How to find if a triangle is obtuse acute or right.

Answer:

C. x=(p−ny)/m

Step-by-step explanation:

mx + ny = p

Subtract ny from each side

mx + ny -ny= p -ny

mx = p-ny

Divide each side by m

mx/m = (p-ny)/m

x=(p−ny)/m

A finite series can be an arithmetic series or a geometric series

The given parameters are:

a1 = 6

r = 2

The above represents a geometric series

The nth term of a geometric series is calculated as:

\(a_n = a_1 * r^{n-1}\)

So, we have:

\(a_2 = 6 * 2^1 = 12\)

\(a_3 = 6 * 2^2 = 24\)

\(a_4 = 6 * 2^3 = 48\)

\(a_5 = 6 * 2^4 = 96\)

\(a_6 = 6 * 2^5 = 192\)

So, we have the following ordered pairs

(x,y) = (1,6) (2,12) (3,24) (4,48) (5,96) (6,192)

See attachment for the graph of the first six terms of the finite series

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Given-

Number of exhibits = 4

Total number of exhibits = 16

Solution-

% of zoos exhibits that features bears :-

\( \frac{4}{16} \times 100\)

\( => 25\)

Therefore, The percentage of zoos exhibits that features bears= 25 %

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The relationship between the corresponding sides of similar triangles indicates that the height of the tree is 60 feet. The correct option is therefore;

Similar triangles are triangles in which the ratio of the corresponding sides of the triangles are equivalent for the three sides of the triangle.

The location of the tree divides the hypotenuse side and the base of the triangle formed by the building into two parts of the same length, therefore;

The length of the hypotenuse side to the building = 2 × 108 ft = 216 ft

The length of the base to the building = 2 × 90 ft = 180 ft

The ratio of corresponding sides of similar triangles and the trigonometric ratio of sines, indicates that we get;

Height of the tree/108 = 120/216

Height of the tree = 108 × (120/216) = 60 feet

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Answer:

3.7

Step-by-step explanation:

Answer:

Step-by-step explanation:

The value of expression 7 (y - 4) - 1 if, y = 11 is 48, so option C is correct.

At least two numbers or variables, one or more arithmetic operations, and a statement are all required components of a mathematical expression.

The term "expression" or "mathematical expression" refers to a finite collection of symbols that are well-formed in line with context-dependent criteria.

Given:

One less than seven times difference between a number and four,

The value of y = 11,

The above statement can be written as shown below,

7 (y - 4) - 1

Put the value of y as shown below,

7 (y - 4) - 1 = 7 (11 - 4) - 1

7 (y - 4) - 1 = 7 × 7 - 1

7 (y - 4) - 1 = 49 - 1

7 (y - 4) - 1 = 48

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Bob travels within the speed limit.

For Bob to travel within the speed limit, the distance travelled by Bob in 3 hours must be less than the distance travelled gotten from the equation y = 70x.

With x = 3, y = 70(3) = 210 miles.

From the straight line graph, Bob travels, 200 miles in 3 hours.

Since this distance is less than that gotten from the equation, Bob travels within the speed limit.

So, Bob travels within the speed limit.

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Answer:

1 is not an irrational number, it is rational

Step-by-step explanation:

Answer:

X+y=23 (x and y added equal the number of baskets made)

2x+3y=53 (since each basket is worth a certain amount of points, x and y must be multiplied by their amount of baskets and added together to get the total number of points)

Hope this helps!

Answer:

The answer is D

Answer:

y=-7

Step-by-step explanation:

A SSS (side-side-side) theorem is kind of Congruence rule where two triangles with three congruent sides. So, we can solve it by showing the congruency between two triangles.

Statement: Side-Side-Side (SSS) ,the congruence theorem states that two triangles are congruent if three of their sides are equal to the corresponding sides of the other triangle.

Proof: Given, AB = DE, BC = EF, AC = DF.

To prove: ΔABC ≅ ΔDEF.

We know that the three sides of both triangles are equal in size and length. With both triangles superimposed, DE is placed on AB, EF is placed on BC, and DF is placed on AC. That is, AB = DE, BC = EF, AC = DF. Therefore, we can say that ΔABC ≅ ΔDEF.

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The Fourier series representation of the derivative of a function dx(t)/dt can be determined by differentiating the Fourier series representation of the function x(t).

1. The Fourier series representation of dx(t)/dt can be expressed as a sum of sine and cosine terms with different frequencies and coefficients. Let x(t) be a periodic function with period T and Fourier series representation given by: x(t) = a0 + ∑(ancos(nωt) + bnsin(nωt)), where ω = 2π/T, and an and bn are the Fourier coefficients.

2. To determine the Fourier series representation of dx(t)/dt, we differentiate each term of the Fourier series representation of x(t). The derivative of a constant term a0 is zero since it does not vary with time. For the cosine term ancos(nωt), its derivative becomes -nωansin(nωt), and for the sine term bnsin(nωt), the derivative becomes nωbncos(nωt).

3. The Fourier series representation of dx(t)/dt is then given by: dx(t)/dt = ∑(-nωansin(nωt) + nωbncos(nωt)), where n takes values from 1 to infinity.

4. In summary, the Fourier series representation of dx(t)/dt is obtained by differentiating the Fourier series representation of x(t) with respect to time. It involves summations of sine and cosine terms with varying frequencies and coefficients, representing the rate of change of the original function.

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Answer: 4:5

Step-by-step explanation: The lowest form

Answer:

Step-by-step explanation:

4:5

Answer:

720

Step-by-step explanation:

first, to figure out the side lengths you do 12*10 = 120 then 120*6 = 720 (because those sides are all equivalent)

The area of the rhombus is  49√6. Option B

The formula for calculating the area of a rhombus is expressed as;

Area = pq/2

Where;

p and q are the diagonals of the rhombus

From the diagram shown, let's determine the value of p

Using the trigonometric identity;

Tan θ = opposite/adjacent

Substitute the values into the formula, we have;

tan 60 = p/7

Find the value of tan 60 and then substitute

√3 = p/7

cross multiply

p = 7√3

But;

Area = 7√3 × 7√3/2

Area = 49√6

Hence, the value is 49√6

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The absolute value is defined as

\(|x|=\begin{cases}x&\text{if }x\ge0\\-x&\text{if }x<0\end{cases}\)

So for example, if x = 3, then |x| = |3| = 3, since 3 is positive. On the other hand, if x = -5, then |x| = |-5| = -(-5) = 5, since -5 is negative. The absolute value is always positive.

For the inequality |7 + 8x| > 5, you consider the two cases where the argument to the absolute value (the expression you find inside the bars) is either positive or negative.

• If 7 + 8x ≥ 0, then |7 + 8x| = 7 + 8x, so that

\(|7+8x|>5\implies 7+8x>5 \implies 8x>-2 \implies x>-\dfrac14\)

• Otherwise, if 7 + 8x < 0, then |7 + 8x| = -(7 + 8x), so that

\(|7+8x|>5\implies-(7+8x)>5\implies7+8x<-5\implies8x<-12\implies x<-\dfrac32\)

The solution to the inequality is the union of these two intervals.

The amount of ascent, or vertical distance, divided by the run, or horizontal distance, is how slope is commonly expressed as a percentage.

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Answer: (5,7)

Step-by-step explanation:

We want to find the image of a point after a given translation.

The image of the point (-5, 2) under the translation T(3, -4) is the point (-2, -2)

First, we can define how a general translation T(a, b) affects a general point (x, y).

It will add a units to the x-value and b units to the y-value, then we have:

T(a,b)[(x, y)] = (x + a, y + b).

Now we just need to apply the translation:

T(3, -4) to the point (-5, 2)

It gives:

T(3, -4)[(-5, 2)] = (-5 + 3, 2 + (-4)) = (-2, -2)

So the image of the point (-5, 2) under the translation T(3, -4) is the point (-2, -2)

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Answer:

7.5

Step-by-step explanation:

You didn't list the right answer choices. But I think 7.5 is the answer.

Answer:

Category A 0.75

Category B 0.25

Hope it helps !!

The value of P(1.41 < Z < 2.85)  is 0.0771.

Hence, the correct answer is d.

A normally distributed random variable with mean μ= 0 and standard deviation σ= 1 is referred to as a standard normal random variable. The letter Z will always be used to represent it.

Because the Standard Normal Distribution is a probability distribution, the area under the curve between two points indicates the likelihood that variables will take on a range of values.

The whole area under the curve is one, or one hundred percent.

The mean and variance of a normal distribution are governed by two factors.

A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.

The probability that a standard normal random variable Z is between 1.41 and 2.85 can be found using a standard normal table with a standard normal cumulative distribution function.

The answer is approximate:

P(1.41 < Z < 2.85)

= P(Z < 2.85) - P(Z < 1.41)

= 0.9927 - 0.9185

= 0.0742

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The coefficient of the x term in the expansion of f[x] best reflects the behavior of the function for x's close to 0.

The behavior of a function for x values close to 0 can be understood by examining its expansion in powers of x. When a function is expanded in a power series, each term represents a different order of approximation to the original function. The coefficient of the x term, which is the term with the lowest power of x, provides crucial information about the behavior of the function near x = 0.

In the expansion of f[x] = a0 + a1x + a2x² + ..., where a0, a1, a2, ... are the coefficients, the term with the lowest power of x is a1x. This term captures the linear behavior of the function around x = 0. It represents the slope of the function at x = 0, indicating whether the function is increasing or decreasing and the rate at which it does so. The sign of a1 determines the direction of the slope, while its magnitude indicates the steepness.

By examining the coefficient a1, we can determine whether the function is increasing or decreasing, and how quickly it does so, as x approaches 0. A positive value of a1 indicates that the function is increasing, while a negative value suggests a decreasing behavior. The absolute value of a1 reflects the steepness of the function near x = 0.

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Answer:

The slope of the model is 0.238

Step-by-step explanation:

The given equation is in slope-intercept form which reads

y = mx + b

m is the slope and b is the constant.

So...

y = (0.238)x + 4.642

y = (slope)x + constant

0.238 is the slope of this model

Answer:

0.238 is the slope and 4.642 is the y-intercept.

given equation: y = 0.238x + 4.642

Formula of slope intercept formula: y = mx + b

                                                             where m is slope and b is y intercept

→ comparing we can see that slope is 0.238 and y-intercept is 4.642.

Answer:

Answer: B. 5x + 1 = x - 1

Step-by-step explanation:

\({ \tt{5x + 1 = x - 1}} \\ { \tt{5x - x = - 1 - 1}} \\ { \tt{4x = - 2}} \\ { \tt{x = - \frac{1}{2} }}\)

Answer:

Step-by-step explanation:

The correct factors for this trinomial are

(x - 4)(x - 2)

I don't know where the two factors suggested in the problem come from, so I can't explain how I know they are wrong other than by giving you the correct factors of the given trinomial.

So the answer is false.

Answer:

D

Step-by-step explanation:

since it is not in a parentheses with x that means it only affects the y axis, resulting in a vertical compression by a factor of 9

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Step-by-step explanation:

the phrasing of the problem statement is not very precise.

the interest rate of the first card is x.

the interest rate of the second card is x + 0.014 (that is 1.4% more that the other card).

I assume that is the correct interpretation of 1.4% more.

e.g. if card 1 has an interest rate of 15%, then card 2 has an interest rate of 15 + 1.4 = 16.4%.

and I don't think that means to add 1.4% of 15% (which would be 15×1.014 = 15.21%)

remember, a n% rate is expressed as n/100.

so, 100% = 1

10% = 0.1

1% = 0.01

if I understand the problem definition correctly, he paid only interest (and no principal = balance) at the end of the year.

and the interest of an amount is that amount multiplied by the interest rate :

7500x + 3500(x + 0.014) = 797

7500x + 3500x + 49 = 797

11000x + 49 = 797

11000x = 748

x = 748/11000 = 0.068 = 6.8%

x + 0.014 = 0.082 = 8.2%

so, the first card (with $7,500) charges 6.8% interest.

the second card (with $3,500) charges 8.2% interest.