the x term in f(x) is 0, so the function can be written as f(x) = ax^2 + bx + c, where a is not equal to 0.

Using the points (−2,4), (−1,1), (0,0), (1,1), and (2,4), we can write a system of equations to solve for a, b, and c:

a(-2)^2 + b(-2) + c = 4

a(-1)^2 + b(-1) + c = 1

a(0)^2 + b(0) + c = 0

a(1)^2 + b(1) + c = 1

a(2)^2 + b(2) + c = 4

Simplifying and rearranging, we get:

4a - 2b + c = 4

a - b + c = 1

c = 0

a + b + c = 1

4a + 2b + c = 4

Substituting c = 0 into the system, we get:

4a - 2b = 4

a - b = 1

a + b = 1

4a + 2b = 4

Solving this system of equations, we get a = 1, b = -1, and c = 0.

Substituting these values into g(x) = f(kx), we get:

g(x) = f(kx) = x^2 - x

Substituting the values from the table into this equation, we get:

g(-2) = 4 = (-2)^2 - (-2) = 4k

g(2) = 4 = (2)^2 - (2) = 4k

Solving for k, we get k = 1 or k = -1/4.

However, we need to check which value of k satisfies all the points in between -2 and 2, so we can check g(-1) = 1 = (-1)^2 - (-1) = k, and g(1) = 1 = (1)^2 - (1) = k.

Thus, the value of k that satisfies all the points is k = 1, and therefore the answer is:

k = 1

We can use the information given to find the value of k.

Since the vertex of the quadratic function f(x) is at (0,0), we know that the equation for f(x) is in the form of f(x) = ax^2 for some constant a.

Using the point (-2, 4) on the graph of f(x), we can set up the equation 4 = 4a, which gives us a = 1.

So, the equation for f(x) is f(x) = x^2.

Now, we can use the table for g(x) = f(kx) to find the value of k.

When x = -2, we have g(-2) = f(k(-2)) = f(-2k) = 4k^2.

Similarly, when x = 2, we have g(2) = f(k(2)) = f(2k) = 4k^2.

We also know that g(0) = f(k(0)) = f(0) = 0, and g(-1) = f(k(-1)) = f(-k) = k^2 and g(1) = f(k(1)) = f(k) = k^2.

Using the values from the table, we can set up the following system of equations:

4k^2 = 64

k^2 = 16

0 = 0

k^2 = 16

The only solution that works for all of these equations is k = 4 or k = -4.

Therefore, the value of k is either k = 4 or k = -4.

The simplified form of the expression 3(w+11) / 6w  is w + 11 / 2w .

Simplifying expressions mean rewriting the same algebraic expression with no like terms and in a compact manner.

In other words, we have to expand any brackets, next multiply or divide any terms and use the laws of indices if necessary, then collect like terms by adding or subtracting and finally rewrite the expression.

Therefore, let's simplify the expression:

3(w+11) / 6w

Hence, let's divide both the numerator and denominator by 3

Therefore,

3(w+11) / 6w =  w + 11 / 2w

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Answer:

The numerical values of the circumference and area are equal

Step-by-step explanation:

Circumference: 12.57

Area: 12.57

12.57=12.57

Hope this helps! :)

The t critical value at 29 degrees of freedom and 0.01 level of significance is 2. 46

Using Critical value calculator we calculate the values.

a) at n = 10

Therefore degrees of freedom is = n - 1= 9, So therefore at 9 degrees of freedom and 0.01 level of significance, t critical value is 2.82

b) at n= 20

Degrees of freedom is 19.

The t critical value at 19 degrees of freedom and 0.01 level of significance is 2.54

c) at n = 30

Degrees of freedom is 29.

So therefore t critical value at 29 degrees of freedom and 0.01 level of significance is 2. 46

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The weight of the contents in the container is approximately 873 pounds.

A shipping container is in the shape of a right rectangular prism with a length of 7 feet, a width of 14 feet, and a height of 13.5 feet.

To find the volume of the container, we multiply the dimensions: 7 ft × 14 ft × 13.5 ft = 1,323 cubic feet. The container is completely filled with contents that weigh, on average, 0.66 pound per cubic foot.

To find the weight of the contents in the container, we multiply the volume by the average weight: 1,323 ft³ × 0.66 lb/ft³ ≈ 873.18 pounds.

Rounded to the nearest pound, the weight of the contents in the container is approximately 873 pounds.

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With the given pay increase Daniel will earn a total of $185,141.90 in 4 years .

To find out how much Daniel will earn in 4 years with a starting salary of $42,000 and a 6.5% pay increase every year, follow these steps:

1. Calculate the annual salary for each year by applying the percentage increase.
2. Sum up the salaries for all 4 years.

Step 1: Calculate the annual salary for each year
Year 1: $42,000
Year 2: $42,000 * (1 + 6.5%) = $42,000 * 1.065 = $44,730
Year 3: $44,730 * (1 + 6.5%) = $44,730 * 1.065 = $47,656.95
Year 4: $47,656.95 * (1 + 6.5%) = $47,656.95 * 1.065 = $50,754.95

Step 2: Sum up the salaries for all 4 years
Total earnings = $42,000 + $44,730 + $47,656.95 + $50,754.95 = $185,141.90

Daniel will earn a total of $185,141.90 in 4 years with the given pay increase.

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Note that the light is about 9.17 x 10³ times faster than sound. See the explanation below.

To arrive a the above, we only need to simplify Jakes observation as follows

[tex]\frac{1.1 * 10^{9} km/h }{1.2 * 10^{3}km/h }[/tex]

dividing the coefficients

1.1/1.2 = 0.91666666666

0.91666666666 x 10 ⁹⁻³

= 9.1666667 x 10 ⁵

further simplified, we have
9.17 x 10³

Thus, we can summarize that light is about 9.17 x 10³ faster than the speed of sound going by Jake observation.

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Full Question:

Jake noted that speed of light is approximately 1.1 × 10⁹ km/h;

the speed of sound is approximately 1.2 x 10³ km/h; and

11 + 12 = 0.916.

Using Jake's figures how many times faster is light than speed?

Write your answer in standard form.

The cost of the stock, including the broker's fee, is $50,454.30.

The cost of the stock can be found by multiplying the number of shares purchased by the price per share. In this case, the investor purchased 500 shares of Exxon-mobil stock at $98.93 per share, so the cost of the stock can be calculated as follows:

Cost of stock = Number of shares × Price per share

Cost of stock = 500 × $98.93

Cost of stock = $49,465

However, the broker charges 2% of the cost of the stock, which is an additional fee that needs to be added to the total cost. To find the broker's fee, we can simply multiply the cost of the stock by 2%:

Broker's fee = 2% × Cost of stock

Broker's fee = 2% × $49,465

Broker's fee = $989.30

Therefore, the total cost of the stock, including the broker's fee, is:

Total cost of stock = Cost of stock + Broker's fee

Total cost of stock = $49,465 + $989.30

Total cost of stock = $50,454.30

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The number of 6-card hands  in which at least one card from each suit is equal to 8,184,220.

Total number of 6-card hands that can be formed from a deck of 60 cards is,

Using combination formula,

C(60, 6) = 50,063,860

Now, subtract the number of 6-card hands that do not contain at least one card from each suit.

There are 5 ways to choose the suit that will be missing from the hand.

Once this suit is chosen, there are 48 cards remaining in the other suits.

Choose 6 cards from this set, so the number of 6-card hands that do not contain any cards from the chosen suit is,

C(48, 6) = 12,271,512

Overcounted the number of hands that are missing more than one suit.

There are C(5, 2) ways to choose 2 suits that will be missing from the hand.

Once these suits are chosen, there are 36 cards remaining in the other 3 suits.

Choose 6 cards from this set, so the number of 6-card hands that do not contain any cards from the chosen suits is,

C(36, 6) = 1,947,792

We cannot have a 6-card hand that is missing more than 2 suits.

3 suits with no cards in the hand, which is not allowed.

Number of 6-card hands that have at least one card from each suit is,

C(60, 6) - 5×C(48, 6) + C(5, 2)×C(36, 6)

=50,063,860 - 5×  12,271,512 + 10 × 1,947,792

= 50,063,860 -61,357,560 + 19,477,920

= 8,184,220

Therefore, there are 8,184,220 of 6-card hands that have at least one card from each suit.

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Answer:

E. 10

Step-by-step explanation:

To solve the equation x + 50 = 60, we need to isolate x on one side of the equation. Subtracting 50 from both sides, we get:

x + 50 - 50 = 60 - 50

x = 10

Therefore, the solution to the equation is x = 10. Checking the answer choices, we see that E. 10 is the only number that belongs to the solution set. Therefore, the answer is:

E. 10

The equation that could represent each of the graphed polynomial function include the following:

First graph: y = x(x + 2)(x - 3)

Second graph: y = x⁴ - 5x² + 4

In Mathematics and Geometry, a polynomial graph simply refers to a type of graph that touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.

Generally speaking, the zero of a polynomial function simply refers to a point where it crosses or cuts the x-axis of a graph.

By critically observing the graph of the polynomial function shown in the image attached above, we can logically deduce that the first graph has a zero of multiplicity 1 at x = 2 and zero of multiplicity 1 at x = -3.

Similarly, we can logically deduce that the second graph has a zero of multiplicity 2 at x = 2 and zero of multiplicity 2 at x = -2.

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Flo ate more of the sandwich than Arnie.

Option A is the correct answer.

We have,

We need to compare the values 3/4 and 2/3 to determine which fraction represents a larger amount of sandwiches eaten.

To make the fractions comparable, we need to find a common denominator.

The least common multiple of 4 and 3 is 12.

So we can rewrite 3/4 and 2/3 with 12 as the denominator:

3/4 = 9/12

2/3 = 8/12

Comparing these fractions, we see that 9/12 (or 3/4) is greater than 8/12

(or 2/3).

Therefore,

Flo ate more of the sandwich than Arnie.

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Answer:

BC= 47.424

I believe that’s correct, but if you really need an answer just get a triangle calculator

Answer:

-12+3(-11)-40-10

Step-by-step explanation:

Answer:

Step-by-step explanation:

-12+12-45-40+1

0-85+1

-84

An expression for the sequence of operations described "Subtract three from the product of seven and eight." is (7 × 8) - 3.

In order to evaluate and solve this expression, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right. Lastly, the mathematical operations of addition or subtraction would be performed from left to right.

Based on the information provided, we have the following mathematical expression:

Expression: (7 × 8) - 3

56 - 3

53

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Marcus is incorrect. The percentage increase in the time he spent doing homework this week compared to last week is 10%.

To determine if Marcus is correct, we need to calculate the percentage increase in the time he spent doing homework this week compared to last week.

First, we calculate the difference in hours:

11 hours - 10 hours = 1 hour

Then, we calculate the percentage increase:

(1 hour / 10 hours) x 100% = 10%

Therefore, Marcus is incorrect. The percentage increase in the time he spent doing homework this week compared to last week is 10%, not 110%.

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