What is the value of x?
M
(3x – 16)
(x+6)°
2
N
: 05
42
o 22
0 38

Answer:

Step-by-step explanation:

The general form of the equation acosx + bsinx = Rsin(x + e) where R is the resultant of the constants 'a' and 'b' and e is the angle between them.

R = √a²+b²

\(e = tan^{-1}\frac{b}{a}\)

Given the function f(x) = 3 cos x + 5 sin x, comparing with the general equation;

a = 3, b = 5

R = √3²+5²

R = √9+25

R =√34

\(e = tan^{-1} \frac{5}{3} \\e = 59.09^{0}\)

in radians;

\(e =\frac{\pi }{180}*59.09\\ e = 0.33\pi rad\)

3 cos x + 5 sin x = √34sin(x + 0.33π)

Answer:

D

Step-by-step explanation:

Answer:

  D. Square

Step-by-step explanation:

You want the best name for the quadrilateral with vertices (-3, 0), (-3, -3), (0, -3), and (0, 0).

A graph of the points is shown in the attachment. We notice the vertices are aligned with the grid, so the corner angles are all right angles.

The differences of x-coordinates and y-coordinates are both 3, so the side lengths of this rectangle are all 3 units.

The figure is all of a rectangle, rhombus, and square.

The most specific name for the figure is Square.

__

Additional comment

A trapezoid has one pair of parallel sides. This figure has two pairs of parallel sides, so is not a trapezoid.

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Answer:

97

Step-by-step explanation:

Answer:

Hello! :) I hope I’m correct!!

Step-by-step explanation:

I think the answer should be the second one.

the angle with the square at the corner is obviously a right angle, 90°. opposite angles have the same angle so opposite to it, angle 3 is also 90°. then add the angle 3 and the given angle (23°). 90°+23°=113° then subtract it to 180° (since a straight line is 180°). 180°-113°=67°

The steps:

To solve m< 2,

\(m< 2 = 180 - (90 + 23)\)

\(m< 2 = 180 - 113\)

\(m< 2 = 67\)

i’m not really sure if this is the answer, but I hope this was helpful!! :)

if you have any questions about these steps, feel free to ask!

by: BrainlyAnime! ^-^

~Thank you!! Have a great day! ~

It will take 3.5 hours for the two cars to be 280 miles apart.

To determine the time it takes for the two cars to be 280 miles apart, we can use the concept of relative velocity.

Since the cars are traveling in opposite directions, their velocities can be added together to find their relative velocity:

Relative velocity = Velocity of car traveling east + Velocity of car traveling west

Relative velocity = 60 mph + 20 mph

Relative velocity = 80 mph

The relative velocity of the cars is 80 mph, which means that they are moving away from each other at a combined speed of 80 mph.

To find the time it takes for them to be 280 miles apart, we can use the formula:

Time = Distance / Speed

Plugging in the values, we have:

Time = 280 miles / 80 mph

Time = 3.5 hours

Therefore, it will take 3.5 hours for the two cars to be 280 miles apart.

During this time, the car traveling east would have covered a distance of 60 mph × 3.5 hours = 210 miles, while the car traveling west would have covered a distance of 20 mph × 3.5 hours = 70 miles.

The sum of these distances is indeed 280 miles, confirming the result.

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Answer:

x = 24°

Step-by-step explanation:

Here we can see that 120° with the right angle is equal to 180° :

120° + right angle = 180°

then:

right angle = 180° - 120° = 60°

The right angle with 5x angle is equal to 180° too ;

right angle + 5x = 180°

solve for x :

5x = 180° - 60°

x = 24°

That its.

Answer:

Step-by-step explanation:

3250 : 156 = y : 40

y = 3250 × 40 : 156

y = 833.(3)                                    3 repeating

--------------------------

check

3250 : 156 = 833.(3) : 40

20,83333333333333 = 20,83333333333333

the answer is good

Answer:

225

Step-by-step explanation:

Answer:

225

Step-by-step explanation:

15

x15

/225

If the sample test exists 1079 then the value of the test statistics exists -7.88.

A statistical test's result, or test statistic, is a numerical value. It describes how distant the observed data is from the null hypothesis, which states that there is no link between the variables or distinction between the sample groups.

The test statistic indicates how dissimilar two or more groups are from the population mean as a whole or how different a linear slope is from the slope implied by the null hypothesis. Various statistical tests employ various test statistics.

Given:

Sample size, n = 1079

Probability of success, p = 0 . 86

The hypotheses are:

\(&H_0\) : p = 0.94

\(&H_a\) : p < 0.94

where:

\($\hat{p}\) = proportion of the sample

p = proportion of the population

n = sample size

The values of the variables exists:

\(&\hat{p}\) = 86 % = 0.86

p = 94 % = 0.94

n = 1074

Substitute the values into the formula and solve for the test statistics:

\($z &=\frac{0.86-0.94}{\sqrt{\frac{0.93(1-0.94)}{1079}}} \\\)

simplifying the above equation, we get

\($z=\frac{-0.08}{\sqrt{\frac{0.93(1-0.94)}{1079}}}$\)

z = -11.12457

Therefore, the value of the test statistics is -7.88.

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Answer:

cost of cookie = $1.95

cost of 15 cookies = $1.95 *15

cost of 15 cookies = $29.25

Step-by-step explanation:

Hey there! :)

Answer:

C. (0, -6).

Step-by-step explanation:

In slope-intercept form ( y = mx + b), the 'b' value represents the y-intercept.

In this instance:

y = 4x - 6

The 'b' value is equal to -6. This means that the y-intercept is at (0, -6).

-------------------------------------------------------------------------------------------

The y-intercept can also be solved for by substituting in 0 for x:

y = 4(0) - 6

y = 0 - 6

y = -6.

Answer:

C. (0, –6)

Step-by-step explanation:

y = 4x - 6

The equation is:

y = mx + b

where b is the y-intercept.

In this case, - 6 is the vertical intercept.

Do not confuse from (-6, 0) because that represents an x-intercept.

Answer:

The component of \(\vec u\) orthogonal to \(\vec a\) is \(\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)\).

Step-by-step explanation:

Let \(\vec u\) and \(\vec a\), from Linear Algebra we get that component of \(\vec u\) parallel to \(\vec a\) by using this formula:

\(\vec u_{\parallel \,\vec a} = \frac{\vec u \bullet\vec a}{\|\vec a\|^{2}} \cdot \vec a\) (Eq. 1)

Where \(\|\vec a\|\) is the norm of \(\vec a\), which is equal to \(\|\vec a\| = \sqrt{\vec a\bullet \vec a}\). (Eq. 2)

If we know that \(\vec u =(2,1,1,2)\) and \(\vec a=(4,-4,2,-2)\), then we get that vector component of \(\vec u\) parallel to \(\vec a\) is:

\(\vec u_{\parallel\,\vec a} = \left[\frac{(2)\cdot (4)+(1)\cdot (-4)+(1)\cdot (2)+(2)\cdot (-2)}{4^{2}+(-4)^{2}+2^{2}+(-2)^{2}} \right]\cdot (4,-4,2,-2)\)

\(\vec u_{\parallel\,\vec a} =\frac{1}{20}\cdot (4,-4,2,-2)\)

\(\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)\)

Lastly, we find the vector component of \(\vec u\) orthogonal to \(\vec a\) by applying this vector sum identity:

\(\vec u_{\perp\,\vec a} = \vec u - \vec u_{\parallel\,\vec a}\) (Eq. 3)

If we get that \(\vec u =(2,1,1,2)\) and \(\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)\), the vector component of \(\vec u\) is:

\(\vec u_{\perp\,\vec a} = (2,1,1,2)-\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)\)

\(\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)\)

The component of \(\vec u\) orthogonal to \(\vec a\) is \(\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)\).

Answer:

Yes

Step-by-step explanation:

If she is reading 20 pages a day, and needs to read 10 pages, then she needs half a day, and since she has 6 days, she can do this.

Answer:

$3.20/gallon

Step-by-step explanation:

to fill up your tank at $3.20/gallon only costs $38.40

The expression for the total number of miles Kyle bikes during the week is given as follows:

N = 10s + 4f.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

For this problem, we have a multi-variable proportional relationship, in which the variables are given as follows:

The constants relative to each variable are the distances multiplied by two, as we must also consider the distance on the return home.

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Using simple division we know that 86 people or citizens dies each day in 2015.

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division.

The other operations are multiplication, addition, and subtraction.

Division in mathematics is the process of dividing an amount into equal parts.

For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on.

So, we know that:

31,500 people died in 2015.

We also know that 2015 had 365 days.

Then, people died easily day would be:

= 31,500/365

= 86.30

Rounding off: 86 people

Therefore, using simple division we know that 86 people or citizens dies each day in 2015.

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The probability of landing on the red shaded circle is 6/18

Probability simply measures the chances at which an event could occur in a sample or population.

Mathematically, Probability is calculated thus:

Here ,

P(red circle ) = 6/18

Therefore, the probability is 6/18

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Answer:

what is the expressio

Step-by-step explanation:

Answer:

The equation of the straight line passing through the points

    7x +y +2=0

Step-by-step explanation:

Step(i):-

Given points are ( -2 , 12 ) and ( 3, -23)

Slope of the line

            \(m = \frac{y_{2}-y_{1} }{x_{2} -x_{1} } = \frac{-23-12}{3-(-2)} = \frac{-35}{5} =-7\)

Step(ii):-

The equation of the straight line passing through the points

            \(y - y_{1} = m( x-x_{1} )\)

           \(y - 12 = -7( x-(-2) )\)

          y - 12 = - 7x -14

         7 x + y - 12 + 14 =0

         7x +y +2=0

∫ (3x^2 + 6x - 4) dx

like last time, but more

x^3 + 3x^2 - 4x + c

use the power rule, so for instance

∫ 3x^2

increase the exponent by 1

3x^3

now divide by the exponent

3x^3 / 3

simplify

x^3

∫ 6x

increase the exponent by 1, 1 + 1 = 2

6x^2

and divide by the exponent

6x^2 / 2

3x^2

Answer:

p=45°, q=45°, s=112.5°

Step-by-step explanation:

Because the triangle is an isosceles right triangle, \(p=q=45^{\circ}\).

In the top triangle, because of the isosceles triangle, the other two angles are each 67.5°.

Therefore, because angles that add to form a straight angle add to 180°, s=112.5°.

The side length of the cube is 5.6 feet (rounded to the nearest tenth).

We can calculate the side length of a cube with a volume of 141 cubic feet using the formula for cube volume , which is \(V = s^3\), where V is the volume and s is the side length.

We can calculate s by taking the cube root of both sides of the equation:

\(s = (V)^{(1/3)\)

Substituting V = 141, we get:

\(s = (141)^{(1/3)\)

By using a calculator to evaluate this expression, we may determine:

s ≈ 5.6

As a result, the cube's side length is roughly 5.6 feet (rounded to the closest tenth). This indicates that if we increase the side length by three, it will become longer. (\(s^3\)), we will get the volume of the cube, which is 141 cubic feet.

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Answer:

f(3) = 425

f(3) is the elevation of a mountain climber after 3 hours of climbing.

Step-by-step explanation:

So we are given a line that relates time to elevation. We are also given that the equation of the line is f(x) = 125x + 50. From looking at the graph given, we can see that x is the time, in hours, and y, or f(x), is the height, in feet. We are asked to find f(3) and interpret it's meaning.

To find f(3), we would have to find what f(x) is when x = 3. To do this, lets plug in 3 for x into the given equation:

f(3) = 125(3) + 50 = 425

So f(3) = 425. Now, we already know that x is the time in hours and y, or f(x), is the elevation in feet. We set x to 3 when solving for f(3). We have also found that f(3), or y when x = 3, is 425. So f(3), or 425, is the elevation after 3 hours.

I hope you find my answer and explanation to be helpful. Happy studying.

always do the PEMDAS it helped me a lot in school