Which of the equations below could be the equation of this parabola?
10+
(0, 0)
10
Vertex
-10
O A. x = 3y2
B. y = 3x2
O C. X=-3y2
D. y = -3x2

ANSWER

EXPLANATION

To graph the solutions of a system of inequalities we have to draw the solutions for each inequality.

For the first one we have y<2x+7, so we have to draw a dashed line y = 2x+7. It has to be dashed because the solutions don't include the points on the line. The solutions of this inequality are all the points below the line:

THen, for the second inequality, we have y≥-5x-4 so we have to draw a continuous line y = -5x - 4 because in this case the solutions do include the points on the line. Then the other solutions are all the points above this line (including the line):

If we graph the two of them in the same graph, the solutions to the system are all the points where the two shaded areas intersect:

The value of the function (f-g)(x)=\(x-4x^{2} -x^{3} -3\).

What is a function?

A function is defined as the relationship between input and output, where each input has exactly one output. The inputs are the elements in the domain and the outputs are elements in the co-domain.

f(x)= x¹ - x² +9

g(x) = x³ + 3x² + 12

To find (f-g)(x):

The operations on functions are as easy as the operations on numbers or polynomials.

We have to subtract the functions to find the above mentioned operation.

(f-g) (x)= f(x)-g(x)

          = (x¹ - x² +9)-(x³ + 3x² + 12)

The minus will change the signs of function g.

          = \(x-x^{2} +9-x^{3}-3x^{2} -12\)

          =\(x-4x^{2} -x^{3} -3\)

Hence, the value of the function (f-g)(x)=\(x-4x^{2} -x^{3} -3\)

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Answer:

let Elijah age be a

Then

2*a + 17 =47

2a=47-17

2a=30

a=15

Step-by-step explanation:

The linear function that describes the distance (in miles) is therefore y = 65x + 80

We have to find the slope and the intercept in other to get the linear function

The data points are:

(1, 145) and (3, 275).

m = (y2 - y1) / (x2 - x1)

fixing the data points we have

m = (275 - 145) / (3 - 1)

= 130 / 2

= 65

y = mx + b

(1, 145):

145 = 65(1) + b

b = 145 - 65

= 80

y intercept is 80

The linear function is therefore y = 65x + 80

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Step-by-step explanation:

a = k/m    or       ma = k    

using 4 and 9     4* 9 = k = 36

then the equation becomes:

    ma = 36    

  using a = 6

      6 * m = 36     shows m = 6 kg

Hello,

Step-by-step explanation:

\(f(x) = ln(x) {}^{4} \)

\((ln(u)') = \frac{u'}{u} \)

\(f'(x) = \frac{4ln {}^{} (x) {}^{3} }{x} \)

\(f'(10) = \frac{4ln {}^{} (10) {}^{3} }{10} = \frac{12ln(x)}{x} \)

\(f(10) = ln(10) {}^{4} \)

\(y = \frac{12ln(x)}{x} (x - 10) + 4ln(10)\)

\(y = f'(a)(x - a) + f(a)\)

The trigonometric ratio for the cosine of the angle W derived as 48.18712, is equal to 0.6667.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

cos W = 10/15 {adjacent/hypotenuse}

cos W = 2/3

W = cos⁻¹(2/3) {cross multiplication}

W = 48.18712

cos W = cos 48.18712

Therefore, the cosine of the angle W is equal to using the trigonometric ratio.

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Answer:

Whats? explication?? khe??

Answer:

Step-by-step explanation:

Answer:

Contestant k

Step-by-step explanation:

I did this on Khan Academy

Answer:b

Step-by-step explanation:

Hello!

x² - 5x + 6

= (x² - 2x) + (-3x + 6)

= x(x - 2) - 3(x - 2)

= (x - 2)(x - 3)

Step-by-step explanation:

\( {x}^{2} - 5x - 2 = 0 \\ a = 1 \: and \: b = - 5 \: and \: c = - 2 \\ x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} \\ x = \frac{ - ( - 5)± \sqrt{ {( - 5)}^{2} - (4 \times 1 \times - 2)} }{(2 \times 1)} \\ x = \frac{5± \sqrt{33} }{2} \\ either : x = \frac{5 + \sqrt{33} }{2} \: or \: \frac{5 - \sqrt{33} }{2} \\ x = 5.4 \: or \: - 0.4\)

The exact solutions of the equation x² - 5x - 2 = 0 are:

x = (5 + √(33)) / 2

x = (5 - √(33)) / 2

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We also find the solution in a system of equations using the substitution or elimination method.

Example:

2x + 4 = 8

The solution is x = 2.

We have,

The quadratic formula is:

x = (-b ± √(b² - 4ac)) / 2a

For the equation x² - 5x - 2 = 0, we have:

a = 1, b = -5, c = -2

Substituting these values into the quadratic formula, we get:

x = (-(-5) ± √((-5)² - 4(1)(-2))) / 2(1)

Simplifying the expression inside the square root:

x = (5 ± √(33)) / 2

Therefore,

The exact solutions of the equation x² - 5x - 2 = 0 are:

x = (5 + √(33)) / 2

x = (5 - √(33)) / 2

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Answer:

11x+6

Step-by-step explanation:

Using FOIL

(x+1)-(-2x-5)-original

F-first=(x+2x)=3x

O-outside=(x+5)=5x

I-inside=(1+2x)=3x

L-last=(1+5)=6

11x+6

Answer:

8/27.

Step-by-step explanation:

Given expression: \((2/3)^3\)

To correctly simplify this expression, you must first understand the role of exponents and base numbers.

The base number is the number being multiplied.

The exponent tells the base number how many times it should be multiplied by itself.

In this case, 2/3 is the base number and 3 is the exponent.

Exponential notations will always be written like this: \(x^n\)

\(x-base\)

\(n-exponent\)

Now that we know the roles of the exponent and base number, we can correctly simplify this expression.

\((2/3)^3\)

\(=2/3*2/3*2/3\)

\(=8/27\)

\(\to \ (2/3)^3=8/27\)

Therefore, the value of \((2/3)^3\) is 8/27.

Answer:

$512

16g+17n= m

Step-by-step explanation:

Multiply 16 and 15 to represent the amount of money from working in the grocery store and 17 and 16 to represent the money from the nusery home. Add them to get 512.

Quadrilateral JKLM has sides with equal lengths (√85), and the slopes of opposite sides are equal. However, it is not a special type of quadrilateral like a rectangle or a square.

To describe quadrilateral JKLM, let's first plot the given points J(9, 7), K(2, 1), L(0, -8), and M(7, -2) on a coordinate plane:

J(9, 7) K(2, 1)

L(0, -8)   M(7, -2)

To find the slopes and lengths of each side of the quadrilateral, we can use the distance formula and the slope formula.

Slope of JK:

Slope (m) = (change in y) / (change in x)

m(JK) = (7 - 1) / (9 - 2) = 6/7

Length of JK:

Length (d) = √[(x2 - x1)^2 + (y2 - y1)^2]

d(JK) = √[(9 - 2)^2 + (7 - 1)^2] = √(49 + 36) = √85

Slope of KL:

m(KL) = (-8 - 1) / (0 - 2) = -9/2

Length of KL:

d(KL) = √[(0 - 2)^2 + (-8 - 1)^2] = √(4 + 81) = √85

Slope of LM:

m(LM) = (-2 - (-8)) / (7 - 0) = 6/7 (same as slope of JK)

Length of LM:

d(LM) = √[(7 - 0)^2 + (-2 - (-8))^2] = √(49 + 36) = √85

Slope of MJ:

m(MJ) = (7 - (-2)) / (9 - 7) = 9

Length of MJ:

d(MJ) = √[(7 - 9)^2 + (-2 - (-8))^2] = √(4 + 36) = √40

Based on the calculations, we can describe quadrilateral JKLM as follows:

The slope of JK and LM is 6/7.

The slope of KL is -9/2.

The slope of MJ is 9.

The length of each side (JK, KL, LM, MJ) is √85.

The quadrilateral is not a rectangle or a square since the slopes of opposite sides (JK and LM) are not perpendicular.

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Answer:

Step-by-step explanation:

a) 126 122 118 114 110, 106, 102, 98

Hint: ( Subtract 4 from each numbers to get the next)

b) -1, 3 , 7, 11 , 15,  19, 23, 27

Hint: ( Add all through by 4)

c)  1, 3, 9, 27, 81, 243, 729

Hint: ( Multiply through by 3)

d) 80, 20 , 5, 1.25, 0.3125, 0.078125, 0.0195

Hint; (Divide all through by 4)

Answer:

11

Step-by-step explanation:

Substituting the values of x, y, and z into the expression, we get:

2x² - y + 2(z-1) = 2(2)² - 3 + 2(4-1)

= 2(4) - 3 + 2(3)

= 8 - 3 + 6

= 11

Therefore, if x = 2, y = 3, and z = 4, then the value of the expression 2x² - y + 2(z-1) is 11.

Answer:

11

Step-by-step explanation:

if x = 2, y = 3, and z = 4.

2x²-y + 2(z-1)

Substituting the given values of x, y, and z, we get:

2x² - y + 2(z-1) = 2(2)² - 3 + 2(4-1)

= 2(4) - 3 + 2(3)

= 8 - 3 + 6

= 11

Therefore, the value of the expression when x = 2, y = 3, and z = 4 is 11.

BODMAS (Brackets, Order, Division, Multiplication, Addition, Subtraction) is used to determine the sequence of operations in a mathematical expression. It is used to avoid confusion and ensure that everyone obtains the same answer from a mathematical expression. The rule states that the operations inside the brackets must be done first, followed by orders, then division and multiplication (from left to right), and finally addition and subtraction (from left to right).

The number of minutes spent higher than 38 meters above the ground on the Ferris wheel ride is approximately 1.0918 minutes.

To solve this problem, we need to determine the angular position of the Ferris wheel when it is 38 meters above the ground.

The Ferris wheel has a diameter of 50 meters, which means its radius is half of that, or 25 meters.

When the Ferris wheel is at its highest point, the radius and the height from the ground are aligned, forming a right triangle.

The height of this right triangle is the sum of the radius (25 meters) and the platform height (4 meters), which equals 29 meters.

To find the angle at which the Ferris wheel is 38 meters above the ground, we can use the inverse sine (arcsine) function.

The formula is:

θ = arcsin(h / r)

where θ is the angle in radians, h is the height above the ground (38 meters), and r is the radius of the Ferris wheel (25 meters).

θ = arcsin(38 / 29) ≈ 1.0918 radians

Now, we know the angle at which the Ferris wheel is 38 meters above the ground.

To calculate the time spent higher than 38 meters, we need to find the fraction of the total revolution that corresponds to this angle.

The Ferris wheel completes one full revolution in 2 minutes, which is equivalent to 2π radians.

Therefore, the fraction of the revolution corresponding to an angle of 1.0918 radians is:

Fraction = θ / (2π) ≈ 1.0918 / (2π)

Finally, we can calculate the time spent higher than 38 meters by multiplying the fraction of the revolution by the total time for one revolution:

Time = Fraction \(\times\) Total time per revolution = (1.0918 / (2π)) \(\times\) 2 minutes

Calculating this expression will give us the answer in minutes.

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The general form representation of the polynomial which is as described in the task content is; f(x) = 4x³ + 38x² + 24x - 360.

It follows from the task content that the Polynomial in discuss has;

Therefore, the factored form of a polynomial can be written as follows;

P(x) = a (x - p) (x - q) (x - r) where p, q and r are the roots of the polynomial and a is the leading coefficient.

Since the factors of the polynomial f(x) are; (x + 6), (x + 6) and (x - 5/2).

Hence, the polynomial f(x) in discuss can be written as follows;

f(x) = 4 (x + 6) (x + 6) (x - 5/2)

f(x) = (x + 6) (x + 6) (4x - 10)

f(x) = 4x³ + 38x² + 24x - 360

Therefore, the required polynomial in standard form is; f(x) = 4x³ + 38x² + 24x - 360.

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we have

f(x) = |x| – 4

Part b

f(4)

so

For x=4

substitute in the expression above

f(4) = |4| – 4

f(4)=4-4

f(4)=0

Part c

f(a+4)

so

For x=(a+4)

substitute

f(a+4) = |(a+4)| – 4

f(a+4)=a+4-4

f(a+4)=a

Step-by-step explanation:

x = number of cards

the production costs (PC) per day are

PC(x) = 264 + 1.1x

the sales (S) are

S(x) = 5.1x

the profit (P) per day is sales minus costs

P(x) = S(x) - PC(x) = 5.1x - (264 + 1.1x) =

= 5.1x - 264 - 1.1x = 4x - 264

we need to find the value of x, so that P(x) = 52.

52 = 4x - 264

316 = 4x

x = 316/4 = 79

79 cards must be delivered daily to make a profit of $52.

Answer:

Explanation:

We can factor the numerator and denominator as;

(

x

−

2

)

(

x

−

1

)

2

x

(

x

−

1

)

We can now cancel common term in the numerator and denominator:

(

x

−

2

)

(

x

−

1

)

2

x

(

x

−

1

)

⇒

x

−

2

2

x

However, we cannot divide by

0

so we must exclude:

2

x

=

0

⇒

x

=

0

and

x

−

1

=

0

⇒

x

1

x

2

−

3

x

+

2

2

x

2

−

2

x

=

x

−

2

2

x

Where:

x

≠

0

and

x

≠

1

Or

x

2

−

3

x

+

2

2

x

2

−

2

x

=

x

2

x

−

2

2

x

=

1

2

−

1

x

Where:

x

≠

0

and

x

≠

1

Step-by-step explanation:

Answer:

\((2x^2+3x)+(4x^2-7)\) =

\(6x^2+3x-7\)

The sequence of the number of circles indicates that for the 10th case,  the number of circles are; 111 circles on the lower left and 111 circles on the top right

Please find attached a drawing of the pattern for the 10th case, created with MS Word

A sequence is an orderly arrangement of values or objects following a specified pattern.

The first pattern indicates that the number of circles in the first column on the left are 2. The number of circles located in the second row from the left side are 3

The second pattern indicates that the number of circles in the first column on the left are 3. The number of circles located in the second row from the left side are 4

The sequence of pattern in the nth case is therefore;

The number of circles in the first column on the left in the nth case are n + 1. The number of circles located in the second row from the left side are n + 2, and the number of squares circles between the column on the left and the row of circles on the top are n each, which indicates;

The number of circles in the first column on the left in the 10th case are 10 + 1 = 11. The number of circles located in the second row from the left side are 10 + 2 = 12

The dimensions of the square of circles to the left of the first column and above which the horizontal row of circles at the top are located are each 10 units wide and 10 units in height

Please find attached the drawing of case 10 creates with MS Word

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Answer:

247.5 is the answer

Step-by-step explanation:

pls mark brainliest it will help me a lot

Step-by-step explanation:

each shelf is 2.475 m long

now we are asking for the total length of 100 of these shelves.

total length = 100 × 2.475 = 247.5 m

you remember, with every power of 10 multiplied with a decimal number the decimal point moves one position to the right. if we run out of provided digits, 0s are being added on the right side.

so, for 100 the decimal point moves 2 positions to the right, as 100 = 10².

for 1000 it would be 3 positions, as 1000 = 10³.

and so on.

and with the division by every power of 10 the decimal point moves one position to the left (filling in 0s between the decimal point and the actual digits, if we are running out of provided digits).

We know that the solution has 2 teaspoons of salt for every gallon of water. We can use the following proportion to find the salt needed for 5 gallons of water.

Let's solve for x

The surface area of the rectangular prism is 502 mm²

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The area of a figure is the amount of space it occupies in its two dimensional state.

The surface area of the prism = 2(8 mm * 13 mm) + 2(8 mm * 7 mm) + 2(7 mm * 13 mm) = 502 mm²

The surface area is 502 mm²

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