Which set of numbers does NOT represent the lengths of the sides of a triangle? (6, 18, 23) (6, 22, 17) (16, 24, 7) (22, 8, 15​

Answer:

an = 7.5 - 5.5(n - 1).

Step-by-step explanation:

The common difference d = -5.5.

The first term is given as 7.5.

Explicit formula is

an = a1 + (n - 1)d

= 7.5 + (n - 1)-5.5

= 7.5 - 5.5(n - 1)

Answer:

secΘ = \(\sqrt{17}\)

Step-by-step explanation:

using the identity

sec²Θ = tan²Θ + 1 , then

sec²Θ = 4² + 1 = 16 + 1 = 17 ( take square root of both sides )

secΘ = ± \(\sqrt{17}\)

since 0° < Θ < 90° , then secΘ > 0

secΘ = \(\sqrt{17}\)

Answer:

The mistake is the problem itself.  It should be

5x=100

x=100÷5

x=20

Step-by-step explanation:

The mistake is the problem itself.  It should be

5x=100

x=100÷5

x=20

Answer:

there's no picture

Step-by-step explanation:

...............

Answer:

225,750 cubic feet.

Explanation:

• Her backyard is ,56 steps long, and ,43 steps wide,.

• Each of her steps is 2.5 feet.

Therefore:

Therefore, the volume of the new garage:

The volume of her new garage is 225,750 cubic feet.

26a - 10

Factor:

2(13a - 5)

10(2.6a - 1)

Answer:

The formula for density (ρ) is:

Density (ρ) = Mass (m) / Volume (V)

Step-by-step explanation:

Where:

To find the domain and range of a function f(x), we need to consider the values that x can take and the corresponding values of f(x).

The domain of a function is the set of all possible input values, or x-values, for which the function is defined. In other words, it is the set of values that x can take without resulting in an undefined output. Typically, the domain is specified by any restrictions on the input, such as square roots, fractions, logarithms, or division by zero.

The range of a function is the set of all possible output values, or y-values, that the function can produce. In other words, it is the set of values that f(x) can take on, as x varies over the domain.

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Given question is incomplete. Subject may be asking: Write the domain and range of function f(x).

The second additional Polar representation of the point (3,-π/6) can be ($\frac{3\sqrt{6}}{2}$, $\frac{5\pi}{3}$) or ($\frac{3\sqrt{6}}{2}$, $-\frac{7\pi}{3}$).

We have a point in polar coordinates (3,-π/6) and we have to find two additional polar representations of this point. Let's recall the formula for converting from Cartesian to polar coordinates :x = rcosθy = rsinθAnd

the formula for converting from polar to Cartesian coordinates :r = √(x²+y²)θ = arctan(y/x)So, we can use the second formula to convert (3,-π/6) to Cartesian coordinates:$$x=3\cos(-\frac{\pi}{6})=3\cdot \frac{\sqrt{3}}{2}=\frac{3\sqrt{3}}{2}$$$$y=3\sin(-\frac{\pi}{6})=3\cdot \frac{-1}{2}=-\frac{3}{2}$$

Now we can use the first formula to convert back to polar coordinates:$$r=\sqrt{(\frac{3\sqrt{3}}{2})^2+(-\frac{3}{2})^2}=\frac{3\sqrt{6}}{2}$$$$\theta=\arctan(-\frac{3}{3\sqrt{3}})=-\frac{\pi}{3}$$

So, the first additional polar representation of the point (3,-π/6) is ($\frac{3\sqrt{6}}{2}$, $-\frac{\pi}{3}$).To find the second polar representation,

we need to add or subtract multiples of π to the angle until it is in the range [-2π, 2π].$$-\frac{\pi}{3}+2\pi=\frac{5\pi}{3}$$$$-\frac{\pi}{3}-2\pi=-\frac{7\pi}{3}$$

So, the second additional polar representation of the point (3,-π/6) can be ($\frac{3\sqrt{6}}{2}$, $\frac{5\pi}{3}$) or ($\frac{3\sqrt{6}}{2}$, $-\frac{7\pi}{3}$).

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Answer:

We have,

3+4(w+5)

=31 Or, 3+20+4w

=31 or, 4w

=31−23

w=8/4

Thus, w comes out to be 2 .

Step-by-step explanation:

Hope it is helpful....

Answer:

w=2

Step-by-step explanation:

3 + 4(w + 5) = 31

distribute 4(w + 5)

4 x w = 4w

4 x 5 = 20

rewrite your equation

3 + 4w + 20 = 31

add like terms

3 + 20 = 23

rewrite equation

4w + 23 = 31

subract 23 on both sides

4w + 23 = 31

-23 -23

4w = 8

divide by 4 on both sides to get w by itself

4w = 8

4      4

w = 2

Ayaan drank 11/4 bottles of water during the soccer game, which can be expressed as a mixed numeral 2 and 3/4.

To convert the fraction 11/4 to a mixed numeral, we need to determine the whole number part and the fractional part.

Divide the numerator (11) by the denominator (4).

11 ÷ 4 = 2 remainder 3

The quotient 2 represents the whole number part, and the remainder 3 represents the fractional part.

Write the mixed numeral using the whole number part and the fractional part.

The mixed numeral for 11/4 is:

2 and 3/4

Therefore, Ayaan drank 11/4 bottles of water during the soccer game, which can be expressed as a mixed numeral 2 and 3/4.

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To solve the savings plan balance, we have to calculate the interest for 19 months. The formula for calculating interest for compound interest is given below:$$A = P \left(1 + \frac{r}{n} \right)^{nt}$$where A is the amount, P is the principal, r is the rate of interest, t is the time period and n is the number of times interest compounded in a year.

The given interest rate is 11% per annum, which will be converted into monthly rate and then used in the above formula. Therefore, the monthly rate is $r = \frac{11\%}{12} = 0.0091667$.

The monthly payment is $PMT = $250. We need to find out the amount after 19 months. Therefore, we will use the formula of annuity.

$$A = PMT \frac{(1+r)^t - 1}{r}$$where t is the number of months of the plan and PMT is the monthly payment. Putting all the values in the above equation, we get:

$$A = 250 \times \frac{(1 + 0.0091667)^{19} - 1}{0.0091667}$$$$\Rightarrow

A = 250 \times \frac{1.0091667^{19} - 1}{0.0091667}$$$$\Rightarrow

A =250 \times 14.398$$$$\Rightarrow A = 3599.99$$

Therefore, the savings plan balance after 19 months with an APR of 11% and monthly payments of $250 is $3599.99 (approx).

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Answer:

A

Step-by-step explanation:

The line starts at -35, meaning that she starts the ascent 35 meters below the surface and goes upwards over time.

Answer:

a

Step-by-step explanation:

the starting point of the graph or also known as the y axis starts at -35

To satisfy the inequality x less-than StartFraction 7 over 12 EndFraction.

Inequalities are called as the mathematical expressions in which both sides are nonequal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs can be used in place of the equal sign in between.

The inequality is 1/4 + x < 5/6 in order to solve this inequality we need to isolate the value of x, that is our variable of interest. This is shown bellow:

1/4 + x < 5/6

x < 5/6 - 1/4

LMC is used to subtract the fractions we have as follows:

x < (2*5 - 3*1)/12

x < (10 - 3)/12

x< 7/12

The inequality must be satisfied for x to be smaller than 7/12.

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Answer:  x < 7/12

Step-by-step explanation:

Given statement solution is :- The correct answer is: The frequency is 3 more than expected.

To determine the expected frequency of landing on an even number when rolling a fair six-sided number cube, we need to calculate the probability of landing on an even number and multiply it by the total number of rolls.

The number cube has six possible outcomes: 1, 2, 3, 4, 5, and 6. Of these, three are even numbers: 2, 4, and 6. Therefore, the probability of rolling an even number is 3/6, which simplifies to 1/2 or 0.5.

The expected frequency can be found by multiplying the probability by the total number of rolls:

Expected frequency = Probability of landing on an even number × Total number of rolls

Expected frequency = 0.5 × 30 = 15

Now, we can compare the expected frequency (15) to the actual frequency (18) given in the problem statement.

The actual frequency is 18, and it is 3 more than the expected frequency (18 - 15 = 3).

Therefore, the correct answer is: The frequency is 3 more than expected.

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Given:

The equation that represents Joe's journey is :

From the equation, we can determine that:

At t = 1 hr

At t = 2hrs:

At t = 3hrs:

We have the points (1, 4), (2, 8), (3, 12)

We can now check the options for the graph that has the points.

Checking through the options, we can see that the graph that has the points we have obtained is the chart A

Answer: Option A

The expression for the total cost of Sal's purchases is 7x + 5y cents.

We know that Sal paid (x + 2y) cents for a quart of milk and (2x + y) cents each for three cartons of orange juice.To find the total cost of Sal's purchases we need to add the cost of the milk and the cost of the three cartons of orange juice and simplify the expression.The cost of the milk is given as (x + 2y) cents. The cost of three cartons of orange juice is (2x + y) cents each.

Therefore, the cost of three cartons of orange juice is (3 × (2x + y)) cents. To find the total cost of Sal's purchases, we add the cost of the milk and the cost of the three cartons of orange juice.(x + 2y) + (3 × (2x + y)) cents = x + 2y + 6x + 3y cents= 7x + 5y cents.

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The final velocity of the parameters is 13.5m/s

In this question, the given parameters are represented as

Formula: v = u + at

Initial velocity = 3m/s

Acceleration = 1.5m/s²

Time = 7 seconds

When these parameters are represented using their required notation, we have the following representations

u = 3m/s

a = 1.5m/s²

t = 7 s

Next, we substitute the above parameters in the above equation

So, we have the following representation

v = 3 + 1.5 * 7

Evaluate the products

This gives

v = 3 + 10.5

Evaluate the sum

So, we have the following representation

v = 13.5

The notation v represents the final velocity

Hence, the final velocity is 13.5m/s

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The value of the composite function (f o g)(3) is 1603

The functions are given as

f(x) = 3x² - 7x - 3

g(x) = -4x - 10

Next, calculate (f o g)(x) using

(f o g)(x) = f(g(x))

So, we have

(f o g)(x) = 3(-4x - 10)² - 7(-4x - 10) - 3

Substitute 3 for x.

So, we have

(f o g)(3) = 3(-4 x 3 - 10)² - 7(-4 x 3 - 10) - 3

Evaluate

(f o g)(3) = 1603

Hence, the value of the composite function (f o g)(3) is 1603

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Answer:

5x-2y =80

x+y=30

Step-by-step explanation:

Basically, 5x is the points earned by correct questions (5 points per right answer) and -2x is the points lost by wrong answers (2 points taken away for every wrong answer). The total points the contestant earned is 80, which is why we set this equation equal to 80. Hence, 5x-2y=80.

They also tell us that the contestant answered a total of 30 questions, so x and y combined would be the total number of questions. Hence, x+y=30.

Answer:

5x-2y =80

x+y=30

Step-by-step explanation:

This situation can be represented by a system of two linear equations, with one equation representing the number of points earned and one equation representing the number of questions answered.

First, determine the equation representing the number of points earned.

Since contestants earn 5 points for every correct answer and x is the number of questions answered correctly, 5x represents the amount of points earned from correct responses. Since contestants lose 2 points for every incorrect answer and y is the number of questions answered incorrectly, 2y represents the amount of points lost from incorrect responses.

The amount of points earned minus the amount of points lost yields the total number of points at the end of the game, 80.

Next, determine the equation representing the number of questions answered.

Since x represents the number of questions answered correctly and y represents the number of questions answered incorrectly, the sum of these values equals the total number of questions, 30.

Together, these two equations create the system that can be used to determine the number of questions answered correctly and the number of questions answered incorrectly by the contestant in this situation.

The values into the slope-intercept form, we have y = -5x - 6

The slope-intercept form of a linear equation is given by:

y = mx + b

where 'm' represents the slope of the line, and 'b' represents the y-intercept.

In this case, the y-intercept is (0, -6), which means that the line crosses the y-axis at the point (0, -6).

The slope is given as -5.

Therefore, substituting the values into the slope-intercept form, we have:

y = -5x - 6

This equation represents the line with a y-intercept of (0, -6) and a slope of -5.

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Since our assumption holds for all values between 6 and k, and we have shown it also holds for k+1, we can conclude by strong induction that it is possible to cut a square into n smaller squares for any n ≥ 6.

To prove this using strong induction, we will first establish a base case and then prove that if the statement holds true for any value k, then it also holds true for k+1.
Base Case: n = 6
Divide the square into four equal smaller squares by drawing two lines, one vertical and one horizontal, each passing through the center.

Then, divide one of these smaller squares into two equal rectangles by drawing a line parallel to the side.

We have now divided the original square into 6 smaller squares.
Inductive Step:
Assume the statement is true for all values n = 6, 7, ..., k,

where k ≥ 6.

We want to prove that the statement is true for n = k+1.
Consider a square that is divided into k smaller squares.

We will show that it is possible to divide this square into k+1 smaller squares.

Choose one of the k squares and label it S.

If S is a rectangle, divide it into two smaller squares by drawing a line parallel to the shorter side.

If S is a square, divide it into two equal rectangles by drawing a line through the center parallel to a side.
In either case, we have replaced one of the original k squares with two smaller squares, resulting in a total of k+1 squares.

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The Formula:

t = cn + 42

Answer:

2x^3+17x^2+10x−50

Step-by-step explanation:

Answer: 3x^3+2x+5

Step-by-step explanation:

I attached my written work but put simply take the value of x which in this case is -2 because x+2 also means x= -2. Then line up the coefficients next to -2 which should be in a box. So the coefficients 3, 6, 2, 9, and 10. Drop the first coefficient down which is 3 and multiply it by your x value. so the combo is multiply, add, drop. starting with 3 drop it down then multiply it by -2 to get -6. Then add -6 to the second coefficient which is 6 to get 0 so drop zero down. Then again multiply 0 by -2 to get 0 then add zero to 2 to get 2 then drop down 2. So continue till the end remmebr the only multiplication you are doing is against the x value which in this case is -2. at the end you should have 5 numbers left. Here we end with 3, 0, 2, 5, 0. So we want a zero as the last number which means we have no remainder. If the last number is not zero do not PANIC. just kidding but seriously though relax. Put the number over your expression x+2 so for example if the last number was 5 instead of zero DONT PANIC just finish your answer with 5/x+2. SO back to the 3, 0, 2, 5, 0. We add the corresponding x's to these numbers so \(3x^{3}+0x^{2} +2x+5\) which also equals \(3x^3+2x+5\)

According to the information, the missing number from the box is number 40.

To find the missing number of the table we must take into account different elements. In particular we must look at the totals and the columns and rows in which the empty space is. Once we identify the totals we can subtract the other values from the total and find the missing number in the table.

According to the above we can infer that the missing number is 40.

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If we assume that I = E(R + r), then I/I = R/E + r/E​.

The inverse of a value of a number is known as the reciprocal of the number. The reciprocal can be found out by replacing the numerator with the denominator and vice versa. For example, reciprocal of a number x will be 1/x and vice versa.

Here, we are given that I = E/(R + r)

Taking reciprocals of both sides we get-

Reciprocal of I will be- 1/I

Reciprocal of E/(R + r) will be- (R + r)/ E

Thus,

1/I = (R + r)/ E

Simplifying the equation further, we get-

1/I = R/E + r/E

Hence, proved

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Answer:

30.4

Step-by-step explanation:

8 boxes = 243.20

find 1 boxes

= 243.20 ÷ 8

= 30.40 / 30.4