The triangle and the rectangle below have the same area.
6 cm
wcm
6 cm
5cm
Calculate the value of w.
Show your working.

I thought it was 10 as triangle do base x height divided by 2

Answer:

The Answer is 2(3x^10-2) Hope this helps :)

-by-step explanation:

Answer:

The perimeter is the sum of the lengths of all the sides of a polygon. Thus, the perimeter of this quadrilateral is:

(10a-6) + (7a+4) + (7a+4) + (10a-6)

Simplifying the expression:

= 34a - 4

Therefore, the perimeter of the quadrilateral is 34a - 4.

Answer:

(-5,3)

Step-by-step explanation:

move five to the left to get 4 to -1 and 3 up to get 3 to 6

Answer:

log(5)= 0.699

Answer:

Step-by-step explanation:

0.7925

5 persons are to be selected to form a committee so that at least 3 men are there on the committee, in 3192 ways the committee can be formed.

Combinations are decisions that are made by choosing some or all of a group of objects, regardless of how they are arranged. the variety of n distinct combinations, each taken r at a time,

We may have four males and one lady or three men and two women (5 men only).

∴ Required number of ways = (⁸C₃ x ⁷C₂) + (⁸C₄ x ⁷C₁) + ⁸C₅

= \(\frac{8*7*6}{3*2*1} *\frac{7*6}{2*1} + \frac{8*7*6*5*4}{4*3*2} *\frac{7}{1} + \frac{8*7*6}{3*2}\)

= 1176 + 1960 + 56

= 3192

Therefore, at least 3 men are there on the committee can be formed 3192 times.

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Answer:

Step-by-step explanation:

The slope of y = -5/4x + 4 is -5/4. The y-intercept is 4.

The slope of y=3/2x-7 is 3/2. The y-intercept is -7.

Answer:

b

Step-by-step explanation:

Answer:

x=23

Step-by-step explanation:

FInd the length of the hypotenuse

4.8+19.2=24

Then make it a ration

24/19.2=x/18.4

Cross multiply

19.2x=(24)(18.4)

19.2x=441.6

x=441.6÷19.2

x=23

The Goblin Girt take 15 minutes to count the coins in the bag alone if Goblin Gryh can count the coins in a bag in 10 minutes. If goblin Girt counts with him, they can count all the coins in 6 minutes.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

Let's suppose the Goblin Girt take x minutes to count the coins in the bag alone.

Then we can frame an equation to find the value of x:

\(\rm \dfrac{1}{x}+\dfrac{1}{10}=\dfrac{1}{6}\)

\(\rm \dfrac{1}{x}=- \dfrac{1}{10}+\dfrac{1}{6}\)

\(\rm \dfrac{1}{x}=\dfrac{1}{15}\)

x = 15 minutes (reciprocal on both sides)

Thus, the Goblin Girt take 15 minutes to count the coins in the bag alone if Goblin Gryh can count the coins in a bag in 10 minutes. If goblin Girt counts with him, they can count all the coins in 6 minutes.

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\(\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ \log(49)=y\implies \log_{10}(49)=y\implies 1.690196\approx y \\\\\\ \log_{10}(49)\approx 1.690196\implies \stackrel{\textit{then we can say}}{10^{1.690196}\approx 49}\)

They are used in navigation, astronomy, and surveying. Rays are also used in computer graphics, physics, and optics. In addition, rays are used in the study of optics to describe the behavior of light as it travels through different mediums.

According to the video above, the geometric object called a ray has the characteristics that it has one endpoint and extends in away from that endpoint without end.A ray is a line that starts at a single point and extends in one direction to infinity. Rays are commonly used in geometry to explain lines and line segments. A ray has one endpoint, called the endpoint of the ray, from which it starts. The other end of the ray continues in the direction in which it is pointed without any limit. A ray is named by using its endpoint and another point on the ray, with the endpoint first. For example, if ray A starts at point P and passes through point Q, we write the name of the ray as ray PAQ or ray QAP. Rays can be part of line segments and other geometric objects. They can also be used to explain angles and the direction of a light source. Rays are commonly used in mathematics, science, and engineering.

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In the context of social psychology, the scenario described, where participants are randomly assigned to different conditions of the experiment, exemplifies the concept of \(\textit{random assignment}.\)

This concept ensures that all individuals have an equal chance of being assigned to any particular condition, minimizing the potential for bias and increasing the internal validity of the study.

Random assignment helps researchers establish cause-and-effect relationships by controlling for potential confounding variables and allowing for meaningful comparisons between different experimental conditions.

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This is the equation of the line tangent to the graph of f(x) = 2sin(x) at x=2π/3 in point-slope form.

We need to find the equation of the line tangent to the graph of f(x) = 2sin(x) at x=2π/3.

The slope of the line tangent to the graph of f(x) at x=a is given by the derivative f'(a).

To find the slope of the tangent line at x=2π/3,

we first need to find the derivative of f(x).f(x) = 2sin(x)

Therefore, f'(x) = 2cos(x)

We can substitute x=2π/3 to get the slope at that point.

f'(2π/3) = 2cos(2π/3)

= -2/2

= -1

Now, we need to find the point on the graph of f(x) at x=2π/3.

We can do this by plugging in x=2π/3 into the equation of f(x).

f(2π/3)

= 2sin(2π/3)

= 2sqrt(3)/2

= sqrt(3)

Therefore, the point on the graph of f(x) at x=2π/3 is (2π/3, sqrt(3)).

Using the point-slope form y - y1 = m(x - x1), we can plug in the values we have found.

y - sqrt(3) = -1(x - 2π/3)

Simplifying this equation, we get:

y - sqrt(3) = -x + 2π/3y

= -x + 2π/3 + sqrt(3)

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The y-intercept of the equation y = a sin(x) + c is (0, c).

In the given equation, y = a sin(x) + c, the term "c" represents a constant value, which is added to the sinusoidal function a sin(x). The y-intercept is the point where the graph of the equation intersects the y-axis, meaning the value of x is 0.

When x is 0, the equation becomes y = a sin(0) + c. The sine of 0 is 0, so the term a sin(0) becomes 0. Therefore, the equation simplifies to y = 0 + c, which is equivalent to y = c.

This means that regardless of the value of "a," the y-intercept will always be (0, c). The y-coordinate of the y-intercept is determined solely by the constant "c" in the equation.

The y-intercept of a function is the point where the graph of the equation intersects the y-axis. It represents the value of the dependent variable (y) when the independent variable (x) is zero. In the equation y = a sin(x) + c, the y-intercept is given by (0, c).

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Answer:

D

Step-by-step explanation:

Find the vertex

¼(x-5) = (y-2)²

x-5 = 4(y-2)²

x = 4(y-2)² + 5

This is a right-opening parabola with vertex (5,2).

focal length p = 1/(4·coefficient of y²) = 0.0625

directrix: x = 5-p = 4.9375

D

The equation of directrix of the parabola will be x = 4, i.e. Option A.

Directrix is a straight line distance to which from any point of a conic section is in fixed ratio to the distance from the same point to a focus. The directrix is perpendicular to the axis of symmetry and does not touch the parabola.

We have,

\(\frac{1}{4} (x - 5) = (y - 2)^2\)

Now,

Rewrite as,

\((x - 5) = 4(y - 2)^2\)

Now,

\(x= 4(y - 2)^2+5\)

Now,

Comparing it with the vertex form,

i.e.

\(x = a ( y - h )^ 2 + k\)

Vertex of parabola = (2, 5),

So,

Focus at (a, 0),

So,

Focus of the parabola = (4, 0),

i.e., a = 4

Now,

The Equation of directrix is given by x = a

So,

The equation of the directrix of this parabola,

x - a = 0,

i.e.

x - 4 = 0

⇒

x = 4

Hence, we can say that the equation of directrix of the parabola will be x = 4, i.e. Option A.

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Step-by-step explanation:

refer to the picture.. hope this helps :)

Answer:

E

Step-by-step explanation:

All these methods can give you the slope of a graph

Answer:

E. All of the Above.

Step-by-step explanation:

While worded differently, these all state the same principle.

To determine the domain of the vector function, we need to consider the restrictions on the individual components of r(t). The domain of the vector function r(t) = (ln(4t), 1/t - 2, sin(t)) is (0, 2) U (2, ∞).

To determine the domain of the vector function, we need to consider the restrictions on the individual components of r(t).

The first component ln(4t) is defined for t > 0 since the natural logarithm is only defined for positive values.

The second component 1/t - 2 is defined for all t except t = 0 and t = 2 since division by zero is undefined.

The third component sin(t) is defined for all real values of t.

Therefore, combining these restrictions, we find that the domain of the vector function r(t) is (0, 2) U (2, ∞), which means that t must be greater than 0 or greater than 2 for all three components of r(t) to be defined.


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Answer:

1 / 3^1

Step-by-step explanation:

3^-1 • 3^0

When multiplying exponents with the same base, we add the exponents

3^ (-1+0)

3 ^-1

We know that a^ - b = 1/a^b

3 ^ -1 = 1/3^1

Answer:

quadrant 2 you're welcome :-)

Answer:

Quadrant 2

Step-by-step explanation:

Since the x coordinate is negative, it must in quadrant 2 or 3

Since the y coordinate is positive, it must in quadrant 1 or 2

It must be in quadrant 2

\(Answer:\large\boxed{y=\frac{2}{3} x+6}\)

Step-by-step explanation:

First let's convert 2x - 3y = 12 into \(y = mx + b\)  form.

In order to do this, solve for y.

\(2x-3y=12\)

\(-3y=-2x+12\)

\(y=\frac{2}{3} x-4\)

This shows us that the slope is   \(\boxed{\frac{2}{3}}\)

Now we use the point-slope formula:

\((y-y1)=m(x-x1)\)

where m is the slope and y1 and x1 are the point the line passes through

Using the point (-6,2) and slope, 2/3, we can find the equation:

\((y-2)=\frac{2}{3} (x-(-6))\)

\((y-2)=\frac{2}{3} (x+6)\)

\((y-2)=\frac{2}{3} x+4\)

\(\large\boxed{y=\frac{2}{3} x+6}\)

The degree of precision in numerical analysis refers to the level of accuracy that a calculation or measurement can achieve. In other words, it is the level of detail or exactness that can be obtained from a calculation or measurement.

The degree of precision is typically expressed as the number of significant digits that are used in a calculation or measurement. For example, if a measurement is made with a precision of two significant digits, it means that the measurement is accurate to within two digits of the true value.

Precision is an important concept in numerical analysis because it determines the level of accuracy that can be achieved in calculations and measurements. It is also important for ensuring that results are reliable and reproducible. However, it is important to note that precision does not necessarily mean accuracy. It is possible for a calculation or measurement to be precise but not accurate if there are systematic errors or biases present.

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so the answer would be 41 cause it goes in

The nth term of sequence 2, 9, 22, 41, 66 will be Tn =  7n + 9.

An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:

Its nth term is

\(T_n = a + (n-1)d\)

where a₁ is the first term and d the common difference

The given sequence is 2, 9, 22, 41, 66

There is a common difference between consecutive terms, that will be;

d = 9 - 2 = 22 - (9) = 7

This indicates the sequence is arithmetic with nth term which is;

\(T_n\) = a₁ + (n - 1)d

Here a₁ = 2 and d = 7 , then

\(T_n\) = 2 + 7(n - 1)

\(T_n\) = 2 + 7n + 7

\(T_n\)  = 7n + 9

Hence, the nth term of sequence 2, 9, 22, 41, 66 will be Tn =  7n + 9.

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Answer:

  x ≈ 95.6

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationship between trig functions and sides of a right triangle. Here, the hypotenuse of the triangle and the side adjacent to the given angle are marked, so the relationship of choice is ...

  Cos = Adjacent/Hypotenuse

__

Using the values shown, we have ...

  cos(15°) = x/99

Solving for x gives ...

  x = 99·cos(15°) ≈ 95.6

The length of the side marked x is about 95.6 units.

1/64 fraction is equal to 0.015625 in decimal form.

To change the fraction 1/64 to a decimal, we need to perform division.

1 divided by 64 can be written as:

0.015625

----------

64 | 1.000000

   0

  10

   0

The result of the division is 0.015625. This means that 1/64 is equal to 0.015625 in decimal form.

Note that in this case, we carried the division out to six decimal places, but the question specified that we should carry it out to three decimal places. In that case, we would round the answer to 0.016.

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b. from x= 2 to x+5 >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

The study of hypnosis and its relationship to hysteria was the starting point for the development of psychoanalysis by Sigmund Freud.

The study of hypnosis and hysteria in the late 19th century by Sigmund Freud and his contemporaries led to the development of psychoanalysis, a form of psychotherapy that emphasizes the role of unconscious thoughts and feelings in shaping behavior. Through his work with patients suffering from hysteria, Freud became interested in the idea that psychological conflicts could be traced back to early childhood experiences, and that these conflicts could be resolved through the exploration of unconscious thoughts and feelings. This eventually led to the development of psychoanalysis as a theory and practice for the treatment of psychological disorders.

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