Evaluate the given expression when x = 3.
2
x + x² +2:

A scalene triangle has at least two congruent sides is a FALSE statement.

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.

In a triangle, the sum of all three angles is 180°

Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.

A scalene triangle is a triangle whose all sides are unequal.

Since congruent sides are the sides that are equal in length but in a scalene triangle, none of the sides are equal to each other.

Hence "A scalene triangle has at least two congruent sides is a FALSE statement".

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The explicit formula for the given sequence is a(n) = 1 + 4(n - 1).

A recursive function is one that iterates or uses its very own previous term to determine subsequent terms, resulting in a series of terms.

The recursive formula for an arithmetic sequence is as follows.

a(1)  = 1 and a(n) = a(n - 1) + 4.

Remember that this formula provides us with two types of data.

Let's look for a formal formula again for sequence.

Thus, by the use of recursive definition, the explicit formula for the sequence is a(n) = 1 + 4(n - 1).

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Answer:

x=3.5

Y=None

Step-by-step explanation:

An arithmetic progression (AP) is a sequence of numbers ordered such that the difference between any two consecutive numbers is a constant value. Also called arithmetic sequence. For example, the sequence of natural numbers: 1, 2, 3, 4, 5, 6, … is an arithmetic sequence in which the common difference between two consecutive terms (e.g., 1 and 2) is 1 (2 - 1) ... It can be seen that the tolerance of two consecutive terms is equal to 2, even for odd and even numbers.

First term a=-3.5,

Common difference d=2.25,

Number of terms n=8

Solution:

Here first term a=-3.5,

Common difference d=2.25

We know that,

f(n)=a+(n-1) d

f (8)=-3.5+(8-1)(2.25)

=-3.5+(15.75)

=12.25

We know that,

Sn=n2[2a+(n-1)d]

∴S8=82⋅[2(-3.5)+(8-1)(2.25)]

=4⋅[-7+(15.75)]

=4⋅[8.75]

=35

Hence, 8th term of the given series is 12.25 and sum of first 8th term is 35.

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Answer:16

Step-by-step explanation:

Answer:29.3 repeating

Step-by-step explanation:Just use

calculator

By substitution, the solution of the system of equations, r + s = -12 and 4r - 6s = 12, is (-6 , -6).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in r and s,

r + s = -12     (equation 1)

4r - 6s = 12     (equation 2)

Using the first equation, find the value of one variable, lets say r, in terms of the other.

r + s = -12     (equation 1)

r = -12 - s

Substitute the value of r to the second equation.

4r - 6s = 12     (equation 2)

4(-12 - s) - 6s = 12

-48 - 4s - 6s = 12

Combining all terms containing the variable s on one side and the constants on the other side of the equality, and solving for s.

-48 - 4s - 6s = 12

-4s - 6s = 12 + 48

-10s = 60

s = -6

Substitute the value of s in the equation of r and solve for r.

r = -12 - s

r = -12 - (-6)

r = -12 + 6

r = -6

Hence, the solution of the given system of equations is (-6 , -6).

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Answer: y = -4x + 13

Step-by-step explanation:

Given points (2, 5) and (3, 1)

First Step find the slope given the two points:

Use the slope formula [tex]m=\frac{y2 - y1}{x2 - x1}[/tex]

[tex]m = \frac{1-5}{3-2} = -4[/tex] (Result)

Slope is equal to -4

Second step plug into y - y1 = m(x - x1) formula (Point Slope Formula)

For this I am using the first coordinate pair given (2, 5)

y - 5 = -4(x-2)

y - 5 = -4x + 8

y = -4x + 13

The card with the number 7 was removed.

So,

Therefore, the card with the number 7 was removed.

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The speed of Caroline in miles per hour is 0.5 miles/hour.

Given that, Caroline walks 9 1/2 inches per second.

How to convert inches to miles. To convert an inch measurement to a mile measurement, divide the length by the conversion ratio. The length in miles is equal to the inches divided by 63,360.

Now, 9.5 inches/second

We know that 1 inch/second=0.0568182 miles/hours

So, 9.5 × 0.0568182=0.5397729 miles/hours

≈0.5 miles/hours

Therefore, the speed of Caroline in miles per hour is 0.5 miles/hour.

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Your question is incomplete, probably the complete question/missing part is:

Give the rate in miles per hour. Round to the nearest tenth. Caroline walks 9 1/2 inches per second.

Answer:

Perimeter: 2(7+12), 2*7+2*12, 7+12+7+12

Area: 7*12, 7*10 + 7*2

neither: 7+12

Step-by-step explanation:

perimeter is like if you want a fence all the way around your property and your yard is 7x12 feet. In that case you could use the first option because you have to count the sides and add them up. If it’s a rectangle then there are 2 12’s and 2 7’s so the first one would work. The fourth one also uses distribution. The Fourth and first one are pretty much the same and have the same answer so the fourth one would work for perimeter.

Another way to do perimeter is to instead of multiplying, is to add the sides. 7+12+7+12 is basically 7 times 2 plus 12 times 2 (the fourth ne) and the answer is still correct so this one works too,

For area you times one of the dimensions by the other so 7*12 would work for area.
7*10 + 7*2 would also work because that uses the distributive property and that’s 70 + 14 which is 84 which is still the same answer.


The only one that falls under neither is the fifth one. 7+12 is half of the perimeter because it only adds two of the sides together and has n multiplying so it’s not area either.

Answer: 4x^4

Step-by-step explanation:

from the law of indices,

( a^x)^y = a^xy

Now from the question

( 8x^6)^2/3

8^2/3X^6x2/3

From another law of indices,

a^x/y = ( y cube root of a)^x

8^2/3 = 2^2 = 4 ——— 1

Now X^6*2/3

= X^4 ——————-2
Now combine 1 & 2 together gives the answer

= 4x^4

The tangent ratio for the ΔABC is tanФ = 1.

Some of the trigonometric ratios are-

For the given right angles triangle ABC.

The sides AC = CB = 15

As, the angle ACB is the right angle i.e, ∠ACB = 90°, so, AB is the hypotenuses of the triangle.

For finding the value of tangent ratio;

tan = perpendicular/base

tan B = AB/ CB

tan B = 15/15

tan B = 1/1

tan B = 1

Thus, the value of tangent ratio = 1.

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Step-by-step explanation: I hope this helps.

Answer: 7.07 units

When P(A | B) = P(A) and P(B ∩ A) = P(B). Then, the given events A and B are independent events.

Independent events are those where the occurrence is unrelated to any other event.

Now, as for the given question.

There are two events given as A and B.

The probability of occurrence of event A is P(A).

The probability of occurrence of event B is P(B).

The occurrence of the event A when B is already happened is denoted by P(A | B).

The intersection of events A and B are given as; P(B ∩ A).

Now, it is given in the question that;

P(A | B) = P(A) and P(B ∩ A) = P(B)

And, we already know that, the formula of the conditional probability for event A when event B has already occurred is;

P(A | B) = P(B ∩ A)/P(B)

This can also be written as;

P(B ∩ A) = P(A | B).P(B)

Now, P(A | B) = P(A), replace in the obtained equation.

P(B ∩ A) = P(A).P(B)

The obtained result is the condition for independent events.

Therefore, the events A and B are found to be independent events.

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Answer:

The statement is true.

Step-by-step explanation:

Let us plug[tex]24=-4(8)-8[/tex] in 8 for [tex]x[/tex] and 24 for [tex]y[/tex] in our equation: [tex]24 =-4 (8) - 8[/tex].

Now we will solve in the order described by PEMDAS.

-4(8)=32

32-8=24

24=24

Thus, our statement is true.

When the thermometer reads 6 degrees the temperature drops 15 degrees overnight, the temperature at 9:00pm will be 16°.

From the information, the thermometer reads 6 degrees the temperature drops 15 degrees overnight the it rises 25 degrees at 9:00am.

Therefore, the temperature at 9:00pm will be:

=6° - 15° + 25°

= 16°

Therefore, the temperature at 9:00pm will be 16°.

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Answer:

Negative. Because he should run all seven weeks to get positive result.

Answer:

$3.90

Step-by-step explanation:

Expected Value formula

[tex]\boxed{\displaystytle E(x)=\sum x_iP(x_i)}[/tex]

where:

Given table:

[tex]\begin{array}{l | ccccc}\sf Payout\:(\$) & 0 & 2 & 4 & 8 & 10\\\cline{1-6} \sf Probability & 0.35 & 0.2 & 0.1 & 0.2 & 0.15\end{array}[/tex]

Substitute the given values into the Expected Value formula:

[tex]\begin{aligned}\implies E(x) & = 0(0.35) + 2(0.2)+4(0.1)+8(0.2)+10(0.15)\\& = 0+0.4+0.4+1.6+1.5\\& = 3.9\end{aligned}[/tex]

Therefore, the expected value is $3.90.

So, on average, you would expect to receive $3.90 in winnings per game.

The image of the point after the translation is (-4, -1)

The point is given as

(1,4)

The translation is given as

Left 5 units and down 5 units

This is represented as

(x, y) = (x - 5, y - 5)

So, we have

(x, y) = (1 - 5, 4 - 5)

Evaluate

(x, y) = (-4, -1)

Hence, the image of the point after the translation is (-4, -1)

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We conclude that MN ≅ RS under the rule in which if a = b, and b = c; then automatically a = c.

So,

Given: MN ≅ PQ, PQ ≅RS

To Prove: MN ≅ RS

This rule satisfies the above condition.

Therefore, MN ≅ RS under the rule in which if a = b, and b = c; then automatically a = c.

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Answer:

C

Step-by-step explanation:

a number is only divisible by 4, if the number formed by the last 2 digits is divisible by 4.

The expression "quantity negative three and one third times n plus one sixth end quantity plus quantity one and three sixths times n minus three twelfths end quantity" or (-3 1/3n + 1/6) + (1 3/6n - 3/12) is equivalent to "negative eleven sixths times n minus one twelfth" or -11/6n - 1/12.

An algebraic expression is a number, variable, or the combination of both and operational symbols.

To determine the equivalent of the expression "quantity negative three and one third times n plus one sixth end quantity plus quantity one and three sixths times n minus three twelfths end quantity" or simply (-3 1/3n + 1/6) + (1 3/6n - 3/12), combine all like terms and perform necessary operations.

(-3 1/3n + 1/6) + (1 3/6n - 3/12)

⇒ -3 1/3n + 1 3/6n + 1/6 - 3/12

⇒ (-3 1/3 + 1 3/6)n + 1/6 - 3/12

⇒ (-10/3 + 9/6)n + 2/12 - 3/12

⇒ (-20/6 + 9/6)n - 1/12

⇒ -11/6n - 1/12

Hence, the equivalent expression is negative eleven sixths times n minus one twelfth" or -11/6n - 1/12.

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For equation (1), we get the Slope as 3 / 4 and y intercept as - 9 and for equation (2), we get the Slope as 3 / 4 and y intercept as - 4.

We are given 2 equations:

y = 3 / 4 x - 9 ...(1)

and y = 3 / 4 x - 4 ... (2)

Slope for equation (1) will be

slope = m1 = 3 / 4

Slope for equation (2) will be

Slope = m2 = 3 / 4

Y intercept for equation (1) will be:

= - 9

Y intercept for equation (2) will be:

= - 4

Also, since the Slope of equation are equal, so, it has no solutions as they are parallel to each other.

Therefore, for equation (1), we get the Slope as 3 / 4 and y intercept as - 9 and for equation (2), we get the Slope as 3 / 4 and y intercept as - 4.

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Answer:

0=-6 (No solution)

Step-by-step explanation:

2(7x-7)=14x-20 - Distribute the 2 to 7x-7

14x -14 = 14x -20 - Subtract +14 from both sides
    + 14          +14

14x = 14x -6

-14x    -14x

0=-6

Based on the information given, the area of the trapezoid will be 89.7cm².

It should be noted that the formula for calculating the area of a trapezoid will be:

= (a + b)/2 × h

where a = 8

b = 13

h = 7.8

Area = (13 + 8)/2 × 7.8

= 21/2 × 7.8

= 11.5 × 7.8

= 89.7cm²

Therefore, based on the information given, the area of the trapezoid will be 89.7cm².

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In horse racing, a trifecta, which is a bet that the first three finishers in a race are​ selected, and they are selected in the correct order, involves selection done in permutation.

Permutation is the method of selecting or arranging objects or numbers in order. It is used when the order or sequence of the elements selected is important. The number of permutations of n objects taken r at a time is determined by the following formula: P(n , r) = n!

On the other hand, combination is the method of selecting or arranging objects or numbers from a group of objects or numbers where order does not matter. The number of combinations of n objects taken r at a time is determined by the following formula: C(n , r) = n!/[r!(n - r)!]

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Answer:

Step-by-step explanation:

Because the order of the first three finishers does not make a​ difference, the trifecta involves permutations

For the given function, we have that:

The domain of a function is the set that contains all possible input values for the function. In a graph, it is the set that contains all the values of x of the function.

Hence, the domain is [-4,4] for the given function.

The zeros of a function are the values of x for which f(x) = 0, on the graph they are the values of x when the function crosses the x-axis.

For this problem, the function does not cross the x-axis, hence it has no zeros.

Looking at a graph, we have that:

Hence, for the given function:

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Answer: $744.25

Step-by-step explanation:

6 * 114.95 = 689.7

689.7 + 54.55 = 744.25