Given tan a = ; and that angle a is in quadrant i, find the exact
value of cos a in simplest radical form using a rational denominator.
9
4

Answer:

6

Step-by-step explanation:

30 ÷ 5 =6

hope it helped:))))

Answer:

z = 6

Step-by-step explanation:

5 x 6 = 30 - 17 = 13

Answer: 38.465 feet

Step-by-step explanation: The diameter (7 feet) divided by 2, equals 3.5. multiply 3.5 squared (12.25 feet) by pi (3.14) equals your answer of 38.465 feet.

Answer:

(1st option) x>-3

Step-by-step explanation:

therefore, x is greater than negative three

x>-3

A quadratic function graph is a parabola 14y=4x-25-x²

A quadratic function graph is a parabola. Many mathematicians used their research to explain the parabola notion. Pascal defined a parabola as the projection of a circle. Galileo explained that projectiles take a path known as a parabolic path once they begin to fall under the effect of uniform gravity. Numerous bodily movements take the form of a curved parabola.

We know that the standard form of the parabola is

F(x)= ax²+bx+c

|y-a|²=(x-a)²+(y-b)²

|y+5|²=(x-2)²+(y+5)²

y²+4-4y=x²+4-4x+y²+25+10y

x²-4x+4y+10y+25=0

14y=4x-25-x²

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The value that fits all the conditions is 35.

Based on the given clues, we can deduce certain conditions about the unknown value:

The value is odd: Since it is stated that the value is odd, we can eliminate any even numbers from consideration.

The value is a multiple of five: The value must be divisible by 5, which narrows down the possibilities further.

t > U: The tens digit is greater than the units digit. This means that the value must have a two-digit format, where the tens digit is larger than the units digit.

The tens digit is a square number: The tens digit must be a perfect square, meaning it can only be 1, 4, or 9.

h = u - 3: The hundreds digit (h) is equal to the units digit (u) minus 3. This indicates that the hundreds digit is three less than the units digit.

Taking all of these clues into account, we can generate a few possible numbers that satisfy the conditions. Let's consider the values that fulfill these conditions: 15, 25, 35, 45, 55, 65, 75, 85, 95.

Out of these options, the value that meets all the given conditions is 35.

Here's how it satisfies each clue:

It is an odd number.

It is a multiple of 5.

The tens digit (3) is greater than the units digit (5).

The tens digit (3) is a square number.

The hundreds digit (3) is equal to the units digit (5) minus 3.

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The value of the given expression [\(87^3+ 13^3/87^2 -87 * 13 + 13^2\)] by simplifying the numerator and denominator using suitable identities is 100.

We will first calculate the numerator:

As  (\(a^3\) + \(b^3\)) = (a + b)(\(a^2\) - ab + \(b^2\)) :

\(87^3\) + \(13^3\) = (87 + 13)(\(87^2\) - \(87 * 13\) + \(13^2\))

= 100(\(87^2\) - 87 * 13 + \(13^2\))

Now, calculate the denominator:

\(87^2 - 87 * 13 + 13^2\)

As,(\(a^2 -2ab +b^2\)) =\((a - b)^2\):

\(87^2 - 87 * 13 + 13^2 = (87 - 13)^2\)

\(= 74^2\)

So by solving the equation further:

\((87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)\)

As we can see the numerator and denominator are the same expressions (\(87^2 - 87 * 13 + 13^2\)). so, they cancel each other:

\((87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100\)

So, the value of the given expression is 100.

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The interquartile range of the data set is equal to 6.

The interquartile range is a measure of statistical dispersion, or data spread. The IQR is also known as the midspread, middle 50%, or middle 50%.

The interquartile range is a measurement of a data set's "middle fifty." A range is a measurement of where a set's beginning and end are located.

Given data set is 2 4 6 8 10 12. The upper range is 8 10 12 and the lower range is 2 4 6.

Calculate the median of the upper range and the lower range and subtract it.

Median upper range = 10

Median lower range = 4

The interquartile range is calculated as,

IQR = 10 - 4 = 6

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The standard form of the equation of the quadratic function is f(x) = 3x² + 12x + 15.

We are given a quadratic function whose vertex is (h, k) and a point (x, y) that lies on the quadratic function. We are to find the standard form of the equation of the quadratic function.

To find the standard form, we use the vertex form of the quadratic equation, which is given by: f(x) = a(x - h)² + k. Here, (h, k) = (-2, 3) represents the vertex of the quadratic function. Therefore, we substitute the values of h and k in the above formula: f(x) = a(x - (-2))² + 3

Simplifying the above equation, we get: f(x) = a(x + 2)² + 3.

Next, we are given a point (x, y) = (-3, 6) that lies on the quadratic function. Therefore, we substitute these values in the above equation and solve for 'a'. 6 = a(-3 + 2)² + 3

We simplify the above equation to get: 3 = a

Simplifying the equation f(x) = a(x + 2)² + 3 and substituting the value of 'a' = 3, we get:f(x) = 3(x + 2)² + 3

Simplifying the above equation, we get: f(x) = 3x² + 12x + 15

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Answer:

9.7 miles

Step-by-step explanation:

The shortest distance between 2 points is a straight line

The distance from point A to point B is

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

d = sqrt( ( 3 - -3)^2 + ( 4-1) ^2)

d = sqrt( ( 6)^2 + ( 3) ^2)

d = sqrt(36+9)

d = sqrt(45)

d =6.7  to the nearest tenth

The distance from point B to point C is

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

d = sqrt( ( 3 - 3)^2 + ( -2-4) ^2)

d = sqrt( ( 0)^2 + ( -6) ^2)

d = sqrt(36)

d = 6

But They only made it half way so 1/2 (6) =3

Add the distances together

6.7+3 = 9.7 is the minimum distance

Answer:

The ground exerts an equal force on the golf ball and a golf ball striking the ground is a collision

Step-by-step explanation:

Answer:

1. and 2.

Step-by-step explanation:

we know that

The difference between a rational number and n irrational number is always an irrational number

Example

Prove by contradiction

The difference between a rational number and an irrational number is a rational number

we have that

therefore

By contradiction, the original statement is true

Answer:

(x+4)(3x-2)(x+1)

Step-by-step explanation:

Answer:

5.57

Step-by-step explanation:

In order to find the are of a square you would use the equation a². However, since you are finding the length of one side and its a square, you use the equation \(\sqrt{a}\). The area of this square is 31 sq in., so you would replace a with 31. The equation then becomes \(\sqrt{31}\). When out into a calculator, the answer is 5.567764... which rounded up to the nearest hundreth is 5.57.

Answer:

5 servings

Step-by-step explanation:

there is not enough juice for 6 or more servings

There are no vectors among the options provided that are parallel to (1²2).

To determine if two vectors are parallel, we can compare their direction ratios.

Two vectors are parallel if their direction ratios are proportional.

Let's compare the given vector (1²2) with each of the options provided:

Vector (7²) (12²) (-22) (3) 12/ (ő) 4 24 3 13/​:

Comparing the direction ratios, we have:

1/7 = 2/12 = 2/-22 = 3/4 = 24/3 = 12/13.

Since the direction ratios of the given vector (1²2) are not proportional to the direction ratios of any of the options, none of the options are parallel to (1²2).

summary, none of the vectors (7²) (12²) (-22) (3) 12/ (ő) 4 24 3 13/​ are parallel to the given vector (1²2).

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Answer:

6.375 tons or 6 3/8 tons

Step-by-step explanation:

According to Given data, calculation are as follows,

Sunburst pebbles = 2 1/2 tons or 2.5 tons

Black polished pebble = 3 1/4 tons or 3.25 tons

River pebble = 5/8 tons or o.625 ton

So, total weight of pebbles are as follows,

Total weight = 2.5 tons + 3.25 tons + 0.625 ton

= 6.375 tons or 6 3/8 tons

Hence, total weight of pebbles was 6 3/8 tons.

You have the expression 3⁰

Take into account that any number powered to 0 is equal to 1.

Then, you have:

3⁰ = 1

Answer:

Simplify the expression.

Exact Form:

37/40

Decimal Form:

0.925

Step-by-step explanation:

Answer:

Step-by-step explanation:In a connected graph G, every minimum spanning tree is a minimum bottleneck tree of G.

A minimum spanning tree of a graph is a tree that spans all the vertices of the graph while minimizing the sum of the edge weights. It represents the minimum cost or distance required to connect all the vertices together.

A bottleneck tree of a graph is a spanning tree that minimizes the maximum weight of any edge in the tree. In other words, it minimizes the bottleneck or the highest-weight edge among all the edges in the tree.

Now, every minimum spanning tree can be considered as a minimum bottleneck tree because the minimum spanning tree already ensures the connectivity of all the vertices while minimizing the total weight. By nature, the maximum weight of any edge in the minimum spanning tree will be less than or equal to the maximum weight of any edge in any other spanning tree of the graph.

Therefore, since the minimum spanning tree has the minimum total weight and the maximum weight of any edge in it is minimized, it automatically becomes a minimum bottleneck tree.

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By evaluating the linear equation in t = 5 seconds, we will see that the distance traveled is 271.93 feet.

Here we know that the line that defines the distance traveled by the ball (y) as a function of time (t) is:

y = 3.98 + 53.59*t

Now we want to predict the distance traveled y the ball if it travels for 5 seconds, so we just need to evaluate the above linear equation in t = 5.

So we will get:

y = 3.98 + 53.59*5  = 271.93

So we conclude that the distance traveled in that time is 271.93 feet.

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Answer: 271.93 feet

Step-by-step explanation:

I took the test

Answer:

AB = 17 meters

Step-by-step explanation:

Given that the triangle, ∆ABC, has 2 congruent sides that are indicated with a single marking on segment AC and segment AB, both segments would be of equal measure.

Therefore, since the measure of segment C is 17 meters, the measure of segment AB = measure of segment AC = 17 meters.

Segment AB = 17 meters. It is congruent to segment AC.

Answer:

13

Step-by-step explanation:

When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.

According to me , independent is the word which is associated with multiplication when computing probabilities . Because when the events are independent then we multiply the probabilities .

According to the multiplication rule of probability, the probability of occurrence of both the events A and B is equal to the product of the probability of B occurring and the conditional probability that event A occurring given that event B occurs.

The probability of the union of two events is equal to the sum of individual probabilities. The union of two set contains all the elements of previous sets. The union is denoted by ∪. The equation for the students earnings will be expressed as P(A∪B). The occurrence of event A changes the probability of B then the events are dependent. If the probability of two events happening together is zero then the events are mutually exclusive.

Therefore,

When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.

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Answer:

A

Step-by-step explanation:

the graph is mostly going in an upward direction therefore both x and y are increasing.

Answer:

-528/25

Step-by-step explanation:

Answer:

Answer: 67.97%

Step-by-step explanation: BEWARE: THE ANSWER IS NOT 39.56%.

Given a point with coordinates (x, y), to rotate 90º counterclockwise, the rule is:

In thisc ase, we have the point:

Applying the rule:

The upper bound is 1842 and lower bound is 1692. By using these boundaries and t-table, the sample mean is 1767 and sample standard deviation = 133.98.

Here, the two boundaries are 1692 and 1842.

Mean = (1692+1842) /2 = 1767

Here the degree of freedom, df = (n-1) = 25-1 =24

Margin of error = (1842-1692)/2 = 75

Confidence level = 99%

From the t table, value of T with confidence level 99% and df= 24 is 2.80

The equation for margin of error is M = Ts/√n

            M= 75 , T= 2.80, n =25

75 = (2.80 × s) / √25

75 = 2.80s/ 5

s = (75×5)/2.80 = 133.928 = 133.93

So the sample mean is 1767 and the standard deviation is 133.93.

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Answer: Yes

Step-by-step explanation:

\(\frac{123}{2}=\frac{246}{4}=\frac{369}{6}=\frac{492}{8}=61.5\).

Since the ratio of distance in miles and the time in hours is constant, the relationship is proportional.