FInd the solution for the ordered pair
2x + y = 5 and x + y = 6

The equation of the polynomial function from the given table is; Option B: h(x) = x³ - 7x + 6

From the given table, we see that the x-intercepts are;

(-3, 0), (1, 0) and (2, 0)

Now, we are told the the x-intercepts have a multiplicity of one which means they occur as roots only once. Thus, we can say that the roots in factor form are;

(x + 3), (x - 1), (x - 2)

Then, the polynomial will be;

h(x) = (x + 3) * (x - 1) * (x - 2)

h(x) = (x + 3)(x² - 3x + 2)

h(x) = x³ + 3x² - 3x² - 9x + 2x + 6

h(x) = x³ - 7x + 6

Thus, the equation of the polynomial function from the given table is; Option B: h(x) = x³ - 7x + 6

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This snow flake-like figure can be generated by rotating an end 60° five times around the center of the hexagon. There are two forms: (i) clockwise, (ii) counterclockwise.

Geometrically speaking, snow flakes represent regular hexagons. Regular hexagons can divided into six concentric regular triangles, whose central angles have a measure of 60°. This fractal figure can be generated by rotating 60° five times around the center.

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Answer:

f(n)={n/2     = if n is even=   n={2/2

       {3n+1                                 {3(2)+1   =7

Step-by-step explanation:

if n is even u can put any even no in that place and u can get odd no or even no.(i think)

The sample mean for students with a grade point average of 3.0–4.0 is greater than students with grade point average of 2.0 - 3.0,  the results tend to

From the question, we have the following highlights

From the above highlights, the sample mean for students with a grade point average of 3.0–4.0 is greater than students with grade point average of 2.0 - 3.0

This is because 6.8 is greater than 6.4

This means that Garret's theory about the hours of sleep is correct

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Answer:

1.894

3.169

2.064

3.690

Step-by-step explanation: 90% ; sample size = 8

Degree of freedom, df = n - 1

t(1 - α/2, 7) = t0.05, 7 = 1.894

Answer: B

Step-by-step explanation:

The line y=2 is solid and shaded above, so it represents [tex]y \geq 2[/tex].

This allows us to eliminate all the options except for B.

Answer is (n + 3) + (n - 7)

Simplified to 2n - 4

Using “n” for number

The recursive function o f the given sequence will be an = an-1 + 4

The formula for calculating the recursive function of n arithmetic sequence is expressed as
an = an-1 + d

Determine the common difference

d = 19 - 15 = 23 -19

d = 4

The recursive function o f the given sequence will be an = an-1 + 4

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[tex]x + y = 55 \\ x - y = 15 \\ \\ 2x = 70 \: \: \: \: \: \: x = 35 \\ y = 55 - x = 55 - 35 = 20[/tex]

Answer: [tex]\cos^{-1} \left(\frac{-22}{\sqrt{754}} \right)[/tex]

Step-by-step explanation:

[tex]a \cdot b=(3)(0)+(-4)(5)+(-1)(2)=-22\\\\|a| |b|=\sqrt{3^2 +4^2 +1^2} \sqrt{5^2 +2^2}=\sqrt{754}\\\\\therefore \cos \theta=\frac{-22}[\sqrt{754}}\\\\\theta=\cos^{-1} \left(\frac{-22}{\sqrt{754}} \right)[/tex]

Answer:

At maximum, she can buy 5 tomatoes.

Step-by-step explanation:

If you solve the inequality, as so:

1.2x+1.8 <=7.8

1.2x <= 6

x <= 5

Answer:

Step-by-step explanation:

will give brainiest wrrwrwvrwvr

Answer:

13

Step-by-step explanation:

7+2x=3x-6

knowing this then you solve it

Step-by-step explanation:

7 more = + 7

twice a number = 2*x = 2x

6 less = -6

3 times the same number = 3 * x = 3x

Putting this together we get:

2x + 7 = 3x - 6

subtract two from both sides to isolate x

(-2x) + 2x + 7 = 3x - 6 (-2x)

7 = x - 6

add 6 to both sides to get your answer

7 (+6) = x - 6 (+6)

13 = x

or

x = 13

Using translation concepts, the equation for function g(x) given in the graph is:

[tex]g(x) = 2^{x + 2}[/tex]

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

The parent function for this problem is given as follows:

[tex]f(x) = 2^x[/tex]

From the graph, function g(x) was shifted 2 units left, hence x -> x + 2 and the definition is:

[tex]g(x) = 2^{x + 2}[/tex]

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Using equivalent angles, we have that the measures are given as follows:

Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.

120º is in the second quadrant, hence the equivalent on the first quadrant is:

180º - 120º = 60º.

The sine on the second quadrant is positive, hence:

[tex]\sin{120^\circ} = \sin{60^{\circ}} = \frac{\sqrt{3}}{2}[/tex]

The cosine on the second quadrant is negative, hence:

[tex]\cos{120^\circ} = \cos{60^{\circ}} = -\frac{1}{2}[/tex]

The tangent is given by the sine divided by the cosine, hence:

[tex]\tan{120^\circ} = \frac{\sin{120^\circ}}{\cos{120^\circ}} = -\sqrt{3}[/tex]

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Answer:

Hope you like it. I have just wrote answers

The minimum production rate of bushels per acre of corn needed this year is 97 for two year's production to reach the goal of 49,100.

To calculate the minimum production rate for this year, we must subtract the production rate of the previous year, with what is expected to be obtained this year.

Then we must divide the minimum that must be obtained by the total area, by the 300 acres that we have, to know how much corresponds to each acre.

According to the above, each acre must produce 97 bushels of corn to reach the goal of 49,100 for both years.

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Answer:

80°

Step-by-step explanation:

Congruent means the same size, so we know that the angle of the shapes made by the lines HK and GJ are the same, meaning that the angle of GOJ is simply 80°.

Given the length of both trail, Trail B is 7/4 miles longer than Trail B.

Given that;

To determine how many miles longer is Trail B more than Trail A, we subtract the length of tail A from Tail B.

Trail B - Trail A

17/2 - 27/4

17/2 is the same as; 34/4

34/4 - 27/4

We combine the numerators over common denominator

(34 - 27 )/4

7/4 miles

Given the length of both trail, Trail B is 7/4 miles longer than Trail B.

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Answer:

30 km

Step-by-step explanation:

Distance = rate x time

Distance = 20 x 1.5

Distance = 30

[tex]20*1.5=30[/tex] [tex]km[/tex]

Correct answer:-

Avg. speed = [tex]20km/h[/tex]

Time = [tex]1.5 hour[/tex]

Distance traveled in 1.5 hours is Distance = Speed x Time

So,

[tex]D = 20 * 1.5 = 30.[/tex]

reference link-

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The resulting coordinates for each row are (-2, 2), (0, 4),()2, 6), (6, 10) and (8,12) respectively

Given the linear function expressed as;

y = x + 4

where

x are the input values and y are the output values

If x = -2

y = -2+4

y = 2

The coordinate (x, y) will be (-2, 2)

If x = 0

y = 0+4

y = 4

The coordinate (x, y) will be (0,4)

If x = 2

y = 2+4

y = 6

The coordinate (x, y) will be (2, 6)

If x = 6

y = 6+4

y = 10

The coordinate (x, y) will be (6,10)

If x = 8

y = 8+4

y = 12

The coordinate (x, y) will be (8, 12)

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Answer:

U-A empty

Step-by-step explanation:

all in a is in u in u is in a therfore empty is found on u but not in a

Answer: Option 1

Step-by-step explanation:

[tex]|x+4|=2\\\\x+4=\pm 2\\\\x=-4\pm 2\\\\x=-6, -2[/tex]

Solve Absolute Value.

| x + 4 | = 2

We know either x + 4 = 2 or x + 4 = −2

x + 4 = 2 (Possibility 1)

x + 4 - 4 = 2 - 4 (Subtract 4 from both sides)

x = -2

x + 4 = −2 (Possibility 2)

x + 4 - 4 = - 2 - 4 (Subtract 4 from both sides)

x = -6

Answer: x = - 2 or x = -6

Therefore we conclude that the solution of the exercise | x + 4 | = 2, is the first number line, since both results are negative.

Answer: A

Step-by-step explanation:

The polynomial has roots at [tex]x=-4, -2, 4[/tex].

So, the equation should have factors of [tex](x+4), (x-2), (x-4)[/tex].

This eliminates everything except for A.

Answer:

180°

cuz when a line (I forgot the name) and radius meet at the circumference they from an angle of 90°

a) The resultant force on the particle is equal to - 225 · x, where x is measured in meters.

b) The particle moves with simple harmonic motion.

c) The motion has a period of approximately 1.257 seconds.

d) The particle has an approximate speed of 2.488 meters per second when it is 0.05 metres from C.

e) The equation for the position of the particle is x(t) = 0.5 · cos 25t, where t is in seconds.

In this case we have a system with a particle under periodic motion due to two reactive forces from two springs. a) The system is represented by the following formula based on Newton's laws:

∑F = - k₁ · x - k₂ · x = m · a      (1)

Where:

If we know that k₁ = k₂ = 112.5 N/m, then the resultant force on the particle is equal to - 225 · x, where x is measured in meters.

b) The particle is under simple harmonic motion has a differential equation of the form:

x'' + ω² · x = 0       (2)

Where:

By some algebraic handling on (1), we find the following differential equation:

x'' + [(k₁ + k₂) / m] · x = 0     (3)

Thus, the particle moves with simple harmonic motion.

c) The period of the motion (T), in seconds, is determined by T = 2π / ω. Then, the period is described by the following expression:

T = 2π · √[m / (k₁ + k₂)]

T = 2π · √(9 kg / 225 N /m)

T ≈ 1.257 s

The motion has a period of approximately 1.257 seconds.

d) The speed of the particle (v), in metres per second, can be found by the principle of energy conservation:

(1 / 2) · k · A² = (1 / 2) · k · x² + (1 / 2) · m · v²      (4)

v = √[k · (A² - x²) / m]

Where:

If we know that k = 225 N / m, A = 0.5 m, x = 0.05 m and m = 9 kg, then the speed of the particle is:

v = √[(225 N / m) · [(0.5 m)² - (0.05 m)²] / (9 kg)]

v ≈ ± 2.488 m / s

The particle has an approximate speed of 2.488 meters per second when it is 0.05 metres from C.

e) The function position for a particle under simple harmonic motion:

x(t) = A · cos ω · t      (5)

If we know that A = 0.5 m and ω = 25 rad / s, then the equation for the position of the particle is:

x(t) = 0.5 · cos 25t

The equation for the position of the particle is x(t) = 0.5 · cos 25t.

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The matrix [tex]\vec C[/tex] resulting from the multiplication between matrices [tex]\vec B[/tex] and [tex]\vec A[/tex] is equal to the matrix [tex]\left[\begin{array}{ccc}37&55&- 20\\23&11&- 20\\25&28&-9\end{array}\right][/tex]. (Correct choice: C)

In this question we must apply the operation of multiplication of two matrices, whose definition is shown below:

[tex]\vec B\, \cdot \, \vec A[/tex], where [tex]\vec B \in \mathbb {R}_{n \times p}[/tex] and [tex]\vec A \in \mathbb{R}_{p \times n}[/tex]     (1)

Where each element of the resulting matrix is equal to the following expression:

[tex]c_{(i, j)} = b_{(i, p)} \,\bullet\, a_{(p, j)}[/tex]     (2)

Where the operator "[tex]\bullet[/tex]" represents a dot product.

Now we proceed to calculate each element of the matrix:

[tex]c_{(1, 1)} = \left[\begin{array}{ccc}5&7&3\end{array}\right] \,\bullet\,\left[\begin{array}{c}1\\5\\- 1\end{array}\right][/tex]

5 · 1 + 7 · 5 + 3 · (- 1)

37

[tex]c_{(1, 2)} = \left[\begin{array}{ccc}5&7&3\end{array}\right] \,\bullet\,\left[\begin{array}{c}7\\2\\2\end{array}\right][/tex]

5 · 7 + 7 · 2 + 3 · 2

55

[tex]c_{(1, 3)} = \left[\begin{array}{ccc}5&7&3\end{array}\right] \,\bullet\,\left[\begin{array}{c}- 3\\1\\- 4\end{array}\right][/tex]

5 · (- 3) + 7 · 1 + 3 · (- 4)

- 20

[tex]c_{(2, 1)} = \left[\begin{array}{ccc}- 3&7&9\end{array}\right] \,\bullet\,\left[\begin{array}{c}1\\5\\- 1\end{array}\right][/tex]

(- 3) · 1 + 7 · 5 + 9 · (- 1)

23

[tex]c_{(2, 2)} = \left[\begin{array}{ccc}- 3&7&9\end{array}\right] \,\bullet\,\left[\begin{array}{c}7\\2\\2\end{array}\right][/tex]

(- 3) · 7 + 7 · 2 + 9 · 2

11

[tex]c_{(2, 3)} = \left[\begin{array}{ccc}- 3&7&9\end{array}\right] \,\bullet\,\left[\begin{array}{c}- 3\\1\\- 4\end{array}\right][/tex]

(- 3) · (- 3) + 7 · 1 + 9 · (- 4)

- 20

[tex]c_{(3, 1)} = \left[\begin{array}{ccc}2&5&2\end{array}\right] \,\bullet\,\left[\begin{array}{c}1\\5\\- 1\end{array}\right][/tex]

2 · 1 + 5 · 5 + 2 · (- 1)

25

[tex]c_{(3, 2)} = \left[\begin{array}{ccc}2&5&2\end{array}\right] \,\bullet\,\left[\begin{array}{c}7\\2\\2\end{array}\right][/tex]

2 · 7 + 5 · 2 + 2 · 2

28

[tex]c_{(3, 3)} = \left[\begin{array}{ccc}2&5&2\end{array}\right] \,\bullet\,\left[\begin{array}{c}- 3\\1\\- 4\end{array}\right][/tex]

2 · (- 3) + 5 · 1 + 2 · (- 4)

- 9

The matrix [tex]\vec C[/tex] resulting from the multiplication between matrices [tex]\vec B[/tex] and [tex]\vec A[/tex] is equal to the matrix [tex]\left[\begin{array}{ccc}37&55&- 20\\23&11&- 20\\25&28&-9\end{array}\right][/tex]. (Correct choice: C)

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The given function has symmetry about the y - axis.

Symmetry of the Function

If we reflect a function's graph about the y-axis, we will get the same graph since if the function is symmetrical about the y-axis. We can reflect a function about the x- and y-axis and obtain the same graph. These two symmetry kinds are known as the even function and odd function.

The given function is,

f(x) = 2x² - 1

It is an even function since the function remains same for both x and -x.

Putting f(x) = 0, we get,

2x² - 1 = 0

2x² = 1

x² = 1/2

x = ±1/2

⇒ Axis of symmetry is, x=0

Hence, the function f(x) is symmetric about y-axis.

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Since both np > 5 and n(1 - p) > 5, the normal curve can be used as an approximation to the binomial distribution.

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The normal approximation can be used if:

In this problem, the parameters are:

n = 107, p = 0.25.

Hence:

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