When you use the distance formula, you are building a(n) _____ whose hypotenuse connects two given points.

A relation that passes through the y-axis twice is not considered a function. A function, by definition, can only output one 'y' value for each unique 'x' value. This relation fails the 'vertical line test' which checks that each 'x' value only connects to a single 'y' value.

In mathematical terms, a relation is a set of ordered pairs, where each first element is related to the second element. A function, on the other hand, is a special type of relation where every input (or 'x' value) corresponds to exactly one output (or 'y' value).

Now, if a relation passes through the y-axis twice, it means that there are two 'y' values for a single 'x' value (which in this case, is zero). This violates the definition of a function. Hence, a relation that passes through the y-axis twice is not a function. It is simply a relation because it doesn't pass the 'vertical line test' (a vertical line passing through more than one point on the graph of a relation means that the relation is not a function).

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Answer:

A) UY

Step-by-step explanation:

From the given figure, TUYX is one of the side of the rectangular prism and UVYZ  is another side of the rectangular prism.

The both sides are intersecting perpendicular in one edge, that is the line segment UY.

You can see it on the figure.

Therefore, the intersecting line is UY.

we know that

The equation in vertex form of a vertical parabola is of the form

[tex]y=a(x-h)^{2}+k[/tex]

where

[tex](h,k)[/tex] is the vertex of the parabola

and

[tex]x=h[/tex] is the axis of symmetry

if [tex]a > 0[/tex] -----> open upward

if [tex]a < 0[/tex] -----> open downward

In this problem we have

[tex]y=3(x+2)^{2}-3[/tex]

[tex]a=3[/tex]

This is a vertical parabola open upward

The vertex is a minimum

therefore

the answer is

the vertex is the point [tex](-2,-3)[/tex]

the axis of symmetry is [tex]x=-2[/tex]

see the attached figure to better understand the problem

The vertex of the function [tex]y=3{\left({x+2}\right)^2}-3[/tex] is [tex]\boxed{\left({-2,-3}\right)}[/tex].

Further Explanation:

The standard form of the parabola is shown below.

[tex]\boxed{y=a{{\left({x-h}\right)}^2}+k}[/tex]

Here, the parabola has vertex at [tex]\left({h,k}\right)[/tex] and has the symmetry parallel to x-axis and it opens left.

Given:

The quadratic function is [tex]y=3{\left({x+2}\right)^2}-3[/tex].

Calculation:

Compare the [tex]y=3{\left({x+2}\right)^2}-3[/tex] with the general equation of the parabola [tex]\boxed{y=a{{\left({x-h}\right)}^2}+k}[/tex]

.

The value [tex]a[/tex] is [tex]3[/tex], the value of [tex]h[/tex] is [tex]-2[/tex] and the value of [tex]k[/tex] is [tex]-3[/tex].

Therefore, the vertex of the parabola is [tex]\left({-2,-3}\right)[/tex].

The function is symmetric about [tex]x=-2[/tex].

The vertex of the function [tex]y=3{\left({x+2}\right)^2}-3[/tex] is [tex]\boxed{\left({-2,-3}\right)}[/tex].

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Conic sections

Keywords: vertex, symmetry, symmetric, axis, y-axis, x-axis, function, graph, parabola, focus, vertical parabola, upward parabola, downward parabola,

I believe the parts are:

A. What is the probability that Upper X greater than 95X>95​?

B. What is the probability that Upper X less than 75X<75?

C.What is the probability that Upper X less than 85X<85 and Upper X greater than 125X>125?

D. 95​% of the values are between what two​ X-values (symmetrically distributed around the​ mean)?

Solution:

We use the equation for z score:

z = (X – μ) / σ

Then use the standard normal probability tables to locate for the value of P at indicated z score value.

A. Z = (95 – 100) / 10 = - 0.5

Using the tables, the probability at z = -0.5 using right tailed test is:

P = 0.6915

B. Z = (75 – 100) / 10 = - 2.5

Using the tables, the probability at z = -2.5 using left tailed test is:

P = 0.0062

C. Z = (85 – 100) / 10 = - 1.5

Using the tables, the probability at z = -2.5 using left tailed test is:

P = 0.0668

Z = (125 – 100) / 10 = 2.5

Using the tables, the probability at z = 2.5 using right tailed test is:

P = 0.0062

So the probability that 85<X and X>125 is:

P(total) = 0.0668 + 0.0062

P(total) = 0.073

D. P(left) = 0.025, Z = -1.96

P(right) = 0.975, Z = 1.96

The X’s are calculated using the formula:

X = σz + μ

At Z = -1.96

X = 10 (-1.96) + 100 = 80.4

At Z = 1.96

X = 10 (1.96) + 100 = 119.6

So 95% of the values are between 80.4 and 119.6 (80.4< X <119.6).

The average number of pairs of adjacent cards in a well-shuffled 52-card deck that are both red is about 12 or 13 pairs. This is calculated based on the probability of drawing red cards.

In a well-shuffled 52-card deck, there are 26 red cards out of the total 52 cards. Thus, the probability of drawing a red card is 26/52 = 0.5.

Now, let's consider two neighboring cards as an ordered pair. There are 51 such pairs in a 52-card deck. We are looking for pairs where both cards are red. The probability that the first card of any given pair is red is 0.5, as already noted. The probability that the next card (in that pair) is also red, assuming the first one is red, is now 25/51 (since one red card is assumed as taken already).

Thus, the probability that a given pair of adjacent cards are both red is 0.5 * (25/51) = 25/102 ≈ 0.245.

Given that we have 51 possible pairs, the expected number of red pairs is 51 * (probability of red pair) which equals about 12.48.

Therefore, on average, you can expect about 12 or 13 pairs of adjacent cards to be both red.

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Actually we can directly check if the quotient has equal or one less amount of places than the given number. This can be checked by looking at the number on the biggest place of the dividend, if it is less than the divisor, the answer will have one less digits place. So in this case since the divisor is 4 and the greatest place of the dividend is thousands and the number is 2, so the quotient will be in the hundreds place.

Hundreds place

Answer:

Step-by-step explanation:Actually we can directly check if the quotient has equal or one less amount of places than the given number. This can be checked by looking at the number on the biggest place of the dividend, if it is less than the divisor, the answer will have one less digits place. So in this case since the divisor is 4 and the greatest place of the dividend is thousands and the number is 2, so the quotient will be in the hundreds place. 

Answer:

The numbers are 5 and 20.

Step-by-step explanation:

To find : What are the numbers?

Solution :

Let the one number be 'x'.

The reciprocal is [tex]\frac{1}{x}[/tex]

The another number be 'y'.

The reciprocal is [tex]\frac{1}{y}[/tex]

One number is four times another number.

i.e. [tex]x=4y[/tex] .....(1)

The sum of their reciprocals is [tex]\frac{1}{4}[/tex].

i.e. [tex]\frac{1}{x}+\frac{1}{y}=\frac{1}{4}[/tex] ....(2)

Substitute (1) in (2),

[tex]\frac{1}{4y}+\frac{1}{y}=\frac{1}{4}[/tex]

[tex]\frac{1+4}{4y}=\frac{1}{4}[/tex]

[tex]4y=20[/tex]

[tex]y=5[/tex]

One number is 4y=4(5)=20.

Therefore, the numbers are 5 and 20.

Answer:

F(1) is not defined

Step-by-step explanation:

calculate the slopes

3-0 / -2 - 2 = 3/-4 = -3/4

3 - -4 / -2 - -1 = 7/-1 = -7/1

0 - -4 / 2 - -1 = 4/3

-3/4 and 4/3 are negative reciprocals so this is a right triangle

Answer is A

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

The probability that a warning would be given is 0.97.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

A hospital has three independent fire alarm systems, with reliabilities of 0.95, 0.97, and 0.99.

This means,

The probability that one alarm will give a warning = 0.95

The probability that one alarm will give a warning = 0.97

The probability that one alarm will give a warning = 0.99

Combining each of them we get,

0.95 + 0.97 + 0.99 = 2.91

Divide by 3.

= 2.91 / 3

= 0.97

This means,

The probability that a warning would be given is 0.97.

Thus,

The probability that a warning would be given is 0.97.

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In the given data set, there are 7 values in the given range.

A data set is a collection of data. In the case of tabular data, a data set corresponds to one or more database tables, where every column of a table represents a particular variable, and each row corresponds to a given record of the data set in question.

Given is a set of data we need to determine how many students are in the range 12 cm to 13.9 cm,

So,

Here we just need to find the number of values between 12cm and 13.9 cm, from the given table, these are:

12.1 cm, 13.5 cm, 12.4 cm, 13.7 cm, 13.8 cm, 12.5 cm, 13.1 cm

So, there are 7 values in the given range, which means that 7 students are in the range of 12cm and 13.9cm.

Then the correct option is 7.

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The number of the fraction 3/8 that we can get in 6, is: 16.

We are asked to find how many of the fraction, 3/8, we will have in 6.

This implies that, what number would we need to multiply with 3/8 to get 6?

To determine this, all we need to do is to divide 6 by the fraction, 3/8.

[tex]6 \div \frac{3}{8}[/tex]

[tex]6 \times \frac{8}{3} \\\\= \frac{6 \times 8}{3} \\\\= \frac{48}{3} \\\\\mathbf{= 16}[/tex]

Therefore, the number of the fraction 3/8 that we can get in 6 is: 16.

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The number -0.5 divided by itself equals to 1. In general, any number (except zero) divided by itself will always equal to 1.

To find the answer to the given number −0.5/-0.5, you should simply divide the negative number -0.5 by itself (-0.5). Here, a negative number divided by another negative number results in a positive result. Therefore, -0.5/-0.5 equals 1.

In general terms, any non-zero number divided by itself will always equal 1. This is because the division operation is asking 'how many times does this number fit into itself?', and the answer is invariably 'once'.

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No Euclidean triangles can have angles that sum to more than 180°, so there are zero triangles with the given measures in Euclidean space; however, exactly one right-angled spherical triangle with these angles exists on a curved surface like a sphere.

The question asks how many triangles exist with the given angle measures of 55°, 45°, and 90°. In Euclidean geometry, the sum of the interior angles of a triangle must equal exactly 180°. Since 55° + 45° + 90° = 190°, which is greater than 180°, no Euclidean triangle can have those angle measures. Therefore, there are zero triangles that can exist with the given angle measures in a flat, two-dimensional Euclidean space.

However, in the context of spherical geometry, triangles can have angles that sum to more than 180°. The provided angles actually describe a right-angled spherical triangle, of which exactly one exists with these measures. This is because on a spherical surface, the sum of the angles of a triangle can be greater than 180° due to the curvature of the space.

To find the distance between two points (1,5) and (7,9), you can use the distance formula sqrt((x2 - x1)^2 + (y2 - y1)^2). Rounding to the nearest tenth, the distance is approximately 7.2.

To find the distance between two points, we can use the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using the given points (1,5) and (7,9), we substitute the values into the formula:

d = sqrt((7 - 1)^2 + (9 - 5)^2) = sqrt(36 + 16) = sqrt(52)

Rounding to the nearest tenth, the distance between the two points is approximately 7.2.