What is the reason for statement 3 in this proof?

Answer:?

Step-by-step explanation:

Answer:

[tex] y = 9.1 [/tex]

Step-by-step explanation:

Use the Law of sines to find y in ∆WXY, given:

m < Y = 106°

m < X = 58°

WY = x = 8

WX = y = ?

Therefore,

[tex] \frac{y}{sin(Y)} = \frac{x}{sin(X)} [/tex]

[tex] \frac{y}{sin(106)} = \frac{8}{sin(58)} [/tex]

[tex] \frac{y}{0.961} = \frac{8}{0.848} [/tex]

[tex] \frac{y}{0.961} = 9.434 [/tex]

Multiply both sides by 0.961 to solve for y

[tex] \frac{y*0.961}{0.961} = 9.434*0.961 [/tex]

[tex] y = 9.434*0.961 [/tex]

[tex] y = 9.1 [/tex] (to nearest tenth)

Answer:

The height of the tree = 15.59m

Step-by-step explanation:

let's make the height of the tree = x

tan30=x/27

x = 27 x tan30

x = 15.59m

Answer:

7.

Step-by-step explanation:

15 - [7 + (-6)+ 1]^3

Using PEMDAS:

= 15 - [ 7-6+1]^3

Next work out what is in the parentheses:

= 15  - 2*3

Now the exponential:

= 15 - 8

= 7.

Step-by-step explanation:

Hi,

I hope you are searching this, right.

=15[7+(-6)+1]^3

=15[7-6+1]^3

=15[2]^3

=15-8

=7...is answer.

Hope it helps..

Answer:

1. 24 x

Step-by-step explanation:

Area = (6x +1)(6x-1)

which means

length = 6x+1

width = 6x -1

as perimeter = 2 (length + width)

                     = 2 (6x +1+6x -1)

                     = 2(12x)

                    =24x

Answer:

The sampling method used is a stratified sampling method

Step-by-step explanation:

sampling is the selection of a predetermined representative subpopulation from a larger population, to estimate the characteristics of the whole population.

Stratified sampling: Here, the total population are divided into subcategories (strata) before sampling is done. The strata are formed based on some common characteristics. In our example, the times of the day (morning, afternoon and evening) has widely varying atmospheric conditions which will add biases to the measurement of air quality. For example, the air in the morning if compared to the afternoon in an industrial area may be purer because of minimal industrial activity, hence effective comparison will be made by stratification.

Answer:

76.

Step-by-step explanation:

It is given that N is a 2-digit number.

Last two digits of N^2 is the same as N.

We know that, a number is even if it ends with 0,2,4,6,8.

[tex]2^2=4,4^2=16,6^2=36,8^2=64[/tex]

If 0 is in end then we get two zeros in the square of that number.

It is clear that, number should ends with 6 to get the same number at the end.

[tex]16^2=256[/tex]

[tex]26^2=676[/tex]

[tex]36^2=1296[/tex]

[tex]46^2=2116[/tex]

[tex]56^2=3136[/tex]

[tex]66^2=4356[/tex]

[tex]76^2=5776[/tex]

[tex]86^2=7396[/tex]

[tex]96^2=9216[/tex]

It is clear that last two digits of (76)^2 is the same as 76.

Therefore, the required number is 76.

Answer:

Step-by-step explanation:

The first thing we are going to do is to fill in the other angles that we need to solve this problem. You could find ALL of them but all of them isn't necessary. So looking at the obtuse angle next to the 35 degree angle...we know that those are supplementary so 180 - 35 = the obtuse angle in the small triangle. 180 - 35 = 145. Within the smaller triangle we have now the 145 and the 10, and since, by the Triangle Angle-Sum Theorem all the angles have to add up to equal 180, then 180 - (10 + 145) = the 3rd angle, so the third angle is 180 - 155 = 25. Now let's get to the problem. If I were you, I'd draw that out like I did to keep track of these angles cuz I'm going to name them by their degree. In order to find d, we need to first find the distance between d and the right angle. We'll call that x. The reference angle is 35, the side opposite that angle is 12 and the side we are looking for, x, is adjacent to that angle. So we will use the tan ratio to find x:

[tex]tan(35)=\frac{12}{x}[/tex] Isolating x:

[tex]x=\frac{12}{tan(35)}[/tex] so

x = 17.1377 m

Now we have everything we need to find d. We will use 25 degrees as our reference angle, and the side opposite it is 12 and the side adjacent to it is

d + 17.1377, so that is the tan ratio as well:

[tex]tan(25)=\frac{12}{d+17.1377}[/tex] and simplifying a bit:

[tex]d+17.1377=\frac{12}{tan(25)}[/tex] and a bit more:

d + 17.1377 = 25.73408 so

d = 8.59, rounded

Answer:

x = 80 degrees

Step-by-step explanation:

y degrees = 180 - 55 - 45 (Angles in a triangle add up to 180 degrees)

y degrees = 80 degrees

x = y (Vertically opposite angles are equal)

So,

x = 80 degrees

Q3, or third quartile, is visually located at the right edge of the box. Movie A shows to have a smaller Q3 value as it is to the left of Q3 for movie B.

Answer:

[tex]\boxed{Volume = 696.9 \ in.^3}[/tex]

Step-by-step explanation:

Diameter = 11 inches

Radius = 11/2 = 5.5 inches

[tex]Volume \ of \ a \ sphere = \frac{4}{3} \pi r^3[/tex]

Where r = 5.5

V = [tex]\frac{4}{3} (3.14)(5.5)^3[/tex]

V = [tex]\frac{4}{3} (3.14)(166.375)[/tex]

V = [tex]\frac{2090.7}{3}[/tex]

V = 696.9 in.³

You get everything you need from factoring the last expression:

[tex]x^4-y^4=-176\sqrt7[/tex]

The left side is a difference of squares, and we get another difference of squares upon factoring. We end up with

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

Plug in everything you know and solve for [tex]x-y[/tex]:

[tex]-176\sqrt7=(x-y)\cdot4\cdot22\implies x-y=\boxed{-2\sqrt7}[/tex]

Answer:

-2sqrt(7)

Step-by-step explanation:

Solution:

From the third equation, $x^4 - y^4 = -176 \sqrt{7}.$

By difference of squares, we can write

\[x^4 - y^4 = (x^2 + y^2)(x^2 - y^2) = (x^2 + y^2)(x + y)(x - y).\]Then $-176 \sqrt{7} = (22)(4)(x - y),$ so $x - y = \boxed{-2 \sqrt{7}}.$

Answer:

Step-by-step explanation:

Equation of the line using point (0, 1) and slope 4/5 is

[tex]y - 1 = \frac{4}{5} (x - 0) \\ \\ 5y - 5 = 4x \\ \\ 5y - 4x = 5[/tex]

Hope this helps you

Answer:

D. [tex]\boxed{5y-4x=5}[/tex]

Step-by-step explanation:

Slope = m = 4/5

y - intercept = b = 1 (As from the point (0,1) , y-intercept is when x = 0)

So, the equation becomes

=> [tex]y = mx+b[/tex]

=> [tex]y = \frac{4}{5} x +1[/tex]

=> [tex]y - \frac{4}{5} x = 1[/tex]

Multiplying both sides by 5

=> [tex]5y-4x = 5[/tex]

Answer:

The answer is

Step-by-step explanation:

f(x) = 36x^5 − 44x⁴ − 28x³

g(x) = 4x²

To find f(x) / g(x) Divide each term of f(x) by g(x)

That's

[tex] \frac{f(x)}{g(x)} = \frac{ {36x}^{5} - {44x}^{4} - {28x}^{3} }{ {4x}^{2} } \\ \\ = \frac{ {36x}^{5} }{ {4x}^{2} } - \frac{ {44x}^{4} }{ {4x}^{2} } - \frac{ {28x}^{3} }{ {4x}^{2} } \\ \\ = {9x}^{3} - {11x}^{2} - 7x[/tex]

Hope this helps you

Answer:

9x³ - 11x² - 7x

Step-by-step explanation:

guy abpove is right or bwlowe

Answer:

Step-by-step explanation:

Hypotenuse always have the highest number than base and perpendicular.

Hypotenuse ( h ) = 15

Base ( b ) = 9

Perpendicular ( p ) = 12

Let's see whether the given triangle is a right triangle or not

Using Pythagoras theorem:

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

Plugging the values,

[tex] {15}^{2} = {12}^{2} + {9}^{2} [/tex]

Evaluate the power

[tex]225 = 144 + 81[/tex]

Calculate the sum

[tex]225 = 225[/tex]

Hypotenuse is equal to the sum of perpendicular and base.

So , we can say that the given lengths of the triangle makes a right triangle.

Hope this helps..

Best regards!!

Answer:

[tex]\boxed{Yes.}[/tex]

Step-by-step explanation:

To solve this equation, we can use the Pythagorean Theorem: [tex]a^2 + b^2 = c^2[/tex], where [tex]a[/tex] and [tex]b[/tex] are regular side lengths and [tex]c[/tex] is the hypotenuse.

Now, just substitute the side lengths into the formula and solve!

[tex]9^2 + 12^2 = 15^2[/tex]    Simplify the equation by taking each value to its power.

[tex]81 + 144 = 225[/tex]    Simplify by adding like terms.

[tex]225 = 255[/tex]

Therefore, this is indeed a right triangle.

Answer:

[tex]\boxed{f[ g(3) ] = 673}[/tex]

Step-by-step explanation:

[tex]f(x) = 4x^2 - 3 \\ g(x) = 5x - 2[/tex]

[tex]f(g(3))[/tex]

[tex]f(5(3)-2)[/tex]

[tex]f(15-2)[/tex]

[tex]f(13)[/tex]

[tex]f(13)=4(13)^2 -3[/tex]

[tex]f(13)=4(169) -3[/tex]

[tex]f(13)=676-3[/tex]

[tex]f(13)=673[/tex]

Answer:

f[g(3)] = 673

Step-by-step explanation:

I took the test

Answer:

1.148 repetent

Step-by-step explanation:

hope this helps

Answer:

rhombus and square

Answer:

Rhombus and square

Step-by-step explanation:

The quadrilaterals that satisfy this condition are rhombi and squares.

Answer:

1. 677 inches = 18.056 yards

677 inches  = 56.416 feet

677 inches = 677 inches

2. QP = 23.5 cm

3. The perimeter = 53.5 cm

Step-by-step explanation:

1. To convert, 677 inches to yards, we have;

1 inch = 0.0277778 yards

677 inches = 677*0.0277778 = 18.056 yards

To convert, 677 inches to feet, we have;

1 inch = 0.083333 feet

677 inches = 677*0.083333  = 56.416 feet

To convert, 677 inches to inches, we have;

1 inch = 1 inch

677 inches = 677*1  = 677 inches

2. We have that ∠PRQ and ∠PRS are supplementary angles (angles on a straight line

Given that ∠PRS = 90°, ∠PRQ = 180° - 90° = 90°;

∠PRQ + ∠PQR + ∠RPQ = 180°, sum of angles in a triangle

∠PQR = 24° given

∠PRQ = 90°

∴  ∠RPQ = 180° - 90° - 24° = 66°

∴∠SPQ = ∠SPR + ∠RPQ = 36° + 66° = 102°

∠QSP + ∠SPQ + ∠PQS = 180° (sum of angles in a triangle)

∠QSP = 180° -∠SPQ - ∠PQS = 180° -102° - 24 = 54°

By sine rule, we have;

a/(sin(A)) = b/(sin(B))

Therefore, we have;

11.8/(sin(24)) = QP/(sin(54°))

QP = (11.8/(sin(24))) × (sin(54°)) = 23.5 cm

3. From trigonometric ratios, we have;

tan(43°) = BC/CA = BC/(16.2 cm)

BC = 16.2 cm × tan(43°) = 15.1

By Pythagoras theorem, we have;

AB = √(15.1² + 16.2²) = 22.2

The perimeter = 15.1 + 16.2 + 22.2 = 53.5 cm

In this problem, there are two parts. We will need to find what q is if 18% of q is 27, and what 27% of 2q is.

First, let's set up and solve the equation for 18% of q is 27.

18 / 100 = 27 / q

100q = 486

q = 4.86

Next, we'll find the value of 2q.

2(4.86) = 9.72

Finally, we'll set up a proportion and solve for 27% of 2q.

27 / 100 = x / 9.72

100x = 262.44

x = 2.6244

If 18% of q is 27, then 27% of 2q is 2.6244 (round to tenths/hundredths place as needed).

Hope this helps!! :)

Answer:

Step-by-step explanation: Let's first find the value of q

[tex]18/100 \times q = 27\\\frac{18q}{100} = \frac{27}{1}\\18q = 2700\\\frac{18q}{18} = \frac{2700}{18} \\q= 150.\\[/tex]

Now we can find 27% of 2q

[tex]27 \% \times 2q = \\27 \% \times 2(150)\\\frac{27}{100} \times 300\\\\= \frac{8100}{100} \\= 81[/tex]

Answer:

The answer is

Step-by-step explanation:

Area of a circle is given by πr²

Where r is the radius

From the question

Area = 64 ft²

So the radius is

64 = πr²

Divide both sides by π

[tex] {r}^{2} = \frac{64}{\pi} [/tex]

Find the square root of both sides

[tex]r = \sqrt{ \frac{64}{\pi} } [/tex]

r = 4 ft

Hope this helps you

The answer is 8 not 4.5 or 4!!!!!!!!

Step-by-step explanation: It's not just "64" its 64pi. when you posted the question your device could not put the pi symbol so people were thinking that it was just 64.

Answer:

[tex]\frac{4}{5}[/tex]

Step-by-step explanation:

The Patel, Lopez, and Russo families all had parties recently. There were 152 adults at the Lopez party. The ratio of adults to children at the Russo party was 5 to 4. What was the ratio of adults to children at the Patel party?

(1) The Russo party had 31 more adults than children, and 47 more adults than did the Patel party.

(2) The Patel party had 40 more children, though 4 fewer people in total, than did the Lopez party, where the ratio of adults to children was 8 to 5.

Answer: Let the number of children in Russo party be x, The Russo party had 31 more adults than children, therefore the number of adults at the Russo party = x + 31. The ratio of adults to children at the Russo party was 5 to 4, we can find the number of children using:

[tex]\frac{5}{4}=\frac{x+31}{x}\\ 5x=4x+124\\x=124[/tex]

The number of children at the Russo party is 124 and the number of adult is 155 (124 + 31).

They  are 47 more adults at the Russo party than the Patel party, the number of adult at the Patel party = 155 - 47 = 108

the ratio of adults to children was 8 to 5 at the Lopez party, There were 152 adults at the party. Let x be the number of children at the Lopez party therefore:

[tex]\frac{8}{5}=\frac{152}{x}\\ 8x=760\\x=95[/tex]

The Patel party had 40 more children than the Lopez, the number of children at the Patel party = 135 (95 + 40).

The ratio of adults to children at the Patel party is [tex]\frac{108}{135} =\frac{4}{5}[/tex]

Answer:

The answer is

Step-by-step explanation:

Equation of a line is y = mx + c

where m is the slope

c is the y intercept

4x + y + 1 = 0

y = - 4x - 1

Comparing with the above formula

Slope / m = - 4

Since the lines are parallel their slope are also the same

That's

Slope of the parallel line is also - 4

Equation of the line using point ( 1 , 2) is

y - 2 = -4(x - 1)

y - 2 = - 4x + 4

4x + y - 2 - 4

We have the final answer as

Hope this helps you

Answer:

  57°

Step-by-step explanation:

There is a right angle at the point of tangency, so the angle of interest is the complement of the one given:

  m∠K = 90° -m∠J = 90° -33°

  m∠K = 57°

Answer:

a. 46.9 m b. 56.1 m

Step-by-step explanation:

a. Width of the river

The angle of depression of the bottom of the second vertical cliff from the first vertical cliff = angle of elevation of the top of the first vertical cliff from the bottom of the second vertical cliff = 58°.

Since the height of the vertical cliff = 75.0 m, its distance from the other cliff which is the width of the river, d is gotten from

tan58° = 75.0 m/d

d = 75.0/tan58° = 46.87 m ≅ 46.9 m

b. Height of the second cliff

Now, the difference in height of the two cliffs is gotten from

tan22° = h/d, since the angle of depression of the top of second cliff from the first cliff is the angle of elevation of the top of the first cliff from the second cliff = 22°

h = dtan22° = 18.94 m

So, the height of the second cliff is h' = 75.0 - h = 75.0 m - 18.94 m = 56.06 m ≅ 56.1 m

Answer: 135

Step-by-step explanation:

took it on edg2020

Answer:

135

Step-by-step explanation:

Just took the test and got it right

Answer: A y = -(2x+8)

Step-by-step explanation:

The first line is y=-2x-8

Thus, the answer that simplifies to y = -2x-8 is the answer.  

a) y=-(2x+8)

Distribute

y=-2x-8

Because it works, no need to try the others.

Hope it helps <3

Answer:

[tex]\boxed{y = -(2x + 8)}[/tex]

Step-by-step explanation:

For the two lines to have infinite [tex]\infty[/tex] solutions, the two equations must be the same.

First equation : y = -2x - 8

A. y = -(2x + 8)

   y = -2x - 8 correct

B. y = -2(x - 8)

   y = -2x + 16 incorrect

C. y = -2(x - 4)

   y = -2x + 8 incorrect

D. y = -(-2x+8)

    y = 2x - 8 incorrect

y = -2x - 8 and y = -(2x + 8) when graphed are the same, they intersect at infinite points and there are infinite solutions.

Answer:

[tex]\large \boxed{\sf \ \ \dfrac{8}{7} \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

The solutions are, for a positive discriminant:

   [tex]\dfrac{-b\pm\sqrt{\Delta}}{2a} \ \text{ where } \Delta=b^2-4ac[/tex]

Here, we have a = -21, b = -11, c = 40, so it gives:

[tex]\Delta =b^2-4ac=11^2+4*21*40=121+3360=3481=59^2[/tex]

So, we have two solutions:

[tex]x_1=\dfrac{11-59}{-42}=\dfrac{48}{42}=\dfrac{6*8}{6*7}=\dfrac{8}{7} \\\\x_2=\dfrac{11+59}{-42}=\dfrac{70}{-42}=-\dfrac{14*5}{14*3}=-\dfrac{5}{3}[/tex]

We only want x > 0 so the solution is

   [tex]\dfrac{8}{7}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

The angles are

∠A = 90°, ∠B = 26.56°, ∠C = 63.43°

Step-by-step explanation:

We have that the angles of a vector are given as follows;

[tex]cos\left ( \theta \right ) = \dfrac{\mathbf{a\cdot b}}{\left | \mathbf{a} \right |\left | \mathbf{b} \right |}[/tex]

Whereby the vertices are represented as

A= (2, 5, 0), B = (4, 11, 0), C = (-1, 6, 0),

AB =(4, 11, 0) - (2, 5, 0) = (2, 6, 0) ,  BA = (-2, -6, 0)

BC = (-1, 6, 0) - (4, 11, 0) = (-5, -5, 0), CB = (5, 5, 0)

AC = (-1, 6, 0) - (2, 5, 0) = (-3, 1, 0), CA = (3, -1, 0)

θ₁ = AB·AC

a·c = a₁c₁ + a₂c₂ + a₃c₃ = 2×(-3) + 6×1 = 0

Therefore, θ₁ = 90°

BA·BC = (-2)×(-5) + (-6)×(-5) = 40

[tex]{\left | \mathbf{}BA \right |\left | \mathbf{}BC \right |}[/tex] = (√((-2)² + (-6)²)) × (√((-5)² + (-5)²)) = 44.72

cos(θ₂) = 40/44.72 = 0.894

cos⁻¹(0.894) =θ₂= 26.56°

CA·CB = 5×3 + 5×(-1) = 10

[tex]{\left | \mathbf{}CA \right |\left | \mathbf{}CB \right |}[/tex] = (√((3)² + (-1)²)) × (√((5)² + (5)²)) = 22.36

10/22.36 = 0.447

cos(θ₃) = 0.447

θ₃ = cos⁻¹(0.447) = 63.43°.