Complete the proof that △STV≅△URV.
U
R
S
T
V

Answer:

Yes

Step-by-step explanation:

The Elephant Building is 335 feet high. A real Asian elephant is 12 feet tall. If 29 real elephants could stand on top of each other, would they reach the top of the building?

They are asking if 29 12' elephants are as tall as as a 335' building:

29 × 12' = 348' elephant stack

because 348' is taller than 335' building then yes, 29 staked elephant would reach and pass the top of a 335' building.  

The pair of expressions which represents the price of an order that was originally x dollars are x - 0.15x and 0.85x

Percentage discount = 15%

Original price of an order = x dollars

New price = Original price of an order - (Percentage discount × Original price of an order)

= x - (15% of x)

= x - 0.15x

= 0.85x

Therefore, x - 0.15x and 0.85x are the expressions which represent the price of an order that was originally x dollars

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Answer:

Please find attached drawing created with Microsoft word, that shows the image of of the triangle ΔABC. with coordinates of the vertices as, A(2, -4), B(0, -5), and C(6, 2), translated down 2 units to give the triangle ΔA prime B prime C prime , with coordinates of the vertices as A prime (2, -6), B prime (0, -7), and C prime (6, 0)

Step-by-step explanation:

Answer:

Here u go

Step-by-step explanation:

Because yeah

A demographer predicts that the population, P, of a town t years from now can be modeled by the function P(t) = 6t^4 - 5t^3 + 200t + 12000. What will the population of the town be two (2) years from now?

To calculate the population of the town be two (2) years from now, replace t into 2:

\( \dashrightarrow \sf{P(t) = 6t^4 - 5t^3 + 200t + 12 \: 000}\)

\(\sf\dashrightarrow \sf{P(2) = 6(2)^4 - 5(2)^3 + 200(2) + 12\:000}\)

\(\dashrightarrow \sf{P(2) = 6(16) - 5(8) + 200(2) + 12\:000}\)

\(\dashrightarrow \sf{P(2) = 96 - 40 + 400 + 12\:000}\)

\( \dashrightarrow\sf{P(2) = 56 + 400 + 12\:000}\)

\( \dashrightarrow\sf{P(2) = 456 + 12\:000}\)

\( \dashrightarrow\sf{P(2) = 12\:456}\)

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Answer:

Step-by-step explanation:

x1=9  x2=8  y1=12  y2=11

=x2-x1

y2-y1

=8-91

1-12

=-1

-1

magintude =\(\sqrt{(xcomp)^2+(y comp)^2\)

=\(\sqrt{(-1)^2+(-1)^2\)

=\(\sqrt{1+1\)

=\(\sqrt{2\)

direction=y component/x component

tan=-1/-1

tan=1

\(tan^{-1}\) 1=45

=45 degree

both x component and y component are negative so it lies on third quadrant.

Answer:

2. Side length =9

Step-by-step explanation:

A square has all sides equal. and it has 4 sides, so 36 divided by 4 =9.

3.x squared =6

answer is x=3

square root both sides.

Vertical lines do not have positive slopes or negative slopes. They have undefined slopes.

Now, According to the question :

What is Vertical line?

A vertical line is a line, parallel to y-axis and goes straight, up and down, in a coordinate plane. Whereas the horizontal line is parallel to x-axis and goes straight, left and right.

Is a vertical line positive or negative?

The slope of a line can be positive, negative, zero, or undefined. A horizontal line has slope zero since it does not rise vertically (i.e. y1 − y2 = 0), while a vertical line has undefined slope since it does not run horizontally (i.e. x1 − x2 = 0).

Hence, Vertical lines do not have positive slopes or negative slopes. They have undefined slopes.

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The equation of the midline of the sinusoidal function is y =0.

What is the equation of the midline of the sinusoidal function?

The mid-line of any Sinusoidal function is a line that goes between the highest and lowest values of y of that function.

Here we will take the middle value of y.

The formula is used to find midline is;

Midline = (highest value + lowest value)/2

According to the given question:

In the given graph, the Highest value of the function is 5 and the Lowest value of the function is -5.

Substitute all the values in the formula;

Midline = (highest value + lowest value)/2

Midline = (5 + (-5))/2

Since we took middle value about y, hence midline is y = 0.

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Answer:

g(x) = (1/2x)^2

Step-by-step explanation:

The function of g(x) is stretched in the graph, so the value is going to be less than 1, which eliminates choice A.

Because the graph g(x) lands on the point (2,1), input this in each of the expressions and see which one is true. C is the only one that truly works.

Answer:

(x + 1)² = 4(y + 10)

Step-by-step explanation:

Equation of parabola:

(x - h)² = 4a(y - k)

with vertex(h, k) and focus (h, k + a)

vertex(h, k) = (-1, -10)

⇒h = -1 and k = -10

focus (h, k + a) = (-1, -9)

⇒ k + a = -9

⇒ -10 + a = -9

⇒ a = 10 - 9

⇒ a = 1

Equation of parabola:

(x - h)² = 4a(y - k):

(x - (-1))² = 4(1)(y - (-1))

= (x + 1)² = 4(y + 10)

To find the polar coordinates (r, θ) corresponding to the Cartesian coordinates (-6, 6), we can use the following formulas:

r = √(x² + y²)

θ = arctan(y / x)

(a) For the given point (-6, 6):

x = -6

y = 6

First, let's find the value of r:

r = √((-6)² + 6²) = √(36 + 36) = √72 = 6√2

Next, let's find the value of θ:

θ = arctan(6 / -6) = arctan(-1) = -π/4 (since the point lies in the third quadrant)

Therefore, the polar coordinates of the point (-6, 6) are (6√2, -π/4).

(b) For r > 0 and 0 ≤ θ < 2:

In this case, the polar coordinates will remain the same: (6√2, -π/4).

(c) For r < 0 and 0 ≤ θ < 2:

Since r cannot be negative in polar coordinates, there are no valid polar coordinates for r < 0 and 0 ≤ θ < 2.

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The only linear transformation from pn → pn which satisfies t(x^k ) = kx^k−1 for all k = 0, 1 . . . , n is differentiation.

Suppose there exists a linear transformation T: Pn → Pn satisfying T(x^k) = kx^(k-1) for all k = 0, 1, ..., n. We need to show that T is the differentiation operator.

Let p(x) = a0 + a1x + a2x^2 + ... + anxn ∈ Pn be an arbitrary polynomial. Then we can write p(x) as a linear combination of the standard basis polynomials {1, x, x^2, ..., x^n}:

p(x) = a0(1) + a1(x) + a2(x^2) + ... + an(x^n)

Now, by the linearity of T, we have

T(p(x)) = a0T(1) + a1T(x) + a2T(x^2) + ... + anT(x^n)

Using the given condition, T(x^k) = kx^(k-1), we get

T(p(x)) = a0(0) + a1(1) + 2a2(x) + ... + nan(x^(n-1))

This can be rewritten as

T(p(x)) = a1 + 2a2(x) + ... + nan(x^(n-1))

which is exactly the derivative of p(x).

Thus, we have shown that any linear transformation T satisfying T(x^k) = kx^(k-1) for all k = 0, 1, ..., n is the differentiation operator. Therefore, differentiation is the only linear transformation satisfying this condition.

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The intercepts of h(x) are x = -4 and y = -1, and the vertical asymptote of h(x) is x = -5. We can find these intercepts and asymptote(s) by analyzing the graph of h(x) as described in the problem statement.

What is the asymptote?

An asymptote is a straight line that constantly approaches a given curve but does not meet at an infinite distance. In other words, Asymptote is a line that a curve approaches as it moves towards infinity. The curves visit these asymptotes but never overtake them.

Based on the given information, we can see that the graph of h(x) follows a vertical line which is 5 units to the left of the y-axis.

This means that as x approaches -5 from either side, the function will approach positive or negative infinity (depending on which direction x is coming from).

Therefore, the vertical line x = -5 is a vertical asymptote of the graph of h(x).

In addition to the vertical asymptote, we can see that the graph of h(x) crosses the x-axis 4 units to the left of the origin (when x = -4) and crosses the y-axis one unit below the origin (when y = -1).

Since the graph continues to decrease to the right in quadrant 4, there are no other intercepts or asymptotes in this region.

Hence, the intercepts of h(x) are x = -4 and y = -1, and the vertical asymptote of h(x) is x = -5. We can find these intercepts and asymptote(s) by analyzing the graph of h(x) as described in the problem statement.

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Answer:

Step-by-step explanation:

The intercepts of h(x) are x = -4 and y = -1, and the vertical asymptote of h(x) is x = -5

Given:

Number of people the auditorium can seat = 320 people

Let's dtetrmine the inequality that best represents the number of people who can sit at the auditorium.

Here, the greatest number of people that can sit at the auditorium is 320 people, from the list of inequalities given, the best inequality which represents the number of, P, who can sit at the auditorium is: p < 321

This means that the number of people, p, must be less than 321.

ANSWER:

p < 321

By knowing the properties of circles, the circle with a central angle ACB of 48° and the arc length AB is 144 inches has a circumference of 1080 inches.

According to the Euclidean geometry, the circular arc (s), in inches, is directly proportional to the central angle (θ), in radians:

s = θ · r   (1)

Where r is the radius of the circle, in inches. Please notice that the arc is directly proportional to the central angle and that the circumference is determined for a central angle of 360° (2π). Hence, we can determine the circumference of the circle by using the following relationship:

s/144 in = 360°/48°

s = (144 in) · (360°/48°)

s = 1080 in

By knowing the properties of circles, the circle with a central angle ACB of 48° and the arc length AB is 144 inches has a circumference of 1080 inches.

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Bring like terms together

on number line, we will have

Step-by-step explanation:

hope you can understand it properly

Rounded to one decimal place, the new forecasted trend for the current period is 31.3.

To calculate the new forecasted trend for the current period using exponential smoothing, we need the current observed value (33), the previous forecasted value (31), and the smoothing constant (β) of 0.15.

Exponential smoothing assigns a weight to the previous forecast and combines it with the current observed value to generate a new forecast. The formula for exponential smoothing is:

New Forecast = (1 - β) * Previous Forecast + β * Current Observed Value

Substituting the given values, we can calculate the new forecasted trend:

New Forecast = (1 - 0.15) * 31 + 0.15 * 33

           = 0.85 * 31 + 0.15 * 33

           = 26.35 + 4.95

           = 31.3

Exponential smoothing is a forecasting technique that assigns more weight to recent observations while considering past forecasts. The smoothing constant, β, determines the rate at which the influence of past forecasts diminishes as new observations become available. In this case, with a β value of 0.15, the new forecast is closer to the current observed value compared to the previous forecast, reflecting a higher sensitivity to recent data.

It's important to note that exponential smoothing assumes a relatively stable trend and does not account for other factors or seasonality that may impact the forecast. It is a simple method that can be useful for generating short-term forecasts based on recent trends, but it may not be suitable for all forecasting scenarios.

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Answer:

given

Step-by-step explanation:

domains is always the horizontal which is (x) so domain is (6,-9)

Answer:

B

Step-by-step explanation:

Answer: $30

Step-by-step explanation:

should be $30 spent in total

Answer:

y = 1/2x + 6

Step-by-step explanation:

y = mx + b is the y-intercept form

m is the slope- rise/run of the line.

b is the y-intercept- where the line crosses the y-axis.

y = mx + b

y = mx + 6

y = 1/2x + 6

If you look i the corner of the graph, you'll see the line goes up 1 and over 2, that's your slope. It's a positive slope since it travels up from left to right.

Answer:

$195.30

Step-by-step explanation:

a) test stratic value =t = (x - μ) / SE

the p-value is approximately 0.0402.

a) SE = s / sqrt(n)

where s is the sample standard deviation and n is the sample size.

In this case, x = 103, s = 11.5, and n = 65.

SE = 11.5 / sqrt(65) ≈ 1.426

The test statistic (t-value) is calculated as the difference between the sample mean and the hypothesized population mean divided by the standard error of the mean:

t = (x - μ) / SE

where x is the sample mean and μ is the hypothesized population mean.

In this case, x = 103 and μ = 100.

t = (103 - 100) / 1.426 ≈ 2.103

To find the p-value, we need to determine the probability of observing a test statistic as extreme as the one calculated (2.103) or more extreme, assuming the null hypothesis is true. Since the alternative hypothesis is two-tailed (≠), we need to consider both tails of the distribution.

Using a t-distribution table or software, we can find the p-value associated with the test statistic. However, without specific degrees of freedom, it's not possible to provide an exact p-value. The degrees of freedom depend on the sample size, which in this case is 65.

Let's assume the degrees of freedom are 64. Using statistical software or a t-distribution table, we can find the p-value associated with a t-value of 2.103 and degrees of freedom of 64. The p-value is approximately 0.0402.

Therefore, the p-value is approximately 0.0402.

Since the p-value (0.0402) is less than the significance level (α = 0.05), we reject the null hypothesis. There is sufficient evidence to support the alternative hypothesis, which suggests that the population mean is not equal to 100.

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