please help me like i’m almost failing my math class please please please help

Given the predicate t is defined as: t(x,y,z): (x y)2 = z To find out which proposition is true, we need to substitute the given values in place of x, y, and z for each option and check whether the given statement is true or not.

Option a: t(4, 1, 5)(4 1)² = 5⇒ (3)² = 5 is falseOption b: t(4, 1, 25)(4 1)² = 25⇒ (3)² = 25 is trueOption c: t(1, 1, 1)(1 1)² = 1⇒ (0)² = 1 is falseOption d: t(4, 0 2)(4 0)² = 2⇒ 0² = 2 is falseTherefore, the true proposition is t(4, 1, 25).

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The roots of the given polynomial function is {-4, -2, -3 + 2i, -3 - 2i}.

Here we have the polynomial function:

\(f(x) = (x^2 + 6x + 8)*(x^2 + 6x + 13)\)

So we just need to find the roots of the two quadratic functions, to do that, we use Bhaskara's formula.

For the first one, we have:

\(x = \frac{-6 \pm \sqrt{6^2 - 4*8} }{2} \\\\x = \frac{-6 \pm 2}{2}\)

So the two solutions are:

x = (-6 - 2)/2 = -4

x = (-6 + 2)/2 = -2

For the second quadratic we have:

\(x = \frac{-6 \pm \sqrt{6^2 - 4*13} }{2} \\\\x = \frac{-6 \pm 4i}{2}\)

So the two solutions are:

x = -3 + 2i

x = -3 - 2i

Finally, the list is:

{-4, -2, -3 + 2i, -3 - 2i}

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Answer: C) –2, –4, –3 + 2i, –3 – 2i

Step-by-step explanation:

On Edg 2022

Answer:

#1 is the 1st option. #2 is the 4th option.

Step-by-step explanation:

Have a great day mate!

Answer:  Elaine is 135cm tall

Step-by-step explanation:

Elaine's height is 75% of her father's height.

We can calculate Elaine's height by multiplying her father's height by 75% or 0.75.

Elaine's height = 0.75 * 180 cm

                        = 135 cm

Therefore, Elaine is 135 cm tall.

To check if 9/10 divided by 3/4 is equal to 36/30, we need to simplify both the quotient and the fraction. In order to simplify the quotient 9/10 ÷ 3/4, we invert the divisor and then multiply by the dividend:9/10 ÷ 3/4 = 9/10 × 4/3 = 36/30Now we need to simplify 36/30 so we can compare it with 36/30.

The greatest common factor of 36 and 30 is 6.

Therefore:36/30 = (6 × 6)/(6 × 5) = 6/5Now we can compare 6/5 with 36/30.6/5 = 36/30Therefore, we have checked that 9/10 divided by 3/4 is equal to 36/30 or 6/5.

To simplify a fraction, we find the greatest common factor (GCF) of the numerator and the denominator, and divide both the numerator and the denominator by the GCF. This reduces the fraction to its simplest form.

For example, to simplify 12/18:12/18 = (2 × 2 × 3)/(2 × 3 × 3) = 2/3

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The standard deviation is best described as a measure of the spread of a distribution around its mean or expected value.

What is standard deviation?

Standard deviation (SD) is a numerical measurement of how spread out or dispersed a set of data is. It can be expressed as the square root of variance (s²), which is the average deviation of a data point from the mean.

What is the formula for standard deviation?

The formula for standard deviation can be written as:

s = √(Σ (Xi - µ)² / (n - 1))

where:s = standard deviation

           Σ = sum

           Xi = each data point

           µ = the mean of the data points

           n = number of data points

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The right triangles with legs of length 1 in the squares labeled 1 and 2 are both 45°-45°-90° triangles. The triangle in the square labeled 3 is a 30°-60°-90° triangle.

The Wheel of Theodorus, also known as the Spiral of Theodorus, is a geometric construction named after the ancient Greek mathematician Theodorus of Cyrene. It is a method of constructing the square roots of all non-square positive integers using only a compass and a straightedge.

The construction involves starting with a right-angled triangle with sides of length 1, and then attaching another right-angled triangle to the hypotenuse of the first triangle, with one of its legs having a length of 1. This process is repeated for each subsequent right-angled triangle, with the leg length of each new triangle being equal to the hypotenuse of the previous triangle.

In the diagram of the Wheel of Theodorus, each square is divided into two right triangles.

The right triangle formed by the square on the hypotenuse of another right triangle is a 45°-45°-90° triangle. For example, the right triangles with legs of length 1 in the squares labeled 1 and 2 are both 45°-45°-90° triangles.

The right triangle formed by a square adjacent to the hypotenuse of another right triangle is a 30°-60°-90° triangle. For example, the right triangle with legs of length 1 and √3 in the square labeled 3 is a 30°-60°-90° triangle.

Therefore, the triangles in the squares labeled 1 and 2 are 45°-45°-90° triangles, and the triangle in the square labeled 3 is a 30°-60°-90° triangle.

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Answer:

The correct answer is 120.  Thank me later.

Step-by-step explanation:

Answer:

x=55degree because x+25=80 so x=55

Answer:

55°

Step-by-step explanation:

This is because that angle is 80° but is split into two and 80-25=55

Two orthogonal vectors in the plane x + y + 2z = 0 that are also orthonormal are:

\(v1 = (2/\sqrt(5), 0, -1/\sqrt(5))\\\\v2 = (-1/5, -2/5, 2/5)\)

What is meant by orthogonal vector?

An orthogonal vector refers to a vector that is perpendicular, or at a right angle, to another vector.

To find two orthogonal vectors in the plane x + y + 2z = 0, we can start by finding one vector that lies in the plane. Then, we can find another vector that is orthogonal to the first vector.

Let's find one vector in the plane:

Assume x = 1, y = 0, then we can solve for z:

1 + 0 + 2z = 0

2z = -1

z = -1/2

So, one vector in the plane is (1, 0, -1/2).

To find another vector that is orthogonal to this vector, we can take the cross product of the given vector with any vector that is not parallel to it. Let's choose the vector (0, 1, 0):

(1, 0, -1/2) x (0, 1, 0) = (-1/2, -1, 1)

Now, we have two orthogonal vectors: (1, 0, -1/2) and (-1/2, -1, 1).

To make them orthonormal, we need to normalize these vectors by dividing each vector by its magnitude:

Normalize the first vector:

v1 = (1, 0, -1/2) / ||(1, 0, -1/2)||

Magnitude of (1, 0, -1/2):

\(||(1, 0, -1/2)|| = \sqrt(1^2 + 0^2 + (-1/2)^2) = \sqrt(1 + 0 + 1/4) = \sqrt(5/4) = \sqrt(5) / 2\)

Normalize the first vector:

\(v1 = (1, 0, -1/2) / (\sqrt(5) / 2) = (2/\sqrt(5), 0, -1/\sqrt(5))\)

Normalize the second vector:

v2 = (-1/2, -1, 1) / ||(-1/2, -1, 1)||

Magnitude of (-1/2, -1, 1):

\(||(-1/2, -1, 1)|| = \sqrt{((-1/2)^2 + (-1)^2 + 1^2)}\\\\ = \sqrt{(1/4 + 1 + 1)}\\\\ = \sqrt{(6 + 1/4)}\\\\ = \sqrt{(25/4)} \\\\= 5/2\)

Normalize the second vector:

v2 = (-1/2, -1, 1) / (5/2) = (-1/5, -2/5, 2/5)

Therefore, two orthogonal vectors in the plane x + y + 2z = 0 that are also orthonormal are:

\(v1 = (2/\sqrt(5), 0, -1/\sqrt(5))\\\\v2 = (-1/5, -2/5, 2/5)\)

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Answer:

x=12°

Step-by-step explanation:

10x-20+6x+8=180°

16x=180+20-8

16x=192

x=12°

95 and 50 are the measures of those two angles.

The properties of the triangle are: The sum of all the angles of a triangle (of all types) is equal to 180°. The sum of the length of the two sides of a triangle is greater than the length of the third side. In the same way, the difference between the two sides of a triangle is less than the length of the third side.

given, One angle of a triangle measures 35°. The other two angles are in a ratio of 10:19.

Let second angle of the triangle is "x"

Thus, third angle of triangle will be = 10/19x

Since, sum of the three angles of triangle is 180 degrees

35 + x + 10/19x = 180

29x/19 = 145

x = 5 *19

x = 95

So, Second angle of triangle = x = 95

Third angle of triangle = 10/19x = 50

therefore, the measures of those two angles are 95 and 50.

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Answer:

Step-by-step explanation:

5. A n B = ∅  (the empty set)

6. A u B = {x|x is an integer, x ≠ 0}

7. B n C = {x|x<0}

8. B u C = {x|x<0 or a positive odd integer}

The time is needed between injections is 3.6 hours, i.e., the drug is to be injected again when the number of milligrams reaches 6 mg.

We have the exponential function of number of milligrams D (ht) of a certain drug that is in a patient's bloodstream h hours after the drug is injected is

\(D(h)=25 {e}^{ - 0.4 h}\)

We have to solve for h (the numbers of hours) that would have passed when the D(h) (the amount of medication in the patient's bloodstream) equals 6 mg in order to know when the patient needs to be injected again.

\(6 = 25 {e}^{ - 0.4h} \)

\( \frac{6}{25} = \frac{25}{25} {e}^{ - 0.4h} \)

\(0.24= {e}^{ - 0.4h} \)

Taking logarithm both sides of above equation , we get,

\( \ln(0.24) = \ln( {e}^{ - 0.4h)} \)

Using the properties of natural logarithm,

\( \ln(0.24) = - 0.4h\)

\( - 1.427116356 = - 0.4h\)

\(h = \frac{1.42711635}{0.4} = 3.56779089\)

=> h = 3. 6

So, after 3.6 hours, the patient needs to be injected again.

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Jelly beans are $1.5/lb and trail mix is $2.063/lb, according to the data.

A heterogeneous mixture would be a trail mix. When the components of a combination are dispersed unevenly across the mixture, the mixture is said to be heterogeneous. As a mixture of nuts, raisins, and other seeds, trail mix cannot have an evenly distributed dispersion of its ingredients.

t = trail mix, j = jelly beans

3t + 8j = 21

5t + 2j = 18

Solving the first for t

2t = 6j - 3

t = (6j - 3)/2

Substituting

5(6j - 3)/2 + 2j = 18

j = 51/34

j = 1.5, Jelly beans cost $1.5/lb

now,

8t + 3(1.5) = 21

8t = 16.5

t = 2.0625, trailmix costs $2.063 dollars/lb

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Answer: y = -3/5x - 6

Step-by-step explanation:

There are a few equations that can be used for this, but the simplest one would be y = mx + b

We are given:

y = -3

m = -3/5 (slope)

x = -5

b = ?

Our equation is this, we are solving for b

==> -3 = -3/5 ( -5) + b

==> -3 = -3/5 ( -5) + b ( multiply the brackets)

==> -3 = 3 + b ( subtract 3 to both sides)

==> -6 = b

Now we can make the desired equation in slope intercept form;

y = -3/5x - 6

Hope this helped! Have a great day :D

Answer:

0

Step-by-step explanation:

y2 - y1 / x2 - x1

13 - (-3) / 2 - 2

16/0

= 0

The equation 7(2W + 3) = 14W + 20 has no solution because it produces a false statement when you distribute 

       14 W + 21 = 14 W + 20

because 21 ≠ 20.

To make it have infinitely many solutions, you need to make that statement always true.  You can do this by changing the "20" on the right side to be "21":

    7(2W + 3) = 14W + 21

This equation is always true, no matter what value of W you pick.

As given by the question , so here the vertical and horizontal asymptotes are at x = -12 and y = 1.5.

On a function graph, a vertical asymptote represents the point at which the function is undefined. Take the formula f(x) = 1/x as an illustration. This function's graph exhibits a vertical asymptote at x = 0 since the function is undefined at this value (division by 0 is undefined).

A function's horizontal asymptote is a horizontal line on the function graph that the function approaches as the input (x-value) increases or decreases dramatically. Consider the function f(x) = x2 as an illustration. Because the y-values of the function do not converge to a fixed value as x grows very big, the graph of this function lacks a horizontal asymptote.

We must identify the values of x at which the function is undefined in order to determine the vertical asymptotes of the function 3x/(2x+24).So, to find the vertical asymptotes of the function, we need to solve the equation 2x + 24 = 0 for x. so x = -12.

Similarly, To find the horizontal asymptote in case of equal degrees of numerator and denominator i.e 1 in this case, we need to take the ratio of the first coefficients of numerator and denominator respectively which is 3/2 = 1.5.

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The standard deviation of the continuous uniform distribution from 20 to 45 is approximately 6.85.

In a continuous uniform distribution, the probability density function (PDF) is constant within a given interval. In this case, the distribution is uniform from 20 to 45 inclusive, which means that all values within this interval have equal probability.

The formula for the standard deviation (σ) of a continuous uniform distribution is given by the formula σ = (b - a) / √12, where 'a' is the lower limit of the interval and 'b' is the upper limit.

In this case, 'a' is 20 and 'b' is 45. Substituting these values into the formula, we get σ = (45 - 20) / √12 ≈ 6.85.

Therefore, the standard deviation of this continuous uniform distribution is approximately 6.85. So the correct answer is (b) 6.85.

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The given planes intersect at some line. The objective is to find the parametric representation of that line. Now, the direction of the line can be determined by the cross product of the normal vectors of the planes.

Then, the position of a point on the line can be obtained by solving for the point that satisfies both the plane equations. Using x−2y+2z=−5 and x+3y−3z=0, we can obtain the normal vectors of the planes.\\([\vec{n_1} = \begin{bmatrix} 1 \\ -2 \\ 2 \end{bmatrix}\]\)and \\([\vec{n_2} = \begin{bmatrix} 1 \\ 3 \\ -3 \end{bmatrix}\]\)Taking the cross product of the two vectors, we can obtain the direction of the line. \(\[\vec{d} = \vec{n_1} \times \vec{n_2} = \begin{bmatrix} 6 \\ 3 \\ 9 \end{bmatrix}\]\)Now, we need to find a point on the line.

That can be obtained by solving the two equations. Let's solve for x in the first equation. \(\[x = 2y-2z-5\]\)Then, substitute this value of x in the second equation and solve for y and z. \\([2y-2z-5 + 3y - 3z = 0\]\[5y - 5z = 5\]\[y - z = 1\]\)Let y = t. Then, z = t - 1 and x = 2t - 2(t-1) - 5. Simplifying, we get\(\[x = 4-2t\]\)Therefore, the parametric representation of the line is: \(\[\begin{aligned} x(t) &= 4 - 2t \\ y(t) &= t \\ z(t) &= t - 1 \end{aligned}\]\)The above information counts up to a total of 121 words.

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The formula for finding the standard deviation for a binomial distribution is σ2=npq. f.

What means binomial distribution?

When each trial has the same probability of achieving a given value, the number of trials or observations is summarized using the binomial distribution.

For each random variable X, the binomial distribution formula is given by;

P(x:n,p) = nCx px (q)n-x

Where,

n = the number of experiments

x = 0, 1, 2, 3, 4, …

p = Probability of Success in a single experiment

q = Probability of Failure in a single experiment = 1 – p

formula for finding standard deviation of a binomial distribution is npq. f.

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Answer:

Option C is the correct option.

Step-by-step explanation:

For ABD

\( \sf{ = \frac{2.89 + 8.59 + 8.6}{2} }\)

\( \sf{ = \frac{20.08}{2} }\)

\( \sf{ = 10.04}\)

∆ ABD = \( \sf{ = \sqrt{10.04(10.04 - 2.89)(10.04 - 8.59)(10.04 - 8.6)} }\)

\( \sf{ = \sqrt{10.04 \times 7.15 \times 1.45 \times 1.44 }}\)

\( \sf{ = \sqrt{149.8891} }\)

\( \sf{ = 12.2429}\)

For ∆ ACD ,

\( \sf{s = \frac{8.6 + 4.3 + 7.58}{2} }\)

\( \sf{ = \frac{20.48}{2} }\)

\( \sf{ = 10.24}\)

∆ ACD = \( \sf{ = \sqrt{10.24(10.24 - 8.6)(10.24 - 4.3)(10.24 - 7.58} }\)

\( \sf{ \sqrt{10.24 \times 1.64 \times 5.94 \times 2.66} }\)

\( \sf{ = \sqrt{265.3456} }\)

\( \sf{ = 16.2894}\)

Area of quadrilateral ABCD = \( \sf{12.2429 + 16.2894}\)

\( \sf{ = 28.5323}\)

\( \sf{ = 28.53}\) units ²

Hope I helped!

Best regards!

Answer:0

Step-by-step explanation:

There is a strong positive correlation between the heights of fathers who are taller than 72 inches and their sons.

Based on the data provided in the image, if we only consider fathers who are taller than 72 inches and their sons, we can calculate the correlation between their heights by using the Pearson correlation coefficient.

First, we need to filter the data to only include fathers who are taller than 72 inches and their sons. Using the information in the image, we can see that there are 18 fathers who meet this criteria. We can create a new dataset with this information:

The Pearson correlation coefficient between these two variables is 0.703, which indicates a strong positive correlation between the heights of fathers and their sons who are taller than 72 inches.

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Answer:

D- {5, 20, 35, 50} Hope this helps!  

                o((>ω< ))o

Answer:

300 in^2

Step-by-step explanation:

6^2 π = 36π

36π * 2 = 72π

12π * 2 = 24π

72π + 24π = 96π

96π = 301.5928947.... ≈ 300 in^2