Write the expression as the sine, cosine, or tangent of an angle. (6 points) cos 94° cos 37° + sin 94° sin 37°

Energía cinética = 1 / 2mv²

Donde m es la masa y v es la velocidad

De la pregunta

la masa es de 16 libras

la velocidad es de 30 m / s

16 libras es equivalente a 7.257 kg

Entonces la energía cinética es

1/2(7.257)(30)²

Espero que esto te ayude

Answer:

[tex]a => b \equiv ( \neg a \ \lor \ b )[/tex]

Step-by-step explanation:

You can understand the statement from many perspectives, but in terms of proposition logic it is best to understand it as   "negation of a" or "  b" in mathematical terms is written like this

[tex]a => b \equiv ( \neg a \ \lor \ b )[/tex]

You can show that they are logically equivalent because they have the same truth table.

Answer:

100yd²

Step-by-step explanation:

length=4x

width=x

perimeter=2(l+w)

50=2(4x+x)

50=2(5x)=10x

50=10x

x=5yd

width=5yd

length=20yd

area=length×width

=20×5

=100yd²

Answer:

[tex]\boxed{\red{100 \: \: {yd} ^{2}}} [/tex]

Step-by-step explanation:

width = x

length = 4x

so,

perimeter of a rectangle

[tex] p= 2(l + w) \\ 50yd = 2(4x + x) \\ 50yd= 2(5x) \\ 50yd= 10x \\ \frac{50yd}{10} = \frac{10x}{10} \\ x = 5 \: \: yd[/tex]

So, in this rectangle,

width = 5 yd

length = 4x

= 4*5

= 20yd

Now, let's find the area of this rectangle

[tex]area = l \times w \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 20 \times 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 100 {yd}^{2} [/tex]

Answer:

(Y-3)= -1/3(x-7)

Or

(Y-4)= -1/3(x-4)

Steb by step explanation:

The condition for the line is (7,3) and (4,4).

Point slope form of equation is in this format below.

(Y-y1)= m(x-x1)

We have the given parameters in the above format except the m

M = gradient

Gradient= (y2-y1)/(x2-x1)

Gradient=(4-3)/(4-7)

Gradient= 1/-3

Gradient= -1/3

So

(Y-y1)= m(x-x1)

(Y-3)= -1/3(x-7)

Or

(Y-4)= -1/3(x-4)

Answer:

Step-by-step explanation:

∆ BCD ~ ∆ DCA

[tex] \frac{bc}{dc} = \frac{dc}{ac} [/tex]

Plug the values:

[tex] \frac{5}{y} = \frac{y}{6 + 5} [/tex]

[tex] \frac{5}{y} = \frac{ y}{11} [/tex]

Apply cross product property

[tex]y \times y = 11 \times 5[/tex]

Calculate the product

[tex] {y}^{2} = 55[/tex]

[tex]y = \sqrt{55} [/tex]

Hope this helps...

Good luck on your assignment..

Answer:

AB = 20 tan55°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan55° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{AB}{20}[/tex] ( multiply both sides by 20 )

20 tan55° = AB

Answer:

Option C.

Step-by-step explanation:

In the given figure we have two parallel lines AB and CD.

A transversal line FB intersect the parallel lines at point B and C.

We know that the if a transversal line intersect two parallel lines, then corresponding angles are congruent.

[tex]\angle ABC=\anle ECF[/tex]

[tex]x=y[/tex]

To prove this by translation, we need a translation along the directed line segment CB maps ine CD onto line AB and angle y onto angle x.

Therefore, the correct option is C.

Answer:

Step-by-step explanation:

1. Preferred Share dividends.

There are 300,000 preference shares and each of them got $2.85. Total dividends are;

= 300,000 * 2.85

= $855,000‬

2. Total dividends = $3,500,000

Dividends left for Common Shareholders (preference gets paid first)

= 3,500,000 - 855,000

= $2,645,000

Common shares number 2,500,000

Dividend per share of common stock = [tex]\frac{2,645,000}{2,500,000}[/tex]

= $1.06

Answer:

interior angle (2)= 70

interior angle (3)= 60

Step-by-step explanation:

Given:

exterior angle=120°

interior angle (1)=50°

Required:

interior angle (2)=?

interior angle (3)=?

Formula:

exterior angle=interior angle (1) + interior angle (2)

Solution:

exterior angle=interior angle (1)+ interior angle (2)

120°=50°+interior angle (2)

120°+50°=interior angle (2)

70°=interior angle (2)

interior angle (3)= 180°-interior angle (1)- interior angle (2)

interior angle (3)=180°-50°+70°

interior angle (3)=180°-120°

interior angle (3)= 60°

Theorem:

Theorem 1.16

The measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.

Hope this helps ;) ❤❤❤

Answer:

See Image Below.

Step-by-step explanation:

The Shaded region is the area of numbers that this equation satisfies.

Answer:

Please see attached image

Step-by-step explanation:

In order to graph the inequality, start from plotting the boundary line defined by the equality;

y = 3 x

You just need two points to accomplish such. so let's use two simple values for x and find what the y-values are:

for x = 0 then y = 3 (0) = 0

for x = 1 then y = 3 (1) = 3

Then use the points (0, 0) and (1, 3) to plot the boundary line.

After this, grab any point on the plane either clearly above the boundary line, or clearly below it and check if the inequality satisfies. For example, you can pick the point (3, 0) which is on the x line, 3 units to the right of the origin, and clearly below the boundary line we just plot.

When you use it in the inequality, you get:

(0)  [tex]\leq[/tex] 3 (3)

0   [tex]\leq[/tex] 9

which is a true statement, therefore, the points below the boundary lie are also solutions of the inequality.

Then the solution consists of all the points in the boundary line we just plotted (and indicated by drawing a solid line), plus all the points below the line, as depicted in the attached image.

Looks like the given function is

[tex]f(x)=\dfrac1{9-x}[/tex]

Recall that for |x| < 1, we have

[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]

We want the series to be centered around [tex]x=4[/tex], so first we rearrange f(x) :

[tex]\dfrac1{9-x}=\dfrac1{5-(x-4)}=\dfrac15\dfrac1{1-\frac{x-4}5}[/tex]

Then

[tex]\dfrac1{9-x}=\displaystyle\frac15\sum_{n=0}^\infty\left(\frac{x-4}5\right)^n[/tex]

which converges for |(x - 4)/5| < 1, or -1 < x < 9.

Answer:

3 pairs

Step-by-step explanation:

Top and Bottom

Front and Back

Side and Side.

Cereal Boxes have 6 sides

Answer:

Hence, none of the options presented are valid. The plane is represented by [tex]3 \cdot x + 3\cdot y + 2\cdot z = 6[/tex].

Step-by-step explanation:

The general equation in rectangular form for a 3-dimension plane is represented by:

[tex]a\cdot x + b\cdot y + c\cdot z = d[/tex]

Where:

[tex]x[/tex], [tex]y[/tex], [tex]z[/tex] - Orthogonal inputs.

[tex]a[/tex], [tex]b[/tex], [tex]c[/tex], [tex]d[/tex] - Plane constants.

The plane presented in the figure contains the following three points: (2, 0, 0),  (0, 2, 0), (0, 0, 3)

For the determination of the resultant equation, three equations of line in three distinct planes orthogonal to each other. That is, expressions for the xy, yz and xz-planes with the resource of the general equation of the line:

xy-plane (2, 0, 0) and (0, 2, 0)

[tex]y = m\cdot x + b[/tex]

[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Where:

[tex]m[/tex] - Slope, dimensionless.

[tex]x_{1}[/tex], [tex]x_{2}[/tex] - Initial and final values for the independent variable, dimensionless.

[tex]y_{1}[/tex], [tex]y_{2}[/tex] - Initial and final values for the dependent variable, dimensionless.

[tex]b[/tex] - x-Intercept, dimensionless.

If [tex]x_{1} = 2[/tex], [tex]y_{1} = 0[/tex], [tex]x_{2} = 0[/tex] and [tex]y_{2} = 2[/tex], then:

Slope

[tex]m = \frac{2-0}{0-2}[/tex]

[tex]m = -1[/tex]

x-Intercept

[tex]b = y_{1} - m\cdot x_{1}[/tex]

[tex]b = 0 -(-1)\cdot (2)[/tex]

[tex]b = 2[/tex]

The equation of the line in the xy-plane is [tex]y = -x+2[/tex] or [tex]x + y = 2[/tex], which is equivalent to [tex]3\cdot x + 3\cdot y = 6[/tex].

yz-plane (0, 2, 0) and (0, 0, 3)

[tex]z = m\cdot y + b[/tex]

[tex]m = \frac{z_{2}-z_{1}}{y_{2}-y_{1}}[/tex]

Where:

[tex]m[/tex] - Slope, dimensionless.

[tex]y_{1}[/tex], [tex]y_{2}[/tex] - Initial and final values for the independent variable, dimensionless.

[tex]z_{1}[/tex], [tex]z_{2}[/tex] - Initial and final values for the dependent variable, dimensionless.

[tex]b[/tex] - y-Intercept, dimensionless.

If [tex]y_{1} = 2[/tex], [tex]z_{1} = 0[/tex], [tex]y_{2} = 0[/tex] and [tex]z_{2} = 3[/tex], then:

Slope

[tex]m = \frac{3-0}{0-2}[/tex]

[tex]m = -\frac{3}{2}[/tex]

y-Intercept

[tex]b = z_{1} - m\cdot y_{1}[/tex]

[tex]b = 0 -\left(-\frac{3}{2} \right)\cdot (2)[/tex]

[tex]b = 3[/tex]

The equation of the line in the yz-plane is [tex]z = -\frac{3}{2}\cdot y+3[/tex] or [tex]3\cdot y + 2\cdot z = 6[/tex].

xz-plane (2, 0, 0) and (0, 0, 3)

[tex]z = m\cdot x + b[/tex]

[tex]m = \frac{z_{2}-z_{1}}{x_{2}-x_{1}}[/tex]

Where:

[tex]m[/tex] - Slope, dimensionless.

[tex]x_{1}[/tex], [tex]x_{2}[/tex] - Initial and final values for the independent variable, dimensionless.

[tex]z_{1}[/tex], [tex]z_{2}[/tex] - Initial and final values for the dependent variable, dimensionless.

[tex]b[/tex] - z-Intercept, dimensionless.

If [tex]x_{1} = 2[/tex], [tex]z_{1} = 0[/tex], [tex]x_{2} = 0[/tex] and [tex]z_{2} = 3[/tex], then:

Slope

[tex]m = \frac{3-0}{0-2}[/tex]

[tex]m = -\frac{3}{2}[/tex]

x-Intercept

[tex]b = z_{1} - m\cdot x_{1}[/tex]

[tex]b = 0 -\left(-\frac{3}{2} \right)\cdot (2)[/tex]

[tex]b = 3[/tex]

The equation of the line in the xz-plane is [tex]z = -\frac{3}{2}\cdot x+3[/tex] or [tex]3\cdot x + 2\cdot z = 6[/tex]

After comparing each equation of the line to the definition of the equation of the plane, the following coefficients are obtained:

[tex]a = 3[/tex], [tex]b = 3[/tex], [tex]c = 2[/tex], [tex]d = 6[/tex]

Hence, none of the options presented are valid. The plane is represented by [tex]3 \cdot x + 3\cdot y + 2\cdot z = 6[/tex].

Answer:

It is A    3x+3y+2z=6

Step-by-step explanation:

Answer:

x≤9  

Step-by-step explanation:

x−15≤−6

Add 15 to each side

x−15+15≤−6+15

x≤9  

Answer:

[tex]\boxed{x\leq 9}[/tex]

Step-by-step explanation:

[tex]x-15 \leq -6[/tex]

[tex]\sf Add \ 15 \ to \ both \ parts.[/tex]

[tex]x-15 +15 \leq -6+15[/tex]

[tex]x\leq 9[/tex]

Answer:

y = x + 0.5

Step-by-step explanation:

This is a very trivial exercise, follow the steps below:

Step 1: Perform the implicit differentiation of the given equation

[tex]x^2 + y^2 = (4x^2 + 2y^2 - x)^2[/tex]

[tex]2x + 2y \frac{dy}{dx} = 2(4x^2 + 2y^2 - x) ( 8x + 4y\frac{dy}{dx} - 1)\\\\[/tex]

Step 2: Make dy/dx the subject of the formula, this will be the slope of the curve:

[tex]x + y \frac{dy}{dx} = (4x^2 + 2y^2 - x) ( 8x + 4y\frac{dy}{dx} - 1)\\\\x + y \frac{dy}{dx} = 32x^3 + 16x^2y \frac{dy}{dx} - 4x^2 + 16xy^2 + 8y^3\frac{dy}{dx} - 2y^2 - 8x^2 - 4xy\frac{dy}{dx} + x \\\\\frac{dy}{dx}(y + 4xy - 8y^3) = 32x^3 - 12x^2 + 16xy^2 - 2y^2\\\\\frac{dy}{dx} = \frac{32x^3 - 12x^2 + 16xy^2 - 2y^2}{y + 4xy - 8y^3}[/tex]

Step 3: Find dy/dx at the point (0, 0.5)

[tex]\frac{dy}{dx}|(0,0.5) = \frac{32(0)^3 - 12(0)^2 + 16(0)(0.5)^2 - 2(0.5)^2}{(0.5) + 4(0)(0.5) - 8(0.5)^3}\\\\\frac{dy}{dx}|(0,0.5) =\frac{-0.5}{-0.5} \\\\\frac{dy}{dx}|(0,0.5) =1\\\\m = \frac{dy}{dx}|(0,0.5) =1[/tex]

Step 4: The equation of the tangent line to a curve at a given point is given by the equation:

[tex]y - y_1 = m(x-x_1)\\\\y - 0.5 = 1(x - 0)\\\\y = x + 0.5[/tex]

Answer:

Step-by-step explanation:

cos^-1(6/13)=62.5136°

sin(2*62.5136°)=0.8189

cos(2*62.5136°)=-0.5740

Answer

B. 27

firist divide 9÷2=4.5

the formula

=1/2×4.5×6

=13.5

cause there are 2 triangles. let's multiply 13.5 with 2

13.5×2= 27²

Answer:

Perimeter of the picture and frame = 38.4inches

Area of the picture and frame = 92.16inches²

Step-by-step explanation:

A square frame is made up of 4 different pieces. The shape of each piece = Rectangle

The perimeter of the rectangle = 24

Perimeter of the rectangle = 24 inches

The perimeter of a rectangle = 2L + 2W

The Width of a Rectangle is always on her than the length hence.

24 = 2L + 2W

24 = 2( L + W)

24/2 = L + W

12 = L + W

Because the width is always longer than the length

W > L

Width of wooden frame = 4 × Length

Therefore;

4 × L = W

Which gives

L + W = 12 inches

4 × L + L = 12 inches

L×(4 + 1)

= 5L = 12 inches

L = 12/5 = 2.4 inches

W = 4 × L = 4 × 12/5

W = 48/5 = 9.6 inches

Side length of wooden frame, L =9.6

The perimeter of the picture frame = 4 × L= 4 × 9.6= 38.4 inches

The area of the picture frame = L²

= L × L

= 9.6 × 9.6 = 92.16inches².

Answer:

1. Y= 7t^5 +C

2. Y= 35/12x^(12/7)+C

Step-by-step explanation:

The general solution will be determined by integrating the equations as the integration is a simple integration.

For dy/dt = 35t^4

The general solution y

= integral (35t^4)dt

The general solution y

=( 35/(4+1))*t^(4+1)

= 35/5t^5

= 7t^5 +C

To prove by differentiating the above.

Y= 7t^5 +C

Dy/Dt= (5*7)t^(5-1) +0

Dy/Dt= 35t^4

For dy/dx = 5x^(5/7)

Y=integral 5x^(5/7)Dx

Y= 5/(5/7 +1)*x^(5/7+1)

Y= 5/(12/7) *x^(12/7)

Y= 35/12x^(12/7)+C

To prove by differentiating

Y= 35/12x^(12/7)+C

Dy/Dx= (35/12)*(12/7) x^(12/7-1) +0

Dy/Dx=(35/7)x^(5/7)

Dy/Dx= 5x^(5/7)

Answer:

16 hours

Step-by-step explanation:

From the above question, we are given the following information

For one wall, working alone,

Amy can paint for 12 hours

Which means, in

1 hour , Amy would have painted = 1/12 of the wall

Bob can paint for 18 hours

Which means ,

in 1 hour, Bob would have painted = 1/18 of the wall.

We are told Amy painted the wall for 4 hours and then Bob took over and completed the wall.

Step 1

Find the portion of the wall Amy painted before Bob took over.

Amy painted the wall for 4 hours before Bob took over.

If:

1 hour = 1/12 of the wall for Amy

4 hours =

Cross multiply

4 × 1/12 ÷ 1

= 4/12 = 1/3

Amy painted one third(1/3) of the wall

Step 2

Find the number of hours left that Bob used in painting the remaining part of the wall

Let the entire wall = 1

If Amy painted 1/3 of the wall

Bob took over and painted = 1 - 1/3

= 2/3 of the wall

If,

Bob painted 1/18 of the wall = 1 hour

2/3 of the wall = ?? = Y

Cross multiply

2/3 × 1 = 1/18 × Y

Y = 2/3 ÷ 1/18

Y = 2/3 × 18/1

Y = 36/3

Y = 12 hours.

This means, the number of hours Bob worked when he took over from Amy = 12 hours.

Step 3

The third and final step is to calculate how many hours it took them to paint the wall

Number of hours painted by Amy + Number of hours painted by Bob

= 4 hours + 12 hours

= 16 hours

Therefore, it took them 16 hours to paint the entire wall.

Answer:

0

Step-by-step explanation:

Hope this helps

Answer:

Point of faulty equipment car = 0.2614 (Approx)

Step-by-step explanation:

Given:

Total number of car = 700

Faulty equipment car = 183

Find:

Point of faulty equipment car

Computation:

Point of faulty equipment car = Faulty equipment car / Total number of car

Point of faulty equipment car = 183 / 700

Point of faulty equipment car = 0.261428571

Point of faulty equipment car = 0.2614 (Approx)

Answer:

Campaign Finance Reform

Gender Gap among Voters in the District

There is a gender gap among women and men who favor campaign finance reform.

Step-by-step explanation:

In issues such as the above, a gender gap always exist between women and men who think that there is the need to reform the campaign finance.  Women ordinarily favor a reduction in the campaign finance.  On the other hand, men do not mind so much about the candidate expenditure in campaigns.  Reducing the huge campaign finance will ensure that political campaigns and aspiration to political offices are not left to money bags.  Many women would like to get involved, but they are limited by funding.  So, anytime the issue of reforming the whole electoral system, especially with respect to campaigns, women favor the reforms more than men.  The gap is always there.  The main issue is how would this gap be measured?

Answer:

44 degrees

Step-by-step explanation:

4 multiplied by 7 is 28.

28 + 2 = 30

angle ABC = 30 degrees

3 multiplied by 7 is 21

21 - 7 = 14.

angle CBD = 14 degrees.

30 + 14 = 44.

The answer is ABD = 44 degrees

Answer:  K = ¹/₃, V = 32in³

Step-by-step explanation:

Volume of s cylinder (V) = πr²h where πr² is the base area.

Now from the question,

V ∞ πr²h

V = kπr²h where k is the constant of proportionality which is also the variation constant.

40 = 6 x 20 x k

40 = 120k and

k   = ⁴⁰/₁₂₀

     = ¹/₃.

Now to find the volume when base area is 8in² and h is 12,

V = 8 x 12 x ¹/₃

V = 32in³

Answer:

59 accidents were investigated.

Step-by-step explanation:

The question above is a probability question that involves 2 elements: causes of accidents.

Let

A = Alcohol

E = Excessive speed

In the question, we are given the following information:

18 accidents involved Alcohol and Excessive speed =P(A ∩ E)

26 involved Alcohol = P(A)

12 accidents involved excessive speed but not alcohol = P( E ) Only

21 accidents involved neither alcohol nor excessive speed = neither A U B

We were given P(A) in the question. P(A Only) = P(A) - P(A ∩ E)

P(A Only) = 26 - 18

= 8

So, only 8 accident involved Alcohol but not excessive speed.

The Total number of Accidents investigated = P(A Only) + P( E only) + P(A ∩ E) + P( neither A U B)

= 8 + 12 + 18 + 21

= 59

Therefore, 59 accidents were investigated.

Answer:

The beryllium atom; 1.99 times larger.

Step-by-step explanation:

The beryllium atom is 0.000000000112 meters, while the nitrogen atom is 0.000000000056 meters. So, the beryllium atom is larger than the other.

(1.12 * 10^-10) / (5.6 * 10^-11)

= (1.112 / 5.6) * (10^-10 + 11)

= 0.1985714286 * 10

= 1.985714286 * 10^0

So, the beryllium atom is about 1.99 times larger than the other.

Hope this helps!

Answer:

P = 0.0714

Step-by-step explanation:

If two faces of the larger cube that share and edge are painted blue, it means that 28 of the 64 unit cubes are painted in at least one side and 36 cubes have no painting faces.

Additionally, from the 28 cubes painted only 4 have exactly two painted faces.

Then, to calculate the number of ways in which we can select x elements from a group of n, we can use the following equation:

[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]

So, the probability that one of two selected unit cubes will have exactly two painted faces while the other unit cube has no painted faces is:

[tex]P=\frac{4C1*36C1}{64C2}=0.0714[/tex]

Because there are 64C2 ways to select 2 cubes from the 64, and from that, there are 4C1*36C1 ways to select one cube with exactly two painted faces and one cube with no painted faces.

Answer:

A. a straight line passing

Step-by-step explanation:

Answer:

a straight line passing

Step-by-step explanation:

Answer:

366

Step-by-step explanation:

2×3+4×100-50+10​

PEMDAS says multiply and divide from left to right

6 + 400 - 50 +10

Then add and subtract

406-50+10

356+10

366

Answer:

[tex]\boxed{366}[/tex]

Step-by-step explanation:

[tex]2 \times 3+4 \times 100-50+10[/tex]

Multiplication is first.

[tex]6+400-50+10[/tex]

Add or subtract the numbers.

[tex]350+10+6[/tex]

[tex]366[/tex]