2. The Table Represents Equivalent Ratios. What Is The Missing Value Of X In The Table? (1 Point)xy8 (2024)

The correct statements regarding the solutions of the quadratic function is given as follows:

Two complex solutions.

What is the discriminant of a quadratic equation and how does it influence the solutions?

A quadratic equation is modeled by the general equation presented as follows:

y = ax² + bx + c

The discriminant of the quadratic function is given by the equation as follows:

Δ = b² - 4ac.

The numeric value of the coefficient and the number of solutions of the quadratic equation are related as follows:

Δ > 0: two real solutions.Δ = 0: one real solution.Δ < 0: two complex solutions.

The function for this problem is given as follows:

y = 2x² - 8x + 10.

The coefficients are given as follows:

a = 2, b = -8 and c = 10.

Hence the discriminant is given as follows:

Δ = (-8)² - 4 x 2 x 10

Δ = 64 - 80

Δ = -16.

Negative discriminant, hence the equation has two complex solutions.

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The trigonometric ratios for angle a are given as follows:

[tex]\sin{a} = \frac{3}{\sqrt{13}}[/tex][tex]\cos{a} = \frac{2}{\sqrt{13}}[/tex]tan(a) = 3/2.

What are the trigonometric ratios?

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.

For this problem, the hypotenuse is of [tex]3\sqrt{13}[/tex], while the side lengths relative to angle A are given as follows:

Opposite: 9.Adjacent: 6.

Hence the trigonometric ratios are given as follows:

[tex]\sin{a} = \frac{3}{\sqrt{13}}[/tex][tex]\cos{a} = \frac{2}{\sqrt{13}}[/tex]tan(a) = 3/2.

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1. The volume of the pyramid = 12 mm³.

2. Slant height (x) x ≈ 4.3 mm

3. Surface area of square pyramid = 86.4 mm²

How to Find the Volume of a Square Pyramid?

1. The volume of the pyramid (V) = 1/3*a²h, where:

a is the base edge = 3 mm

h is the height = 4 mm

Plug in the values:

The volume of the pyramid (V) = 1/3*3²*4 = 12 mm³.

2. Slant height (x) = √(1.5² + 4²)

x ≈ 4.3 mm

3. Surface area of square pyramid = 6bs + b² = 6(3)(4.3) + 3²

= 86.4 mm²

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well, we know the number of bacteria is decreasing, so we can use a Decay equation for that, with a 75% rate of decay.

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &200000\\ r=rate\to 75\%\to \frac{75}{100}\dotfill &0.75\\ t=hours \end{cases} \\\\\\ A = 200000(1 - 0.75)^{t} \implies A = 200000(0.25)^t[/tex]

Elimination is the best method for solving this system of equations since we can eliminate the x-term by adding the two equations together.

Option C is the correct answer.

We have,

Elimination is the best method for solving this system of equations since we can eliminate the x-term by adding the two equations together.

This will give us a single equation in y, which we can then solve for y, and use to find the value of x.

In this case, we can eliminate the x term by adding the equations.

3x + 2y = 4

-3x + y = 2

If we add the two equations, the x term will cancel out:

3x + 2y = 4

(-3x + y = 2)

0x + 3y = 6

Simplifying, we get:

3y = 6

y = 2

Now that we have found the value of y, we can substitute it into one of the equations to find the value of x.

Let's use the second equation:

-3x + y = 2

-3x + 2 = 2

-3x = 0

x = 0

Therefore, the solution to the system of equations is (x, y) = (0, 2).

Thus,

Elimination is the best method for solving this system of equations since we can eliminate the x-term by adding the two equations together.

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Answer: 5/21

Step-by-step explanation: it just is

Answer: The simple interest on a sum of money invested at 3% per annum for 2 1/2 years is N9.225, and the principal is N3,000.

Step-by-step explanation:

We can use the formula for simple interest:

I = P * r * t

where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

Given that the interest is N123, the interest rate is 3% per annum, and the time is 2 1/2 years, we can plug these values into the formula and solve for the principal:

123 = P * 0.03 * 2.5

Simplifying, we get:

123 = 0.075P

P = 123 / 0.075

P ≈ 1,640

Therefore, the principal is approximately N1,640.

However, this principal value does not correspond to the given interest amount of N9.225. To obtain the correct principal, we need to use the correct interest amount:

We can convert the time of 2 1/2 years to 5/2 years, and use the formula for simple interest:

I = P * r * t

where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

Given that the interest is N9.225, the interest rate is 3% per annum, and the time is 5/2 years, we can plug these values into the formula and solve for the principal:

9.225 = P * 0.03 * 5/2

Simplifying, we get:

9.225 = 0.0375P

P = 9.225 / 0.0375

P = 246

Therefore, the principal is N246.

The volume of a rectangular prism is given by the formula V = lwh, where l, w, and h are the length, width, and height of the prism, respectively.

In this case, the width is x^2 inches, the length is xy^2 inches, and the height is xy inches.

Substituting these values into the formula, we get:

V = (xy^2)(x^2)(xy)

Simplifying, we get:

V = x^4y^3

Therefore, the expression that represents the volume of the rectangular prism in cubic inches is x^4y^3.

Answer:

0.90

Step-by-step explanation:

Just like a decimal to a percentage number, you must multiply by 100. By converting a percentage number to a decimal point, you must divide it by 100. Which means, the decimal must move 2 times.

For example,

0.90 x 100 = 90%

This is decimal to percentage number, but in this case it is percentage to decimal.

90%.

Since the number ended at 0, put the decimal there and move it 2 times to get to your decimal point.

.90 = 0.90

There you'll get your answer! ^^

90% = 0.90

The y-values are 5, 2, 1, 2, 5, 10 and 17.

Given that an equation of a curve, y = x²+1, we need to find the values of the y-intercept corresponding to the given x-intercept,

So,

y = x²+1

Putting the values of x,

x = -2,

y = (-2)²+1

y = 5

(-2, 5)

x = -1

y = (-1)²+1

y = 2
x = 0,

y = (0)²+1

y = 1

x = 1

y = 2

x = 2,

y = 2²+1

y = 5

x = 3,

y = 3²+1

y = 10

when x = 4,

y = 4²+1

y = 17

Hence, the y-values are 5, 2, 1, 2, 5, 10 and 17.

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The length of the rectangle is 43 inches.

The width of the rectangle is 18 inches.

Given that,

The length of a rectangle is seven more than double the width.

Let width = x

Length = 7 + 2x

Perimeter of the rectangle = 122 inches

The formula to find the perimeter of a rectangle is,

Perimeter = 2 (length + width)

Substituting,

122 = 2 (7 + 2x + x)

61 = 7 + 3x

3x = 54

x = 18

Width = 18 inches

Length = 7 + 2x = 7 + 36 = 43 inches

Hence the length and width are 43 inches and 18 inches respectively.

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The graph of f(x) = x(x+5)(x+3) / (x+3)(x+5) bears resemblance to the line y=x since both plots share similar linear characteristics.

How to explain the information

Both the numerator and denominator of f(x) = x(x+5)(x+3) / (x+3)(x+5) cancel out the factors (x+3) and (x+5), giving us a simplified expression for the function, f(x) = x.

A line with a slope of 1 passes through the origin in an upward direction. When we examine the graph of y=x, which is a straight line passing through the origin with a slope of 1, it becomes apparent that adding 1 to x also adds 1 to y.

Since the simplified expression is merely f(x) = x, we can deduce that the graph of this function follows a linear path passing through the origin with a slope of 1.

In conclusion, the graph of f(x) = x(x+5)(x+3) / (x+3)(x+5) bears resemblance to the line y=x since both plots share similar linear characteristics.

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Answer:

w(w + 4) = 117

w^2 + 4w = 117

w^2 + 4w - 117 = 0

(w - 9)(w + 13) = 0

w = 9 meters

The width of the rectangle is 9 meters, and the length of the rectangle is 13 meters.

The expression 7/12x - y/6x² in its simplest form is (7x - 2y)/(12x²).

We have,

To simplify the expression 7/12x - y/6x², we need to find a common denominator for the two terms.

The common denominator is 12x^2.

Multiplying the first term by x/x and the second term by 2/2, we get:

(7x)/(12x²) - (2y)/(12x²)

Combining the two terms, we get:

(7x - 2y)/(12x²)

Therefore,

7/12x - y/6x² in its simplest form is (7x - 2y)/(12x^2).

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The mean of the data set is 3.33.

The variance of the data set is 0.47.

We have,

To find the mean of the data set,

We need to add up all the numbers and divide by the total number of values:

Mean = (2 + 2 + 3 + 3 + 3 + 4 + 4 + 4 + 4) / 9

= 3.33 (rounded to two decimal places)

To find the variance,

We need to first find the squared difference between each value and the mean:

(2 - 3.33)^2 = 1.11

(2 - 3.33)^2 = 1.11

(3 - 3.33)^2 = 0.11

(3 - 3.33)^2 = 0.11

(3 - 3.33)^2 = 0.11

(4 - 3.33)^2 = 0.44

(4 - 3.33)^2 = 0.44

(4 - 3.33)^2 = 0.44

(4 - 3.33)^2 = 0.44

Next, we need to find the average of these squared differences:

Average of squared differences

= (1.11 + 1.11 + 0.11 + 0.11 + 0.11 + 0.44 + 0.44 + 0.44 + 0.44) / 9

= 0.47 (rounded to two decimal places)

Thus,

The mean of the data set is 3.33.

The variance of the data set is 0.47.

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The correct statement about the product of 5/12 and 7 is given as follows:

C. The product is greater than 5/12 but less than 7.

How to calculate the product?

The multiplication operation for this problem is given as follows:

5/12 x 7.

The factors of the operation are given as follows:

5/12 and 7.

When two fractions multiply each other, the product is given by the multiplication of the numerators divided by the multiplication of the denominators, hence:

5/12 x 7 = (5 x 7)/(12 x 1) = 35/12.

35/12 is a number close to 3, which is:

Greater than 5/12.Less than 7.

Hence option C is the correct statement.

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The inverse of the given function include the following: A. G⁻¹(x) = (x + 2)/5

What is an inverse function?

In Mathematics and Geometry, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).

In this exercise, you are required to determine the inverse of the function f(x). This ultimately implies that, we would have to swap (interchange) both the independent value (x-value) and dependent value (y-value) as follows;

g(x) = y = 5x - 2

x = 5y - 2

5y = x + 2

By dividing all through by 5, we have;

G⁻¹(x) = y⁻¹ = (x + 2)/5

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Answer:

The answer to your problem is, A. 5/2 and 25/4

Step-by-step explanation:

In the problem the twosimilarfigures, with side lengths 30 yds and 12 yds.

In order to solve the problem we need to find theratioof theperimetersand the ratio of theareasof the larger figure to the smaller figure.

Using this information we know the the ratio of theperimeterof similar figure is equal to thescale factorand the ratio of the areas equal to thesquareof the scale factor.

the scale factor = 30/12 = 5/2

the ratio of theperimeter= 5/2

the ratio of theareas= (5/2)² = 25/4

Thus the answer to your problem is, A. 5/2 and 25/4

If total sales including tax are $2739.45 , the portion that is the tax amount is $155.06. So, correct option is C.

To find the portion that is the tax amount, we need to first determine the portion of the total sales that is the cost of the item before taxes. To do this, we can use the fact that the sales tax is 6%, which means that the total sales including tax is 106% of the cost before taxes.

Thus, we can set up the equation:

total sales including tax = cost before taxes + tax amount

Or, in terms of percentages:

106% cost before taxes = cost before taxes + tax amount

Simplifying this equation, we get:

0.06 cost before taxes = tax amount

Now we can substitute the given information into this equation. If total sales including tax are $2739.45, then the cost before taxes is:

cost before taxes = total sales including tax / 1.06

cost before taxes = $2584.39

Finally, we can calculate the tax amount:

tax amount = 0.06 * $2584.39

tax amount = $155.06

Therefore, the answer is option C, $155.06.

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Answer:

C -1

Step-by-step explanation:

in such a case the simplest way is to simply try the 4 numbers and see :

x² - 3x - 4 = |x + 3| - 2

x² - 3x - 2 = |x + 3|

A x = -4

(-4)² - 3×-4 - 2 = |-4 + 3|

16 + 12 - 2 = 1

26 = 1

wrong.

B x = -3

(-3)² - 3×-3 - 2 = |-3 + 3|

9 + 9 - 2 = 0

16 = 0

wrong.

C x = -1

(-1)² - 3×-1 - 2 = |-1 + 3|

1 + 3 - 2 = 2

2 = 2

correct.

D x = 4

4² - 3×4 - 2 = |4 + 3|

16 - 12 - 2 = 7

2 = 7

wrong.

7. Radius of circle P = 2 Radius of circle Q = 1

Coordinates of the point of tangency (4,2)

The equation of the tangency line is x = 4

8. AB is not a tangent. BC² ≠ AB² + AC²

9. The three radii of the circle are; CB, CF and CD

A diameter of the circle is BD

A tangent of the circle is GE

A chord of the circle is BD

A secant of the circle is AD

A point of tangency is F

How do we find the radius of a circle?

7. To find the radius, identify the diameter of the circle. For the diagram, it can be said that the diameter of the circle P is 4.

The radius then is 4/2 = 2.

The radius of circle q is 2/2 = 1

You could also use the formula

Distance = sqrt((x2 - x1)² + (y2 - y1)²)

8. √4² + √12² = √160

√13 = 169

Therefore AB is not tangent. It is less than BC

9. The line that cuts the circle into two halves is the diameter. The lines than further cuts the diameter into equal parts are the radii's

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Let's call the number "x".

The sentence "7 times a number is 30 greater than the sum of twice the number and 5" can be written as:

7x = 2x + 5 + 30

Simplifying the right side of the equation:

7x = 2x + 35

Subtracting 2x from both sides:

5x = 35

Dividing both sides by 5:

x = 7

Therefore, the number is 7.

The length x in the similar triangle is 7.06 units.

How to find the side of similar triangle?

Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other.

Therefore, let's use the similarity of the triangle to find the value of x in the triangle.

Hence, using the proportion,

y / 8 = 8 / 17

cross multiply

17y = 64

y = 64 / 17

y = 3.76470588235

y = 3.76

Therefore,

17 - 3.76 = 13.24

Hence,

13.24 / x = x / 3.76

cross multiply

x² = 49.7824

x = √49.7824

x = 7.05566439111

Hence,

x = 7.06 units

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The formula for the volume of a rectangular prism is:

V = l x w x h

where V is the volume, l is the length, w is the width, and h is the height.

We know that the volume of Caleigh's jewelry box is 14 cubic inches, and the area of the base is 7 square inches. Since the base of the box is a rectangle, we can use the formula for the area of a rectangle to find the length and width of the base:

A = l x w

7 = l x w

We don't know the exact values of l and w, but we do know that their product is 7.

Now we can use the formula for the volume of a rectangular prism to find the height:

14 = l x w x h

We know that l x w = 7, so we can substitute 7 for l x w:

14 = 7 x h

Dividing both sides by 7 gives:

h = 2

Therefore, the height of Caleigh's jewelry box is 2 inches.

Step-by-step explanation:

r=26

t=3

d=rt

d=26×3

d=78

The value of x from the given isosceles triangle is 5.6 units.

Given that, the measure of equal sides of an isosceles triangle is 6 units and the base measures 5.9 units.

Draw perpendicular bisector to base, so we get halves as 5.9/2 =2.95

Let the length of perpendicular bisector be x.

By using Pythagoras theorem, we get

6²=2.95²+x²

36=8.7025+x²

x²=36-8.7025

x²=27.2975

x=5.2 units

We know that, sinθ=Opposite/Hypotenuse

sin68°=5.2/x

x=5.6 units

Therefore, the value of x from the given isosceles triangle is 5.6 units.

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all

Gina wants to go to the water park with her friends. They have a total of www dollars to buy 555 tickets. Each ticket costs 151515 dollars.

Select the equation that matches this situation.

Choose 1 answer:

Choose 1 answer:

(Choice A) 5 = 15 \times w5=15×w5, equals, 15, times, w

A

5 = 15 \times w5=15×w5, equals, 15, times, w

(Choice B) w = 15 +5w=15+5w, equals, 15, plus, 5

B

w = 15 +5w=15+5w, equals, 15, plus, 5

(Choice C) w = 5 \times 15w=5×15w, equals, 5, times, 15

C

w = 5 \times 15w=5×15

Answer:

less than 60 is 59 and greater than 60 is 61

Answer:40 and 20

Step-by-step explanation: Mathematically the first fill in the blank can be any number less than 60 here in I have taken it as 40.In the second fill in the blank the it can be any number less than 40 so 20 can be answer I hv chosen here.